LMFDB - Embedded newform 720.2.bm.h.109.13

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:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.13
Character	$\chi$	$=$	720.109
Dual form			720.2.bm.h.469.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.345118 + 1.37146i) q^{2} +(-1.76179 + 0.946629i) q^{4} +(-2.16437 - 0.561697i) q^{5} +4.51614 q^{7} +(-1.90629 - 2.08952i) q^{8} +(0.0233792 - 3.16219i) q^{10} +(3.44000 - 3.44000i) q^{11} +(-0.113618 + 0.113618i) q^{13} +(1.55860 + 6.19370i) q^{14} +(2.20779 - 3.33552i) q^{16} +5.03305i q^{17} +(-0.992498 - 0.992498i) q^{19} +(4.34488 - 1.05927i) q^{20} +(5.90502 + 3.53061i) q^{22} +8.00517 q^{23} +(4.36899 + 2.43144i) q^{25} +(-0.195033 - 0.116610i) q^{26} +(-7.95648 + 4.27512i) q^{28} +(1.01722 + 1.01722i) q^{29} -6.42697 q^{31} +(5.33647 + 1.87673i) q^{32} +(-6.90261 + 1.73700i) q^{34} +(-9.77461 - 2.53670i) q^{35} +(1.63459 + 1.63459i) q^{37} +(1.01864 - 1.70370i) q^{38} +(2.95223 + 5.59324i) q^{40} -3.35633i q^{41} +(5.68196 + 5.68196i) q^{43} +(-2.80414 + 9.31696i) q^{44} +(2.76273 + 10.9787i) q^{46} +9.10261i q^{47} +13.3956 q^{49} +(-1.82679 + 6.83102i) q^{50} +(0.0926163 - 0.307724i) q^{52} +(-3.27113 - 3.27113i) q^{53} +(-9.37767 + 5.51320i) q^{55} +(-8.60906 - 9.43655i) q^{56} +(-1.04401 + 1.74614i) q^{58} +(5.30843 - 5.30843i) q^{59} +(-5.87487 - 5.87487i) q^{61} +(-2.21806 - 8.81431i) q^{62} +(-0.732149 + 7.96643i) q^{64} +(0.309729 - 0.182092i) q^{65} +(-1.87639 + 1.87639i) q^{67} +(-4.76443 - 8.86716i) q^{68} +(0.105584 - 14.2809i) q^{70} +0.635312i q^{71} +6.14208 q^{73} +(-1.67765 + 2.80590i) q^{74} +(2.68810 + 0.809042i) q^{76} +(15.5355 - 15.5355i) q^{77} +1.76500 q^{79} +(-6.65201 + 5.97919i) q^{80} +(4.60307 - 1.15833i) q^{82} +(6.39170 - 6.39170i) q^{83} +(2.82705 - 10.8934i) q^{85} +(-5.83162 + 9.75352i) q^{86} +(-13.7456 - 0.630310i) q^{88} -0.579554i q^{89} +(-0.513114 + 0.513114i) q^{91} +(-14.1034 + 7.57793i) q^{92} +(-12.4838 + 3.14148i) q^{94} +(1.59065 + 2.70562i) q^{95} -15.2769i q^{97} +(4.62305 + 18.3714i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{10} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 48 q^{31} - 28 q^{34} - 24 q^{35} - 16 q^{40} + 40 q^{44} - 4 q^{46} + 48 q^{49} + 32 q^{50} - 48 q^{56} + 32 q^{59} + 16 q^{61} + 48 q^{64}+ \cdots + 48 q^{95}+O(q^{100}) $ 48 * q + 12 * q^10 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 48 * q^31 - 28 * q^34 - 24 * q^35 - 16 * q^40 + 40 * q^44 - 4 * q^46 + 48 * q^49 + 32 * q^50 - 48 * q^56 + 32 * q^59 + 16 * q^61 + 48 * q^64 - 16 * q^65 - 40 * q^74 + 60 * q^76 - 96 * q^79 - 72 * q^80 - 16 * q^86 - 32 * q^91 + 44 * q^94 + 48 * q^95

Character values

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

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$1$

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 $

$2$	0.345118	+	1.37146i	0.244035	+	0.969766i
$2$	0.345118	+	1.37146i	0.244035	+	0.969766i
$3$		0			0
$3$		0			0
$4$	−1.76179	+	0.946629i	−0.880893	+	0.473315i
$5$	−2.16437	−	0.561697i	−0.967936	−	0.251198i
$5$	−2.16437	−	0.561697i	−0.967936	−	0.251198i
$6$		0			0
$7$	4.51614			1.70694			0.853471	−	0.521140i	$-0.174493\pi$
$7$	4.51614			1.70694			0.853471	+	0.521140i	$0.174493\pi$
$8$	−1.90629	−	2.08952i	−0.673974	−	0.738755i
$9$		0			0
$10$	0.0233792	−	3.16219i	0.00739317	−	0.999973i
$11$	3.44000	−	3.44000i	1.03720	−	1.03720i	0.0379186	−	0.999281i	$-0.487927\pi$
$11$	3.44000	−	3.44000i	1.03720	−	1.03720i	0.999281	−	0.0379186i	$-0.0120728\pi$
$12$		0			0
$13$	−0.113618	+	0.113618i	−0.0315119	+	0.0315119i	−0.722687	−	0.691175i	$-0.757093\pi$
$13$	−0.113618	+	0.113618i	−0.0315119	+	0.0315119i	0.691175	+	0.722687i	$0.257093\pi$
$14$	1.55860	+	6.19370i	0.416554	+	1.65534i
$15$		0			0
$16$	2.20779	−	3.33552i	0.551946	−	0.833880i
$17$			5.03305i			1.22069i	0.792134	+	0.610347i	$0.208970\pi$
$17$			5.03305i			1.22069i	−0.792134	+	0.610347i	$0.791030\pi$
$18$		0			0
$19$	−0.992498	−	0.992498i	−0.227695	−	0.227695i	0.584034	−	0.811729i	$-0.301473\pi$
$19$	−0.992498	−	0.992498i	−0.227695	−	0.227695i	−0.811729	+	0.584034i	$0.801473\pi$
$20$	4.34488	−	1.05927i	0.971544	−	0.236859i
$21$		0			0
$22$	5.90502	+	3.53061i	1.25895	+	0.752728i
$23$	8.00517			1.66919			0.834596	−	0.550862i	$-0.185701\pi$
$23$	8.00517			1.66919			0.834596	+	0.550862i	$0.185701\pi$
$24$		0			0
$25$	4.36899	+	2.43144i	0.873799	+	0.486288i
$26$	−0.195033	−	0.116610i	−0.0382492	−	0.0228691i
$27$		0			0
$28$	−7.95648	+	4.27512i	−1.50363	+	0.807921i
$29$	1.01722	+	1.01722i	0.188894	+	0.188894i	0.795218	−	0.606324i	$-0.207357\pi$
$29$	1.01722	+	1.01722i	0.188894	+	0.188894i	−0.606324	+	0.795218i	$0.707357\pi$
$30$		0			0
$31$	−6.42697			−1.15432			−0.577159	−	0.816632i	$-0.695839\pi$
$31$	−6.42697			−1.15432			−0.577159	+	0.816632i	$0.695839\pi$
$32$	5.33647	+	1.87673i	0.943363	+	0.331763i
$33$		0			0
$34$	−6.90261	+	1.73700i	−1.18379	+	0.297893i
$35$	−9.77461	−	2.53670i	−1.65221	−	0.428781i
$36$		0			0
$37$	1.63459	+	1.63459i	0.268726	+	0.268726i	0.828587	−	0.559861i	$-0.189145\pi$
$37$	1.63459	+	1.63459i	0.268726	+	0.268726i	−0.559861	+	0.828587i	$0.689145\pi$
$38$	1.01864	−	1.70370i	0.165245	−	0.276376i
$39$		0			0
$40$	2.95223	+	5.59324i	0.466789	+	0.884369i
$41$		−	3.35633i		−	0.524171i	−0.965045	−	0.262086i	$-0.915590\pi$
$41$		−	3.35633i		−	0.524171i	0.965045	−	0.262086i	$-0.0844103\pi$
$42$		0			0
$43$	5.68196	+	5.68196i	0.866491	+	0.866491i	0.992082	−	0.125591i	$-0.0400826\pi$
$43$	5.68196	+	5.68196i	0.866491	+	0.866491i	−0.125591	+	0.992082i	$0.540083\pi$
$44$	−2.80414	+	9.31696i	−0.422740	+	1.40458i
$45$		0			0
$46$	2.76273	+	10.9787i	0.407342	+	1.61873i
$47$			9.10261i			1.32775i	0.747842	+	0.663876i	$0.231090\pi$
$47$			9.10261i			1.32775i	−0.747842	+	0.663876i	$0.768910\pi$
$48$		0			0
$49$	13.3956			1.91365
$50$	−1.82679	+	6.83102i	−0.258348	+	0.966052i
$51$		0			0
$52$	0.0926163	−	0.307724i	0.0128436	−	0.0426736i
$53$	−3.27113	−	3.27113i	−0.449324	−	0.449324i	0.445806	−	0.895130i	$-0.352917\pi$
$53$	−3.27113	−	3.27113i	−0.449324	−	0.449324i	−0.895130	+	0.445806i	$0.852917\pi$
$54$		0			0
$55$	−9.37767	+	5.51320i	−1.26449	+	0.743399i
$56$	−8.60906	−	9.43655i	−1.15043	−	1.26101i
$57$		0			0
$58$	−1.04401	+	1.74614i	−0.137086	+	0.229279i
$59$	5.30843	−	5.30843i	0.691098	−	0.691098i	−0.271375	−	0.962474i	$-0.587478\pi$
$59$	5.30843	−	5.30843i	0.691098	−	0.691098i	0.962474	+	0.271375i	$0.0874785\pi$
$60$		0			0
$61$	−5.87487	−	5.87487i	−0.752199	−	0.752199i	0.222690	−	0.974889i	$-0.428516\pi$
$61$	−5.87487	−	5.87487i	−0.752199	−	0.752199i	−0.974889	+	0.222690i	$0.928516\pi$
$62$	−2.21806	−	8.81431i	−0.281694	−	1.11942i
$63$		0			0
$64$	−0.732149	+	7.96643i	−0.0915186	+	0.995803i
$65$	0.309729	−	0.182092i	0.0384172	−	0.0225857i
$66$		0			0
$67$	−1.87639	+	1.87639i	−0.229238	+	0.229238i	−0.812374	−	0.583137i	$-0.801825\pi$
$67$	−1.87639	+	1.87639i	−0.229238	+	0.229238i	0.583137	+	0.812374i	$0.301825\pi$
$68$	−4.76443	−	8.86716i	−0.577772	−	1.07530i
$69$		0			0
$70$	0.105584	−	14.2809i	0.0126197	−	1.70690i
$71$			0.635312i			0.0753977i	0.999289	+	0.0376988i	$0.0120028\pi$
$71$			0.635312i			0.0753977i	−0.999289	+	0.0376988i	$0.987997\pi$
$72$		0			0
$73$	6.14208			0.718876			0.359438	−	0.933169i	$-0.382968\pi$
$73$	6.14208			0.718876			0.359438	+	0.933169i	$0.382968\pi$
$74$	−1.67765	+	2.80590i	−0.195023	+	0.326180i
$75$		0			0
$76$	2.68810	+	0.809042i	0.308346	+	0.0928035i
$77$	15.5355	−	15.5355i	1.77044	−	1.77044i
$78$		0			0
$79$	1.76500			0.198578			0.0992888	−	0.995059i	$-0.468343\pi$
$79$	1.76500			0.198578			0.0992888	+	0.995059i	$0.468343\pi$
$80$	−6.65201	+	5.97919i	−0.743718	+	0.668494i
$81$		0			0
$82$	4.60307	−	1.15833i	0.508324	−	0.127916i
$83$	6.39170	−	6.39170i	0.701580	−	0.701580i	−0.263169	−	0.964750i	$-0.584768\pi$
$83$	6.39170	−	6.39170i	0.701580	−	0.701580i	0.964750	+	0.263169i	$0.0847678\pi$
$84$		0			0
$85$	2.82705	−	10.8934i	0.306636	−	1.18155i
$86$	−5.83162	+	9.75352i	−0.628840	+	1.05175i
$87$		0			0
$88$	−13.7456	−	0.630310i	−1.46528	−	0.0671913i
$89$		−	0.579554i		−	0.0614326i	−0.999528	−	0.0307163i	$-0.990221\pi$
$89$		−	0.579554i		−	0.0614326i	0.999528	−	0.0307163i	$-0.00977884\pi$
$90$		0			0
$91$	−0.513114	+	0.513114i	−0.0537889	+	0.0537889i
$92$	−14.1034	+	7.57793i	−1.47038	+	0.790053i
$93$		0			0
$94$	−12.4838	+	3.14148i	−1.28761	+	0.324019i
$95$	1.59065	+	2.70562i	0.163197	+	0.277590i
$96$		0			0
$97$		−	15.2769i		−	1.55113i	−0.631265	−	0.775567i	$-0.717464\pi$
$97$		−	15.2769i		−	1.55113i	0.631265	−	0.775567i	$-0.282536\pi$
$98$	4.62305	+	18.3714i	0.466999	+	1.85580i
$99$		0			0
$100$	−9.99891	−	0.147859i	−0.999891	−	0.0147859i
$101$	2.60639	−	2.60639i	0.259346	−	0.259346i	−0.565442	−	0.824788i	$-0.691294\pi$
$101$	2.60639	−	2.60639i	0.259346	−	0.259346i	0.824788	+	0.565442i	$0.191294\pi$
$102$		0			0
$103$	−9.26272			−0.912683			−0.456341	−	0.889805i	$-0.650840\pi$
$103$	−9.26272			−0.912683			−0.456341	+	0.889805i	$0.650840\pi$
$104$	0.453994	+	0.0208181i	0.0445177	+	0.00204138i
$105$		0			0
$106$	3.35729	−	5.61514i	0.326089	−	0.545391i
$107$	−4.72776	−	4.72776i	−0.457050	−	0.457050i	0.440636	−	0.897686i	$-0.354753\pi$
$107$	−4.72776	−	4.72776i	−0.457050	−	0.457050i	−0.897686	+	0.440636i	$0.854753\pi$
$108$		0			0
$109$	0.160713	+	0.160713i	0.0153935	+	0.0153935i	0.714762	−	0.699368i	$-0.246535\pi$
$109$	0.160713	+	0.160713i	0.0153935	+	0.0153935i	−0.699368	+	0.714762i	$0.746535\pi$
$110$	−10.7975	−	10.9584i	−1.02950	−	1.04484i
$111$		0			0
$112$	9.97068	−	15.0637i	0.942141	−	1.42338i
$113$			1.02489i			0.0964131i	0.998837	+	0.0482066i	$0.0153506\pi$
$113$			1.02489i			0.0964131i	−0.998837	+	0.0482066i	$0.984649\pi$
$114$		0			0
$115$	−17.3261	−	4.49648i	−1.61567	−	0.419298i
$116$	−2.75506	−	0.829197i	−0.255801	−	0.0769890i
$117$		0			0
$118$	9.11231	+	5.44824i	0.838856	+	0.501551i
$119$			22.7300i			2.08365i
$120$		0			0
$121$		−	12.6672i		−	1.15157i
$122$	6.02960	−	10.0846i	0.545894	−	0.913021i
$123$		0			0
$124$	11.3229	−	6.08396i	1.01683	−	0.546355i
$125$	−8.09039	−	7.71658i	−0.723626	−	0.690192i
$126$		0			0
$127$			9.29167i			0.824502i	0.911070	+	0.412251i	$0.135257\pi$
$127$			9.29167i			0.824502i	−0.911070	+	0.412251i	$0.864743\pi$
$128$	−11.1783	+	1.74525i	−0.988030	+	0.154260i
$129$		0			0
$130$	0.356624	+	0.361937i	0.0312780	+	0.0317440i
$131$	4.53759	+	4.53759i	0.396451	+	0.396451i	0.876979	−	0.480528i	$-0.159555\pi$
$131$	4.53759	+	4.53759i	0.396451	+	0.396451i	−0.480528	+	0.876979i	$0.659555\pi$
$132$		0			0
$133$	−4.48226	−	4.48226i	−0.388662	−	0.388662i
$134$	−3.22096	−	1.92581i	−0.278249	−	0.166365i
$135$		0			0
$136$	10.5166	−	9.59443i	0.901794	−	0.822716i
$137$	−0.448842			−0.0383471			−0.0191736	−	0.999816i	$-0.506104\pi$
$137$	−0.448842			−0.0383471			−0.0191736	+	0.999816i	$0.506104\pi$
$138$		0			0
$139$	−5.12669	+	5.12669i	−0.434840	+	0.434840i	−0.890271	−	0.455431i	$-0.849485\pi$
$139$	−5.12669	+	5.12669i	−0.434840	+	0.434840i	0.455431	+	0.890271i	$0.349485\pi$
$140$	19.6221	−	4.78380i	1.65837	−	0.404305i
$141$		0			0
$142$	−0.871303	+	0.219258i	−0.0731181	+	0.0183997i
$143$			0.781690i			0.0653682i
$144$		0			0
$145$	−1.63028	−	2.77302i	−0.135387	−	0.230287i
$146$	2.11974	+	8.42360i	0.175431	+	0.697142i
$147$		0			0
$148$	−4.42716	−	1.33245i	−0.363911	−	0.109527i
$149$	−4.56510	+	4.56510i	−0.373988	+	0.373988i	−0.868927	−	0.494940i	$-0.835190\pi$
$149$	−4.56510	+	4.56510i	−0.373988	+	0.373988i	0.494940	+	0.868927i	$0.335190\pi$
$150$		0			0
$151$		−	6.84317i		−	0.556890i	−0.960452	−	0.278445i	$-0.910181\pi$
$151$		−	6.84317i		−	0.556890i	0.960452	−	0.278445i	$-0.0898189\pi$
$152$	−0.181855	+	3.96582i	−0.0147504	+	0.321671i
$153$		0			0
$154$	26.6679	+	15.9447i	2.14896	+	1.28486i
$155$	13.9103	+	3.61001i	1.11730	+	0.289963i
$156$		0			0
$157$	−1.85978	+	1.85978i	−0.148426	+	0.148426i	−0.777415	−	0.628988i	$-0.783469\pi$
$157$	−1.85978	+	1.85978i	−0.148426	+	0.148426i	0.628988	+	0.777415i	$0.283469\pi$
$158$	0.609132	+	2.42062i	0.0484600	+	0.192574i
$159$		0			0
$160$	−10.4959	−	7.05942i	−0.829776	−	0.558096i
$161$	36.1525			2.84922
$162$		0			0
$163$	9.43033	−	9.43033i	0.738641	−	0.738641i	−0.233674	−	0.972315i	$-0.575075\pi$
$163$	9.43033	−	9.43033i	0.738641	−	0.738641i	0.972315	+	0.233674i	$0.0750750\pi$
$164$	3.17720	+	5.91314i	0.248098	+	0.461739i
$165$		0			0
$166$	10.9718	+	6.56005i	0.851580	+	0.509159i
$167$	−21.2570			−1.64492			−0.822459	−	0.568824i	$-0.807398\pi$
$167$	−21.2570			−1.64492			−0.822459	+	0.568824i	$0.807398\pi$
$168$		0			0
$169$			12.9742i			0.998014i
$170$	15.9155	+	0.117669i	1.22066	+	0.00902479i
$171$		0			0
$172$	−15.3891	−	4.63170i	−1.17341	−	0.353164i
$173$	−3.90989	+	3.90989i	−0.297263	+	0.297263i	−0.839941	−	0.542678i	$-0.817410\pi$
$173$	−3.90989	+	3.90989i	−0.297263	+	0.297263i	0.542678	+	0.839941i	$0.317410\pi$
$174$		0			0
$175$	19.7310	+	10.9807i	1.49152	+	0.830065i
$176$	−3.87940	−	19.0690i	−0.292421	−	1.43738i
$177$		0			0
$178$	0.794834	−	0.200015i	0.0595753	−	0.0149917i
$179$	−16.8281	−	16.8281i	−1.25779	−	1.25779i	−0.952144	−	0.305651i	$-0.901126\pi$
$179$	−16.8281	−	16.8281i	−1.25779	−	1.25779i	−0.305651	−	0.952144i	$-0.598874\pi$
$180$		0			0
$181$	−10.4003	+	10.4003i	−0.773050	+	0.773050i	−0.978639	−	0.205588i	$-0.934089\pi$
$181$	−10.4003	+	10.4003i	−0.773050	+	0.773050i	0.205588	+	0.978639i	$0.434089\pi$
$182$	−0.880798	−	0.526628i	−0.0652891	−	0.0390363i
$183$		0			0
$184$	−15.2601	−	16.7269i	−1.12499	−	1.23312i
$185$	−2.61972	−	4.45601i	−0.192606	−	0.327613i
$186$		0			0
$187$	17.3137	+	17.3137i	1.26610	+	1.26610i
$188$	−8.61680	−	16.0369i	−0.628445	−	1.16961i
$189$		0			0
$190$	−3.16167	+	3.11526i	−0.229372	+	0.226005i
$191$	−20.8245			−1.50681			−0.753404	−	0.657558i	$-0.771589\pi$
$191$	−20.8245			−1.50681			−0.753404	+	0.657558i	$0.771589\pi$
$192$		0			0
$193$		−	5.82531i		−	0.419315i	−0.977775	−	0.209657i	$-0.932765\pi$
$193$		−	5.82531i		−	0.419315i	0.977775	−	0.209657i	$-0.0672349\pi$
$194$	20.9516	−	5.27234i	1.50424	−	0.378532i
$195$		0			0
$196$	−23.6001	+	12.6806i	−1.68572	+	0.905760i
$197$	11.0656	+	11.0656i	0.788391	+	0.788391i	0.981230	−	0.192839i	$-0.0617695\pi$
$197$	11.0656	+	11.0656i	0.788391	+	0.788391i	−0.192839	+	0.981230i	$0.561770\pi$
$198$		0			0
$199$		−	7.04564i		−	0.499452i	−0.968317	−	0.249726i	$-0.919659\pi$
$199$		−	7.04564i		−	0.499452i	0.968317	−	0.249726i	$-0.0803406\pi$
$200$	−3.24802	−	13.7641i	−0.229670	−	0.973269i
$201$		0			0
$202$	4.47407	+	2.67504i	0.314794	+	0.188215i
$203$	4.59393	+	4.59393i	0.322430	+	0.322430i
$204$		0			0
$205$	−1.88524	+	7.26435i	−0.131671	+	0.507364i
$206$	−3.19673	−	12.7034i	−0.222727	−	0.885089i
$207$		0			0
$208$	0.128130	+	0.629817i	0.00888424	+	0.0436700i
$209$	−6.82839			−0.472329
$210$		0			0
$211$	0.158025	+	0.158025i	0.0108789	+	0.0108789i	0.712525	−	0.701646i	$-0.247551\pi$
$211$	0.158025	+	0.158025i	0.0108789	+	0.0108789i	−0.701646	+	0.712525i	$0.747551\pi$
$212$	8.85958	+	2.66649i	0.608479	+	0.183135i
$213$		0			0
$214$	4.85229	−	8.11556i	0.331695	−	0.554768i
$215$	−9.10633	−	15.4894i	−0.621047	−	1.05637i
$216$		0			0
$217$	−29.0251			−1.97035
$218$	−0.164946	+	0.275876i	−0.0111715	+	0.0186847i
$219$		0			0
$220$	11.3025	−	18.5903i	0.762015	−	1.25336i
$221$	−0.571843	−	0.571843i	−0.0384663	−	0.0384663i
$222$		0			0
$223$		−	8.38138i		−	0.561259i	−0.959816	−	0.280629i	$-0.909457\pi$
$223$		−	8.38138i		−	0.561259i	0.959816	−	0.280629i	$-0.0905432\pi$
$224$	24.1003	+	8.47561i	1.61027	+	0.566300i
$225$		0			0
$226$	−1.40559	+	0.353707i	−0.0934982	+	0.0235282i
$227$	−6.73568	+	6.73568i	−0.447063	+	0.447063i	−0.894377	−	0.447314i	$-0.852381\pi$
$227$	−6.73568	+	6.73568i	−0.447063	+	0.447063i	0.447314	+	0.894377i	$0.352381\pi$
$228$		0			0
$229$	−13.6770	+	13.6770i	−0.903800	+	0.903800i	−0.995762	−	0.0919626i	$-0.970686\pi$
$229$	−13.6770	+	13.6770i	−0.903800	+	0.903800i	0.0919626	+	0.995762i	$0.470686\pi$
$230$	0.187155	−	25.3139i	0.0123406	−	1.66915i
$231$		0			0
$232$	0.186385	−	4.06462i	0.0122368	−	0.266855i
$233$	1.62741			0.106615			0.0533077	−	0.998578i	$-0.483024\pi$
$233$	1.62741			0.106615			0.0533077	+	0.998578i	$0.483024\pi$
$234$		0			0
$235$	5.11291	−	19.7014i	0.333529	−	1.28518i
$236$	−4.32720	+	14.3774i	−0.281677	+	0.935891i
$237$		0			0
$238$	−31.1732	+	7.84453i	−2.02066	+	0.508485i
$239$	12.6908			0.820902			0.410451	−	0.911883i	$-0.365371\pi$
$239$	12.6908			0.820902			0.410451	+	0.911883i	$0.365371\pi$
$240$		0			0
$241$	21.1033			1.35938			0.679692	−	0.733498i	$-0.262114\pi$
$241$	21.1033			1.35938			0.679692	+	0.733498i	$0.262114\pi$
$242$	17.3725	−	4.37169i	1.11675	−	0.281023i
$243$		0			0
$244$	15.9116	+	4.78894i	1.01863	+	0.306581i
$245$	−28.9930	−	7.52424i	−1.85229	−	0.480706i
$246$		0			0
$247$	0.225531			0.0143502
$248$	12.2516	+	13.4292i	0.777980	+	0.852758i
$249$		0			0
$250$	7.79082	−	13.7587i	0.492735	−	0.870180i
$251$	−17.4935	+	17.4935i	−1.10418	+	1.10418i	−0.110282	+	0.993900i	$0.535176\pi$
$251$	−17.4935	+	17.4935i	−1.10418	+	1.10418i	−0.993900	+	0.110282i	$0.964824\pi$
$252$		0			0
$253$	27.5378	−	27.5378i	1.73129	−	1.73129i
$254$	−12.7431	+	3.20672i	−0.799574	+	0.201208i
$255$		0			0
$256$	−6.25136	−	14.7282i	−0.390710	−	0.920514i
$257$		−	7.80177i		−	0.486661i	−0.969943	−	0.243331i	$-0.921760\pi$
$257$		−	7.80177i		−	0.486661i	0.969943	−	0.243331i	$-0.0782400\pi$
$258$		0			0
$259$	7.38207	+	7.38207i	0.458699	+	0.458699i
$260$	−0.373303	+	0.614006i	−0.0231513	+	0.0380790i
$261$		0			0
$262$	−4.65710	+	7.78911i	−0.287717	+	0.481213i
$263$	−11.9238			−0.735252			−0.367626	−	0.929974i	$-0.619829\pi$
$263$	−11.9238			−0.735252			−0.367626	+	0.929974i	$0.619829\pi$
$264$		0			0
$265$	5.24255	+	8.91732i	0.322047	+	0.547787i
$266$	4.60032	−	7.69414i	0.282064	−	0.471758i
$267$		0			0
$268$	1.52955	−	5.08205i	0.0934324	−	0.310435i
$269$	8.24368	+	8.24368i	0.502626	+	0.502626i	0.912253	−	0.409627i	$-0.134341\pi$
$269$	8.24368	+	8.24368i	0.502626	+	0.502626i	−0.409627	+	0.912253i	$0.634341\pi$
$270$		0			0
$271$	−26.8960			−1.63381			−0.816907	−	0.576770i	$-0.804313\pi$
$271$	−26.8960			−1.63381			−0.816907	+	0.576770i	$0.804313\pi$
$272$	16.7878	+	11.1119i	1.01791	+	0.673758i
$273$		0			0
$274$	−0.154903	−	0.615567i	−0.00935806	−	0.0371878i
$275$	23.3935	−	6.66519i	1.41068	−	0.401926i
$276$		0			0
$277$	−15.8294	−	15.8294i	−0.951099	−	0.951099i	0.0477597	−	0.998859i	$-0.484792\pi$
$277$	−15.8294	−	15.8294i	−0.951099	−	0.951099i	−0.998859	+	0.0477597i	$0.984792\pi$
$278$	−8.80035	−	5.26172i	−0.527810	−	0.315577i
$279$		0			0
$280$	13.3327	+	25.2599i	0.796782	+	1.50957i
$281$		−	27.8550i		−	1.66169i	−0.556503	−	0.830845i	$-0.687857\pi$
$281$		−	27.8550i		−	1.66169i	0.556503	−	0.830845i	$-0.312143\pi$
$282$		0			0
$283$	2.62285	+	2.62285i	0.155913	+	0.155913i	0.780753	−	0.624840i	$-0.214836\pi$
$283$	2.62285	+	2.62285i	0.155913	+	0.155913i	−0.624840	+	0.780753i	$0.714836\pi$
$284$	−0.601405	−	1.11928i	−0.0356868	−	0.0664173i
$285$		0			0
$286$	−1.07205	+	0.269775i	−0.0633919	+	0.0159522i
$287$		−	15.1577i		−	0.894730i
$288$		0			0
$289$	−8.33160			−0.490094
$290$	3.24043	−	3.19287i	0.190285	−	0.187492i
$291$		0			0
$292$	−10.8210	+	5.81428i	−0.633253	+	0.340255i
$293$	−7.75559	−	7.75559i	−0.453086	−	0.453086i	0.443291	−	0.896378i	$-0.353811\pi$
$293$	−7.75559	−	7.75559i	−0.453086	−	0.453086i	−0.896378	+	0.443291i	$0.853811\pi$
$294$		0			0
$295$	−14.4711	+	8.50767i	−0.842541	+	0.495336i
$296$	0.299506	−	6.53152i	0.0174084	−	0.379637i
$297$		0			0
$298$	−7.83634	−	4.68534i	−0.453947	−	0.271414i
$299$	−0.909528	+	0.909528i	−0.0525994	+	0.0525994i
$300$		0			0
$301$	25.6606	+	25.6606i	1.47905	+	1.47905i
$302$	9.38512	−	2.36170i	0.540053	−	0.135901i
$303$		0			0
$304$	−5.50172	+	1.11927i	−0.315545	+	0.0641946i
$305$	9.41549	+	16.0153i	0.539129	+	0.917032i
$306$		0			0
$307$	−2.60764	+	2.60764i	−0.148826	+	0.148826i	−0.777593	−	0.628767i	$-0.783560\pi$
$307$	−2.60764	+	2.60764i	−0.148826	+	0.148826i	0.628767	+	0.777593i	$0.283560\pi$
$308$	−12.6639	+	42.0767i	−0.721594	+	2.39754i
$309$		0			0
$310$	−0.150258	+	20.3233i	−0.00853406	+	1.15429i
$311$			20.1642i			1.14340i	0.820461	+	0.571702i	$0.193717\pi$
$311$			20.1642i			1.14340i	−0.820461	+	0.571702i	$0.806283\pi$
$312$		0			0
$313$	23.2572			1.31457			0.657286	−	0.753641i	$-0.271704\pi$
$313$	23.2572			1.31457			0.657286	+	0.753641i	$0.271704\pi$
$314$	−3.19245	−	1.90876i	−0.180160	−	0.107718i
$315$		0			0
$316$	−3.10955	+	1.67080i	−0.174926	+	0.0939897i
$317$	−17.1360	+	17.1360i	−0.962451	+	0.962451i	−0.999320	−	0.0368693i	$-0.988261\pi$
$317$	−17.1360	+	17.1360i	−0.962451	+	0.962451i	0.0368693	+	0.999320i	$0.488261\pi$
$318$		0			0
$319$	6.99850			0.391841
$320$	6.05936	−	16.8310i	0.338728	−	0.940884i
$321$		0			0
$322$	12.4769	+	49.5816i	0.695309	+	2.76307i
$323$	4.99529	−	4.99529i	0.277945	−	0.277945i
$324$		0			0
$325$	−0.772649	+	0.220140i	−0.0428589	+	0.0122112i
$326$	16.1879	+	9.67871i	0.896563	+	0.536054i
$327$		0			0
$328$	−7.01311	+	6.39813i	−0.387234	+	0.353278i
$329$			41.1087i			2.26640i
$330$		0			0
$331$	−2.06668	+	2.06668i	−0.113595	+	0.113595i	−0.761619	−	0.648025i	$-0.775595\pi$
$331$	−2.06668	+	2.06668i	−0.113595	+	0.113595i	0.648025	+	0.761619i	$0.275595\pi$
$332$	−5.21024	+	17.3114i	−0.285949	+	0.950086i
$333$		0			0
$334$	−7.33619	−	29.1531i	−0.401418	−	1.59519i
$335$	5.11517	−	3.00724i	0.279471	−	0.164303i
$336$		0			0
$337$			35.2657i			1.92105i	0.278201	+	0.960523i	$0.410262\pi$
$337$			35.2657i			1.92105i	−0.278201	+	0.960523i	$0.589738\pi$
$338$	−17.7935	+	4.47763i	−0.967840	+	0.243551i
$339$		0			0
$340$	5.33134	+	21.8680i	0.289132	+	1.18596i
$341$	−22.1088	+	22.1088i	−1.19726	+	1.19726i
$342$		0			0
$343$	28.8833			1.55955
$344$	1.04110	−	22.7040i	0.0561326	−	1.22412i
$345$		0			0
$346$	−6.71161	−	4.01287i	−0.360818	−	0.215733i
$347$	−2.03686	−	2.03686i	−0.109344	−	0.109344i	0.650318	−	0.759662i	$-0.274636\pi$
$347$	−2.03686	−	2.03686i	−0.109344	−	0.109344i	−0.759662	+	0.650318i	$0.774636\pi$
$348$		0			0
$349$	−19.7731	−	19.7731i	−1.05843	−	1.05843i	−0.998184	−	0.0602455i	$-0.980812\pi$
$349$	−19.7731	−	19.7731i	−1.05843	−	1.05843i	−0.0602455	−	0.998184i	$-0.519188\pi$
$350$	−8.25006	+	30.8499i	−0.440984	+	1.64900i
$351$		0			0
$352$	24.8134	−	11.9015i	1.32256	−	0.634351i
$353$			10.5799i			0.563110i	0.959545	+	0.281555i	$0.0908502\pi$
$353$			10.5799i			0.563110i	−0.959545	+	0.281555i	$0.909150\pi$
$354$		0			0
$355$	0.356853	−	1.37505i	0.0189398	−	0.0729801i
$356$	0.548623	+	1.02105i	0.0290770	+	0.0541156i
$357$		0			0
$358$	17.2714	−	28.8868i	0.912820	−	1.52671i
$359$			32.7257i			1.72719i	0.504183	+	0.863597i	$0.331794\pi$
$359$			32.7257i			1.72719i	−0.504183	+	0.863597i	$0.668206\pi$
$360$		0			0
$361$		−	17.0299i		−	0.896310i
$362$	−17.8529	−	10.6743i	−0.938330	−	0.561026i
$363$		0			0
$364$	0.418269	−	1.38973i	0.0219232	−	0.0728414i
$365$	−13.2937	−	3.44999i	−0.695826	−	0.180581i
$366$		0			0
$367$		−	22.0267i		−	1.14978i	−0.818230	−	0.574891i	$-0.805044\pi$
$367$		−	22.0267i		−	1.14978i	0.818230	−	0.574891i	$-0.194956\pi$
$368$	17.6737	−	26.7014i	0.921305	−	1.39191i
$369$		0			0
$370$	5.20712	−	5.13069i	0.270705	−	0.266732i
$371$	−14.7729	−	14.7729i	−0.766971	−	0.766971i
$372$		0			0
$373$	9.69407	+	9.69407i	0.501940	+	0.501940i	0.912040	−	0.410100i	$-0.134506\pi$
$373$	9.69407	+	9.69407i	0.501940	+	0.501940i	−0.410100	+	0.912040i	$0.634506\pi$
$374$	−17.7697	+	29.7203i	−0.918850	+	1.53680i
$375$		0			0
$376$	19.0201	−	17.3522i	0.980884	−	0.894871i
$377$	−0.231149			−0.0119048
$378$		0			0
$379$	−7.44766	+	7.44766i	−0.382560	+	0.382560i	−0.872024	−	0.489463i	$-0.837193\pi$
$379$	−7.44766	+	7.44766i	−0.382560	+	0.382560i	0.489463	+	0.872024i	$0.337193\pi$
$380$	−5.36360	−	3.26096i	−0.275147	−	0.167284i
$381$		0			0
$382$	−7.18691	−	28.5599i	−0.367714	−	1.46125i
$383$			7.30581i			0.373309i	0.982426	+	0.186655i	$0.0597645\pi$
$383$			7.30581i			0.373309i	−0.982426	+	0.186655i	$0.940235\pi$
$384$		0			0
$385$	−42.3509	+	24.8984i	−2.15840	+	1.26894i
$386$	7.98916	−	2.01042i	0.406637	−	0.102328i
$387$		0			0
$388$	14.4616	+	26.9147i	0.734175	+	1.36638i
$389$	10.6571	−	10.6571i	0.540338	−	0.540338i	−0.383290	−	0.923628i	$-0.625209\pi$
$389$	10.6571	−	10.6571i	0.540338	−	0.540338i	0.923628	+	0.383290i	$0.125209\pi$
$390$		0			0
$391$			40.2904i			2.03757i
$392$	−25.5358	−	27.9902i	−1.28975	−	1.41372i
$393$		0			0
$394$	−11.3571	+	18.9949i	−0.572160	+	0.956951i
$395$	−3.82011	−	0.991393i	−0.192210	−	0.0498824i
$396$		0			0
$397$	−3.10102	+	3.10102i	−0.155636	+	0.155636i	−0.780630	−	0.624994i	$-0.785101\pi$
$397$	−3.10102	+	3.10102i	−0.155636	+	0.155636i	0.624994	+	0.780630i	$0.285101\pi$
$398$	9.66279	−	2.43158i	0.484352	−	0.121884i
$399$		0			0
$400$	17.7559	−	9.20476i	0.887796	−	0.460238i
$401$	9.88608			0.493687			0.246844	−	0.969055i	$-0.420607\pi$
$401$	9.88608			0.493687			0.246844	+	0.969055i	$0.420607\pi$
$402$		0			0
$403$	0.730217	−	0.730217i	0.0363747	−	0.0363747i
$404$	−2.12462	+	7.05920i	−0.105704	+	0.351208i
$405$		0			0
$406$	−4.71492	+	7.88582i	−0.233998	+	0.391367i
$407$	11.2460			0.557444
$408$		0			0
$409$		−	11.6903i		−	0.578048i	−0.957322	−	0.289024i	$-0.906669\pi$
$409$		−	11.6903i		−	0.578048i	0.957322	−	0.289024i	$-0.0933307\pi$
$410$	−10.6134	−	0.0784685i	−0.524157	−	0.00387528i
$411$		0			0
$412$	16.3189	−	8.76836i	0.803976	−	0.431986i
$413$	23.9736	−	23.9736i	1.17966	−	1.17966i
$414$		0			0
$415$	−17.4242	+	10.2438i	−0.855321	+	0.502849i
$416$	−0.819547	+	0.393086i	−0.0401816	+	0.0192727i
$417$		0			0
$418$	−2.35660	−	9.36484i	−0.115265	−	0.458049i
$419$	−5.66521	−	5.66521i	−0.276764	−	0.276764i	0.555052	−	0.831816i	$-0.312698\pi$
$419$	−5.66521	−	5.66521i	−0.276764	−	0.276764i	−0.831816	+	0.555052i	$0.812698\pi$
$420$		0			0
$421$	19.7440	−	19.7440i	0.962263	−	0.962263i	−0.0370502	−	0.999313i	$-0.511796\pi$
$421$	19.7440	−	19.7440i	0.962263	−	0.962263i	0.999313	+	0.0370502i	$0.0117961\pi$
$422$	−0.162187	+	0.271261i	−0.00789514	+	0.0132048i
$423$		0			0
$424$	−0.599368	+	13.0708i	−0.0291079	+	0.634773i
$425$	−12.2376	+	21.9894i	−0.593609	+	1.06664i
$426$		0			0
$427$	−26.5317	−	26.5317i	−1.28396	−	1.28396i
$428$	12.8048	+	3.85387i	0.618941	+	0.186284i
$429$		0			0
$430$	18.1003	−	17.8346i	0.872874	−	0.860062i
$431$	10.8449			0.522382			0.261191	−	0.965287i	$-0.415885\pi$
$431$	10.8449			0.522382			0.261191	+	0.965287i	$0.415885\pi$
$432$		0			0
$433$			15.4885i			0.744330i	0.928167	+	0.372165i	$0.121384\pi$
$433$			15.4885i			0.744330i	−0.928167	+	0.372165i	$0.878616\pi$
$434$	−10.0171	−	39.8067i	−0.480836	−	1.91078i
$435$		0			0
$436$	−0.435277	−	0.131006i	−0.0208460	−	0.00627407i
$437$	−7.94511	−	7.94511i	−0.380066	−	0.380066i
$438$		0			0
$439$			10.4685i			0.499633i	0.968293	+	0.249816i	$0.0803702\pi$
$439$			10.4685i			0.499633i	−0.968293	+	0.249816i	$0.919630\pi$
$440$	29.3964	+	9.08506i	1.40142	+	0.433113i
$441$		0			0
$442$	0.586905	−	0.981612i	0.0279162	−	0.0466905i
$443$	15.6375	+	15.6375i	0.742961	+	0.742961i	0.973147	−	0.230186i	$-0.0739334\pi$
$443$	15.6375	+	15.6375i	0.742961	+	0.742961i	−0.230186	+	0.973147i	$0.573933\pi$
$444$		0			0
$445$	−0.325534	+	1.25437i	−0.0154318	+	0.0594628i
$446$	11.4947	−	2.89257i	0.544290	−	0.136967i
$447$		0			0
$448$	−3.30649	+	35.9775i	−0.156217	+	1.69978i
$449$	−22.2119			−1.04825			−0.524123	−	0.851642i	$-0.675607\pi$
$449$	−22.2119			−1.04825			−0.524123	+	0.851642i	$0.675607\pi$
$450$		0			0
$451$	−11.5458	−	11.5458i	−0.543670	−	0.543670i
$452$	−0.970187	−	1.80563i	−0.0456337	−	0.0849297i
$453$		0			0
$454$	−11.5623	−	6.91308i	−0.542645	−	0.324447i
$455$	1.39878	−	0.822354i	0.0655759	−	0.0385525i
$456$		0			0
$457$	−28.4752			−1.33201			−0.666006	−	0.745946i	$-0.731998\pi$
$457$	−28.4752			−1.33201			−0.666006	+	0.745946i	$0.731998\pi$
$458$	−23.4776	−	14.0372i	−1.09703	−	0.655916i
$459$		0			0
$460$	34.7815	−	8.47960i	1.62169	−	0.395363i
$461$	−22.7778	−	22.7778i	−1.06087	−	1.06087i	−0.998023	−	0.0628456i	$-0.979982\pi$
$461$	−22.7778	−	22.7778i	−1.06087	−	1.06087i	−0.0628456	−	0.998023i	$-0.520018\pi$
$462$		0			0
$463$			24.5804i			1.14235i	0.820829	+	0.571174i	$0.193512\pi$
$463$			24.5804i			1.14235i	−0.820829	+	0.571174i	$0.806488\pi$
$464$	5.63877	−	1.14715i	0.261774	−	0.0532553i
$465$		0			0
$466$	0.561650	+	2.23193i	0.0260179	+	0.103392i
$467$	−15.6837	+	15.6837i	−0.725757	+	0.725757i	−0.969772	−	0.244015i	$-0.921536\pi$
$467$	−15.6837	+	15.6837i	−0.725757	+	0.725757i	0.244015	+	0.969772i	$0.421536\pi$
$468$		0			0
$469$	−8.47405	+	8.47405i	−0.391295	+	0.391295i
$470$	28.7842	+	0.212812i	1.32772	+	0.00981629i
$471$		0			0
$472$	−21.2114	−	0.972661i	−0.976334	−	0.0447703i
$473$	39.0919			1.79745
$474$		0			0
$475$	−1.92302	−	6.74941i	−0.0882342	−	0.309684i
$476$	−21.5169	−	40.0454i	−0.986224	−	1.83548i
$477$		0			0
$478$	4.37984	+	17.4049i	0.200329	+	0.796083i
$479$	9.45943			0.432212			0.216106	−	0.976370i	$-0.430664\pi$
$479$	9.45943			0.432212			0.216106	+	0.976370i	$0.430664\pi$
$480$		0			0
$481$	−0.371438			−0.0169361
$482$	7.28314	+	28.9423i	0.331738	+	1.31828i
$483$		0			0
$484$	11.9912	+	22.3169i	0.545053	+	1.01441i
$485$	−8.58099	+	33.0649i	−0.389643	+	1.50140i
$486$		0			0
$487$	9.95957			0.451311			0.225656	−	0.974207i	$-0.427548\pi$
$487$	9.95957			0.451311			0.225656	+	0.974207i	$0.427548\pi$
$488$	−1.07645	+	23.4748i	−0.0487286	+	1.06265i
$489$		0			0
$490$	0.313178	−	42.3593i	0.0141479	−	1.91360i
$491$	−4.35184	+	4.35184i	−0.196396	+	0.196396i	−0.798453	−	0.602057i	$-0.794348\pi$
$491$	−4.35184	+	4.35184i	−0.196396	+	0.196396i	0.602057	+	0.798453i	$0.294348\pi$
$492$		0			0
$493$	−5.11973	+	5.11973i	−0.230581	+	0.230581i
$494$	0.0778347	+	0.309305i	0.00350195	+	0.0139163i
$495$		0			0
$496$	−14.1894	+	21.4373i	−0.637121	+	0.962562i
$497$			2.86916i			0.128700i
$498$		0			0
$499$	3.09455	+	3.09455i	0.138531	+	0.138531i	0.772972	−	0.634440i	$-0.218769\pi$
$499$	3.09455	+	3.09455i	0.138531	+	0.138531i	−0.634440	+	0.772972i	$0.718769\pi$
$500$	21.5583	+	5.93637i	0.964116	+	0.265483i
$501$		0			0
$502$	−30.0290	−	17.9543i	−1.34026	−	0.801339i
$503$	−5.84356			−0.260552			−0.130276	−	0.991478i	$-0.541586\pi$
$503$	−5.84356			−0.260552			−0.130276	+	0.991478i	$0.541586\pi$
$504$		0			0
$505$	−7.10520	+	4.17720i	−0.316177	+	0.185883i
$506$	47.2707	+	28.2631i	2.10144	+	1.25645i
$507$		0			0
$508$	−8.79576	−	16.3699i	−0.390249	−	0.726298i
$509$	−2.16459	−	2.16459i	−0.0959436	−	0.0959436i	0.657506	−	0.753449i	$-0.271611\pi$
$509$	−2.16459	−	2.16459i	−0.0959436	−	0.0959436i	−0.753449	+	0.657506i	$0.771611\pi$
$510$		0			0
$511$	27.7385			1.22708
$512$	18.0417	−	13.6564i	0.797336	−	0.603536i
$513$		0			0
$514$	10.6998	−	2.69253i	0.471948	−	0.118763i
$515$	20.0479	+	5.20284i	0.883418	+	0.229264i
$516$		0			0
$517$	31.3130	+	31.3130i	1.37714	+	1.37714i
$518$	−7.57650	+	12.6719i	−0.332892	+	0.556770i
$519$		0			0
$520$	−0.970916	−	0.300065i	−0.0425775	−	0.0131587i
$521$			4.80746i			0.210619i	0.994440	+	0.105309i	$0.0335833\pi$
$521$			4.80746i			0.210619i	−0.994440	+	0.105309i	$0.966417\pi$
$522$		0			0
$523$	−23.6204	−	23.6204i	−1.03285	−	1.03285i	−0.999442	−	0.0334047i	$-0.989365\pi$
$523$	−23.6204	−	23.6204i	−1.03285	−	1.03285i	−0.0334047	−	0.999442i	$-0.510635\pi$
$524$	−12.2897	−	3.69885i	−0.536877	−	0.161585i
$525$		0			0
$526$	−4.11512	−	16.3530i	−0.179428	−	0.713023i
$527$		−	32.3473i		−	1.40907i
$528$		0			0
$529$	41.0827			1.78620
$530$	−10.4204	+	10.2675i	−0.452634	+	0.445990i
$531$		0			0
$532$	12.1398	+	3.65375i	0.526329	+	0.158410i
$533$	0.381339	+	0.381339i	0.0165176	+	0.0165176i
$534$		0			0
$535$	7.57706	+	12.8882i	0.327585	+	0.557205i
$536$	7.49768	+	0.343810i	0.323851	+	0.0148503i
$537$		0			0
$538$	−8.46080	+	14.1509i	−0.364771	+	0.610088i
$539$	46.0808	−	46.0808i	1.98484	−	1.98484i
$540$		0			0
$541$	−22.9002	−	22.9002i	−0.984558	−	0.984558i	0.0153248	−	0.999883i	$-0.495122\pi$
$541$	−22.9002	−	22.9002i	−0.984558	−	0.984558i	−0.999883	+	0.0153248i	$0.995122\pi$
$542$	−9.28229	−	36.8866i	−0.398708	−	1.58442i
$543$		0			0
$544$	−9.44570	+	26.8587i	−0.404981	+	1.15156i
$545$	−0.257570	−	0.438114i	−0.0110331	−	0.0187667i
$546$		0			0
$547$	−24.1611	+	24.1611i	−1.03306	+	1.03306i	−0.0336209	+	0.999435i	$0.510704\pi$
$547$	−24.1611	+	24.1611i	−1.03306	+	1.03306i	−0.999435	+	0.0336209i	$0.989296\pi$
$548$	0.790764	−	0.424887i	0.0337797	−	0.0181503i
$549$		0			0
$550$	17.2145	+	29.7829i	0.734031	+	1.26995i
$551$		−	2.01918i		−	0.0860201i
$552$		0			0
$553$	7.97098			0.338961
$554$	16.2464	−	27.1724i	0.690242	−	1.15445i
$555$		0			0
$556$	4.17906	−	13.8852i	0.177232	−	0.588864i
$557$	−4.87106	+	4.87106i	−0.206393	+	0.206393i	−0.802733	−	0.596339i	$-0.796621\pi$
$557$	−4.87106	+	4.87106i	−0.206393	+	0.206393i	0.596339	+	0.802733i	$0.296621\pi$
$558$		0			0
$559$	−1.29114			−0.0546095
$560$	−30.0415	+	27.0029i	−1.26948	+	1.14108i
$561$		0			0
$562$	38.2019	−	9.61327i	1.61145	−	0.405511i
$563$	1.64374	−	1.64374i	0.0692752	−	0.0692752i	−0.671620	−	0.740896i	$-0.734401\pi$
$563$	1.64374	−	1.64374i	0.0692752	−	0.0692752i	0.740896	+	0.671620i	$0.234401\pi$
$564$		0			0
$565$	0.575675	−	2.21823i	0.0242188	−	0.0933217i
$566$	−2.69194	+	4.50233i	−0.113151	+	0.189247i
$567$		0			0
$568$	1.32749	−	1.21109i	0.0557004	−	0.0508161i
$569$		−	30.0890i		−	1.26140i	−0.776028	−	0.630699i	$-0.782768\pi$
$569$		−	30.0890i		−	1.26140i	0.776028	−	0.630699i	$-0.217232\pi$
$570$		0			0
$571$	12.4422	−	12.4422i	0.520688	−	0.520688i	−0.397091	−	0.917779i	$-0.629980\pi$
$571$	12.4422	−	12.4422i	0.520688	−	0.520688i	0.917779	+	0.397091i	$0.129980\pi$
$572$	−0.739970	−	1.37717i	−0.0309397	−	0.0575824i
$573$		0			0
$574$	20.7881	−	5.23119i	0.867679	−	0.218346i
$575$	34.9745	+	19.4641i	1.45854	+	0.811708i
$576$		0			0
$577$		−	38.4529i		−	1.60081i	−0.599457	−	0.800407i	$-0.704617\pi$
$577$		−	38.4529i		−	1.60081i	0.599457	−	0.800407i	$-0.295383\pi$
$578$	−2.87539	−	11.4264i	−0.119600	−	0.475277i
$579$		0			0
$580$	5.49722	+	3.34220i	0.228260	+	0.138777i
$581$	28.8659	−	28.8659i	1.19756	−	1.19756i
$582$		0			0
$583$	−22.5054			−0.932078
$584$	−11.7086	−	12.8340i	−0.484504	−	0.531074i
$585$		0			0
$586$	7.95986	−	13.3131i	0.328819	−	0.549957i
$587$	20.0374	+	20.0374i	0.827031	+	0.827031i	0.987105	−	0.160074i	$-0.0511734\pi$
$587$	20.0374	+	20.0374i	0.827031	+	0.827031i	−0.160074	+	0.987105i	$0.551173\pi$
$588$		0			0
$589$	6.37875	+	6.37875i	0.262832	+	0.262832i
$590$	−16.6621	−	16.9104i	−0.685970	−	0.696189i
$591$		0			0
$592$	9.06106	−	1.84339i	0.372407	−	0.0757627i
$593$		−	39.5143i		−	1.62266i	−0.584590	−	0.811329i	$-0.698745\pi$
$593$		−	39.5143i		−	1.62266i	0.584590	−	0.811329i	$-0.301255\pi$
$594$		0			0
$595$	12.7674	−	49.1961i	0.523411	−	2.01684i
$596$	3.72128	−	12.3642i	0.152429	−	0.506457i
$597$		0			0
$598$	−1.56127	−	0.933484i	−0.0638452	−	0.0381730i
$599$		−	46.6476i		−	1.90597i	−0.303022	−	0.952984i	$-0.597996\pi$
$599$		−	46.6476i		−	1.90597i	0.303022	−	0.952984i	$-0.402004\pi$
$600$		0			0
$601$			39.8224i			1.62439i	0.583386	+	0.812195i	$0.301727\pi$
$601$			39.8224i			1.62439i	−0.583386	+	0.812195i	$0.698273\pi$
$602$	−26.3364	+	44.0483i	−1.07339	+	1.79527i
$603$		0			0
$604$	6.47795	+	12.0562i	0.263584	+	0.490560i
$605$	−7.11514	+	27.4165i	−0.289271	+	1.11464i
$606$		0			0
$607$		−	29.2165i		−	1.18586i	−0.805254	−	0.592930i	$-0.797971\pi$
$607$		−	29.2165i		−	1.18586i	0.805254	−	0.592930i	$-0.202029\pi$
$608$	−3.43378	−	7.15909i	−0.139258	−	0.290339i
$609$		0			0
$610$	−18.7148	+	18.4401i	−0.757740	+	0.746618i
$611$	−1.03422	−	1.03422i	−0.0418400	−	0.0418400i
$612$		0			0
$613$	−19.6885	−	19.6885i	−0.795212	−	0.795212i	0.187124	−	0.982336i	$-0.440083\pi$
$613$	−19.6885	−	19.6885i	−0.795212	−	0.795212i	−0.982336	+	0.187124i	$0.940083\pi$
$614$	−4.47622	−	2.67633i	−0.180645	−	0.108008i
$615$		0			0
$616$	−62.0769	−	2.84657i	−2.50115	−	0.114692i
$617$	10.8873			0.438306			0.219153	−	0.975691i	$-0.429671\pi$
$617$	10.8873			0.438306			0.219153	+	0.975691i	$0.429671\pi$
$618$		0			0
$619$	31.2108	−	31.2108i	1.25447	−	1.25447i	0.300773	−	0.953696i	$-0.402755\pi$
$619$	31.2108	−	31.2108i	1.25447	−	1.25447i	0.953696	−	0.300773i	$-0.0972445\pi$
$620$	−27.9244	+	6.80787i	−1.12147	+	0.273411i
$621$		0			0
$622$	−27.6543	+	6.95902i	−1.10884	+	0.279031i
$623$		−	2.61735i		−	0.104862i
$624$		0			0
$625$	13.1762	+	21.2459i	0.527048	+	0.849835i
$626$	8.02647	+	31.8962i	0.320802	+	1.27483i
$627$		0			0
$628$	1.51601	−	5.03705i	0.0604955	−	0.201000i
$629$	−8.22700	+	8.22700i	−0.328032	+	0.328032i
$630$		0			0
$631$			15.8570i			0.631257i	0.948883	+	0.315629i	$0.102215\pi$
$631$			15.8570i			0.631257i	−0.948883	+	0.315629i	$0.897785\pi$
$632$	−3.36459	−	3.68799i	−0.133836	−	0.146700i
$633$		0			0
$634$	−29.4151	−	17.5873i	−1.16822	−	0.698480i
$635$	5.21910	−	20.1106i	0.207114	−	0.798065i
$636$		0			0
$637$	−1.52197	+	1.52197i	−0.0603027	+	0.0603027i
$638$	2.41531	+	9.59813i	0.0956230	+	0.379994i
$639$		0			0
$640$	25.1742	+	2.50144i	0.995100	+	0.0988783i
$641$	10.9256			0.431535			0.215767	−	0.976445i	$-0.430775\pi$
$641$	10.9256			0.431535			0.215767	+	0.976445i	$0.430775\pi$
$642$		0			0
$643$	34.9865	−	34.9865i	1.37973	−	1.37973i	0.534675	−	0.845058i	$-0.320434\pi$
$643$	34.9865	−	34.9865i	1.37973	−	1.37973i	0.845058	−	0.534675i	$-0.179566\pi$
$644$	−63.6930	+	34.2230i	−2.50986	+	1.34858i
$645$		0			0
$646$	8.57479	+	5.12686i	0.337371	+	0.201714i
$647$	−8.60364			−0.338244			−0.169122	−	0.985595i	$-0.554093\pi$
$647$	−8.60364			−0.338244			−0.169122	+	0.985595i	$0.554093\pi$
$648$		0			0
$649$		−	36.5220i		−	1.43361i
$650$	−0.568568	−	0.983680i	−0.0223011	−	0.0385831i
$651$		0			0
$652$	−7.68721	+	25.5413i	−0.301054	+	1.00027i
$653$	−9.44853	+	9.44853i	−0.369750	+	0.369750i	−0.867386	−	0.497636i	$-0.834201\pi$
$653$	−9.44853	+	9.44853i	−0.369750	+	0.369750i	0.497636	+	0.867386i	$0.334201\pi$
$654$		0			0
$655$	−7.27227	−	12.3698i	−0.284151	−	0.483327i
$656$	−11.1951	−	7.41006i	−0.437096	−	0.289314i
$657$		0			0
$658$	−56.3788	+	14.1874i	−2.19788	+	0.553081i
$659$	4.77731	+	4.77731i	0.186098	+	0.186098i	0.794007	−	0.607909i	$-0.207991\pi$
$659$	4.77731	+	4.77731i	0.186098	+	0.186098i	−0.607909	+	0.794007i	$0.707991\pi$
$660$		0			0
$661$	14.2928	−	14.2928i	0.555927	−	0.555927i	−0.372218	−	0.928145i	$-0.621403\pi$
$661$	14.2928	−	14.2928i	0.555927	−	0.555927i	0.928145	+	0.372218i	$0.121403\pi$
$662$	−3.54761	−	2.12111i	−0.137882	−	0.0824394i
$663$		0			0
$664$	−25.5400	−	1.17115i	−0.991143	−	0.0454494i
$665$	7.18360	+	12.2189i	0.278568	+	0.473831i
$666$		0			0
$667$	8.14304	+	8.14304i	0.315300	+	0.315300i
$668$	37.4504	−	20.1225i	1.44900	−	0.778564i
$669$		0			0
$670$	5.88964	+	5.97737i	0.227537	+	0.230926i
$671$	−40.4191			−1.56036
$672$		0			0
$673$			19.6076i			0.755818i	0.925843	+	0.377909i	$0.123357\pi$
$673$			19.6076i			0.755818i	−0.925843	+	0.377909i	$0.876643\pi$
$674$	−48.3654	+	12.1708i	−1.86297	+	0.468803i
$675$		0			0
$676$	−12.2817	−	22.8577i	−0.472375	−	0.879144i
$677$	1.22231	+	1.22231i	0.0469773	+	0.0469773i	0.730205	−	0.683228i	$-0.239424\pi$
$677$	1.22231	+	1.22231i	0.0469773	+	0.0469773i	−0.683228	+	0.730205i	$0.739424\pi$
$678$		0			0
$679$		−	68.9927i		−	2.64770i
$680$	−28.1511	+	14.8587i	−1.07954	+	0.569807i
$681$		0			0
$682$	−37.9514	−	22.6911i	−1.45323	−	0.868887i
$683$	−27.1537	−	27.1537i	−1.03901	−	1.03901i	−0.999208	−	0.0398011i	$-0.987328\pi$
$683$	−27.1537	−	27.1537i	−1.03901	−	1.03901i	−0.0398011	−	0.999208i	$-0.512672\pi$
$684$		0			0
$685$	0.971460	+	0.252113i	0.0371176	+	0.00963274i
$686$	9.96815	+	39.6122i	0.380586	+	1.51240i
$687$		0			0
$688$	31.4969	−	6.40773i	1.20081	−	0.244293i
$689$	0.743316			0.0283181
$690$		0			0
$691$	14.8065	+	14.8065i	0.563266	+	0.563266i	0.930234	−	0.366968i	$-0.119604\pi$
$691$	14.8065	+	14.8065i	0.563266	+	0.563266i	−0.366968	+	0.930234i	$0.619604\pi$
$692$	3.18717	−	10.5896i	0.121158	−	0.402556i
$693$		0			0
$694$	2.09051	−	3.49643i	0.0793547	−	0.132723i
$695$	13.9757	−	8.21641i	0.530129	−	0.311666i
$696$		0			0
$697$	16.8926			0.639853
$698$	20.2939	−	33.9420i	0.768135	−	1.28472i
$699$		0			0
$700$	−45.1565	−	0.667754i	−1.70676	−	0.0252387i
$701$	0.259714	+	0.259714i	0.00980927	+	0.00980927i	0.711994	−	0.702185i	$-0.247792\pi$
$701$	0.259714	+	0.259714i	0.00980927	+	0.00980927i	−0.702185	+	0.711994i	$0.747792\pi$
$702$		0			0
$703$		−	3.24466i		−	0.122375i
$704$	24.8859	+	29.9231i	0.937924	+	1.12777i
$705$		0			0
$706$	−14.5098	+	3.65131i	−0.546085	+	0.137419i
$707$	11.7708	−	11.7708i	0.442688	−	0.442688i
$708$		0			0
$709$	−16.6998	+	16.6998i	−0.627173	+	0.627173i	−0.947356	−	0.320183i	$-0.896256\pi$
$709$	−16.6998	+	16.6998i	−0.627173	+	0.627173i	0.320183	+	0.947356i	$0.396256\pi$
$710$	2.00898	+	0.0148531i	0.0753956	+	0.000557428i
$711$		0			0
$712$	−1.21099	+	1.10480i	−0.0453837	+	0.0414040i
$713$	−51.4489			−1.92678
$714$		0			0
$715$	0.439073	−	1.69187i	0.0164204	−	0.0632722i
$716$	45.5776	+	13.7176i	1.70332	+	0.512650i
$717$		0			0
$718$	−44.8818	+	11.2942i	−1.67497	+	0.421496i
$719$	−0.0356124			−0.00132812			−0.000664059	−	1.00000i	$-0.500211\pi$
$719$	−0.0356124			−0.00132812			−0.000664059		1.00000i	$0.500211\pi$
$720$		0			0
$721$	−41.8318			−1.55790
$722$	23.3558	−	5.87733i	0.869212	−	0.218731i
$723$		0			0
$724$	8.47791	−	28.1684i	0.315079	−	1.04687i
$725$	1.97093	+	6.91755i	0.0731983	+	0.256912i
$726$		0			0
$727$	35.1597			1.30400			0.652000	−	0.758219i	$-0.273930\pi$
$727$	35.1597			1.30400			0.652000	+	0.758219i	$0.273930\pi$
$728$	2.05030	+	0.0940176i	0.0759892	+	0.00348453i
$729$		0			0
$730$	0.143597	−	19.4224i	0.00531477	−	0.718857i
$731$	−28.5976	+	28.5976i	−1.05772	+	1.05772i
$732$		0			0
$733$	−27.9959	+	27.9959i	−1.03405	+	1.03405i	−0.0346524	+	0.999399i	$0.511032\pi$
$733$	−27.9959	+	27.9959i	−1.03405	+	1.03405i	−0.999399	+	0.0346524i	$0.988968\pi$
$734$	30.2086	−	7.60180i	1.11502	−	0.280588i
$735$		0			0
$736$	42.7193	+	15.0236i	1.57465	+	0.553776i
$737$			12.9096i			0.475530i
$738$		0			0
$739$	22.3803	+	22.3803i	0.823274	+	0.823274i	0.986576	−	0.163302i	$-0.0522145\pi$
$739$	22.3803	+	22.3803i	0.823274	+	0.823274i	−0.163302	+	0.986576i	$0.552215\pi$
$740$	8.83358	+	5.37064i	0.324729	+	0.197429i
$741$		0			0
$742$	15.1620	−	25.3588i	0.556614	−	0.930950i
$743$	−11.3806			−0.417514			−0.208757	−	0.977968i	$-0.566942\pi$
$743$	−11.3806			−0.417514			−0.208757	+	0.977968i	$0.566942\pi$
$744$		0			0
$745$	12.4448	−	7.31637i	0.455941	−	0.268051i
$746$	−9.94940	+	16.6406i	−0.364273	+	0.609256i
$747$		0			0
$748$	−46.8927	−	14.1134i	−1.71457	−	0.516037i
$749$	−21.3513	−	21.3513i	−0.780158	−	0.780158i
$750$		0			0
$751$	54.6781			1.99523			0.997616	−	0.0690113i	$-0.0219845\pi$
$751$	54.6781			1.99523			0.997616	+	0.0690113i	$0.0219845\pi$
$752$	30.3619	+	20.0966i	1.10719	+	0.732848i
$753$		0			0
$754$	−0.0797737	−	0.317011i	−0.00290519	−	0.0115448i
$755$	−3.84379	+	14.8112i	−0.139890	+	0.539033i
$756$		0			0
$757$	32.3418	+	32.3418i	1.17548	+	1.17548i	0.980882	+	0.194602i	$0.0623416\pi$
$757$	32.3418	+	32.3418i	1.17548	+	1.17548i	0.194602	+	0.980882i	$0.437658\pi$
$758$	−12.7845	−	7.64382i	−0.464353	−	0.277636i
$759$		0			0
$760$	2.62119	−	8.48136i	0.0950806	−	0.307651i
$761$			0.392110i			0.0142140i	0.999975	+	0.00710700i	$0.00226225\pi$
$761$			0.392110i			0.0142140i	−0.999975	+	0.00710700i	$0.997738\pi$
$762$		0			0
$763$	0.725803	+	0.725803i	0.0262758	+	0.0262758i
$764$	36.6883	−	19.7131i	1.32734	−	0.713194i
$765$		0			0
$766$	−10.0196	+	2.52137i	−0.362023	+	0.0911007i
$767$			1.20626i			0.0435556i
$768$		0			0
$769$	−4.36080			−0.157255			−0.0786273	−	0.996904i	$-0.525054\pi$
$769$	−4.36080			−0.157255			−0.0786273	+	0.996904i	$0.525054\pi$
$770$	−48.7632	−	49.4896i	−1.75730	−	1.78348i
$771$		0			0
$772$	5.51441	+	10.2630i	0.198468	+	0.369372i
$773$	17.2357	+	17.2357i	0.619923	+	0.619923i	0.945512	−	0.325588i	$-0.105562\pi$
$773$	17.2357	+	17.2357i	0.619923	+	0.619923i	−0.325588	+	0.945512i	$0.605562\pi$
$774$		0			0
$775$	−28.0794	−	15.6268i	−1.00864	−	0.561330i
$776$	−31.9213	+	29.1221i	−1.14591	+	1.04542i
$777$		0			0
$778$	18.2938	+	10.9378i	0.655863	+	0.392140i
$779$	−3.33115	+	3.33115i	−0.119351	+	0.119351i
$780$		0			0
$781$	2.18548	+	2.18548i	0.0782024	+	0.0782024i
$782$	−55.2565	+	13.9050i	−1.97597	+	0.497240i
$783$		0			0
$784$	29.5745	−	44.6811i	1.05623	−	1.59576i
$785$	5.06988	−	2.98062i	0.180952	−	0.106383i
$786$		0			0
$787$	−24.9814	+	24.9814i	−0.890490	+	0.890490i	−0.994569	−	0.104079i	$-0.966811\pi$
$787$	−24.9814	+	24.9814i	−0.890490	+	0.890490i	0.104079	+	0.994569i	$0.466811\pi$
$788$	−29.9703	−	9.02021i	−1.06765	−	0.321332i
$789$		0			0
$790$	0.0412643	−	5.58126i	0.00146812	−	0.198572i
$791$			4.62853i			0.164572i
$792$		0			0
$793$	1.33498			0.0474064
$794$	−5.32314	−	3.18270i	−0.188911	−	0.112950i
$795$		0			0
$796$	6.66961	+	12.4129i	0.236398	+	0.439964i
$797$	−18.8067	+	18.8067i	−0.666166	+	0.666166i	−0.956826	−	0.290660i	$-0.906125\pi$
$797$	−18.8067	+	18.8067i	−0.666166	+	0.666166i	0.290660	+	0.956826i	$0.406125\pi$
$798$		0			0
$799$	−45.8139			−1.62078
$800$	18.7518	+	21.1747i	0.662977	+	0.748640i
$801$		0			0
$802$	3.41187	+	13.5583i	0.120477	+	0.478761i
$803$	21.1288	−	21.1288i	0.745618	−	0.745618i
$804$		0			0
$805$	−78.2474	−	20.3067i	−2.75786	−	0.715718i
$806$	1.25347	+	0.749450i	0.0441517	+	0.0263982i
$807$		0			0
$808$	−10.4146	−	0.477568i	−0.366385	−	0.0168008i
$809$		−	48.5593i		−	1.70726i	−0.520883	−	0.853628i	$-0.674397\pi$
$809$		−	48.5593i		−	1.70726i	0.520883	−	0.853628i	$-0.325603\pi$
$810$		0			0
$811$	−14.4543	+	14.4543i	−0.507560	+	0.507560i	−0.913777	−	0.406217i	$-0.866848\pi$
$811$	−14.4543	+	14.4543i	−0.507560	+	0.507560i	0.406217	+	0.913777i	$0.366848\pi$
$812$	−12.4423	−	3.74477i	−0.436638	−	0.131416i
$813$		0			0
$814$	3.88121	+	15.4234i	0.136036	+	0.540591i
$815$	−25.7077	+	15.1137i	−0.900502	+	0.529411i
$816$		0			0
$817$		−	11.2787i		−	0.394591i
$818$	16.0327	−	4.03453i	0.560571	−	0.141064i
$819$		0			0
$820$	−3.55525	−	14.5829i	−0.124155	−	0.509255i
$821$	29.1579	−	29.1579i	1.01762	−	1.01762i	0.0177763	−	0.999842i	$-0.494341\pi$
$821$	29.1579	−	29.1579i	1.01762	−	1.01762i	0.999842	−	0.0177763i	$-0.00565868\pi$
$822$		0			0
$823$	7.17233			0.250012			0.125006	−	0.992156i	$-0.460105\pi$
$823$	7.17233			0.250012			0.125006	+	0.992156i	$0.460105\pi$
$824$	17.6574	+	19.3546i	0.615124	+	0.674249i
$825$		0			0
$826$	41.1525	+	24.6050i	1.43188	+	0.856119i
$827$	21.6132	+	21.6132i	0.751564	+	0.751564i	0.974771	−	0.223207i	$-0.0716526\pi$
$827$	21.6132	+	21.6132i	0.751564	+	0.751564i	−0.223207	+	0.974771i	$0.571653\pi$
$828$		0			0
$829$	−21.3762	−	21.3762i	−0.742424	−	0.742424i	0.230620	−	0.973044i	$-0.425925\pi$
$829$	−21.3762	−	21.3762i	−0.742424	−	0.742424i	−0.973044	+	0.230620i	$0.925925\pi$
$830$	−20.0623	−	20.3612i	−0.696374	−	0.706748i
$831$		0			0
$832$	−0.821942	−	0.988312i	−0.0284957	−	0.0342635i
$833$			67.4205i			2.33598i
$834$		0			0
$835$	46.0081	+	11.9400i	1.59217	+	0.413201i
$836$	12.0302	−	6.46395i	0.416072	−	0.223560i
$837$		0			0
$838$	5.81443	−	9.72476i	0.200856	−	0.335936i
$839$			1.15350i			0.0398234i	0.999802	+	0.0199117i	$0.00633851\pi$
$839$			1.15350i			0.0398234i	−0.999802	+	0.0199117i	$0.993661\pi$
$840$		0			0
$841$		−	26.9305i		−	0.928638i
$842$	33.8920	+	20.2640i	1.16800	+	0.698344i
$843$		0			0
$844$	−0.427997	−	0.128815i	−0.0147323	−	0.00443400i
$845$	7.28755	−	28.0809i	0.250700	−	0.966013i
$846$		0			0
$847$		−	57.2070i		−	1.96566i
$848$	−18.1329	+	3.68896i	−0.622685	+	0.126679i
$849$		0			0
$850$	−34.3809	−	9.19434i	−1.17925	−	0.315363i
$851$	13.0852	+	13.0852i	0.448555	+	0.448555i
$852$		0			0
$853$	27.6979	+	27.6979i	0.948358	+	0.948358i	0.998730	−	0.0503728i	$-0.0160410\pi$
$853$	27.6979	+	27.6979i	0.948358	+	0.948358i	−0.0503728	+	0.998730i	$0.516041\pi$
$854$	27.2305	−	45.5437i	0.931810	−	1.55847i
$855$		0			0
$856$	−0.866266	+	18.8912i	−0.0296084	+	0.645688i
$857$	−49.0796			−1.67653			−0.838263	−	0.545266i	$-0.816429\pi$
$857$	−49.0796			−1.67653			−0.838263	+	0.545266i	$0.816429\pi$
$858$		0			0
$859$	−28.4421	+	28.4421i	−0.970433	+	0.970433i	−0.999575	−	0.0291421i	$-0.990722\pi$
$859$	−28.4421	+	28.4421i	−0.970433	+	0.970433i	0.0291421	+	0.999575i	$0.490722\pi$
$860$	30.7061	+	18.6687i	1.04707	+	0.636598i
$861$		0			0
$862$	3.74278	+	14.8734i	0.127480	+	0.506589i
$863$		−	24.2991i		−	0.827151i	−0.910470	−	0.413576i	$-0.864280\pi$
$863$		−	24.2991i		−	0.827151i	0.910470	−	0.413576i	$-0.135720\pi$
$864$		0			0
$865$	10.6586	−	6.26627i	0.362404	−	0.213060i
$866$	−21.2418	+	5.34536i	−0.721826	+	0.181643i
$867$		0			0
$868$	51.1361	−	27.4760i	1.73567	−	0.932597i
$869$	6.07159	−	6.07159i	0.205965	−	0.205965i
$870$		0			0
$871$		−	0.426382i		−	0.0144474i
$872$	0.0294474	−	0.642177i	0.000997214	−	0.0217469i
$873$		0			0
$874$	8.15437	−	13.6384i	0.275826	−	0.461325i
$875$	−36.5374	−	34.8492i	−1.23519	−	1.17812i
$876$		0			0
$877$	−14.7778	+	14.7778i	−0.499010	+	0.499010i	−0.911130	−	0.412120i	$-0.864789\pi$
$877$	−14.7778	+	14.7778i	−0.499010	+	0.499010i	0.412120	+	0.911130i	$0.364789\pi$
$878$	−14.3570	+	3.61286i	−0.484527	+	0.121928i
$879$		0			0
$880$	−2.31452	+	43.4514i	−0.0780225	+	1.46475i
$881$	−29.8866			−1.00691			−0.503453	−	0.864023i	$-0.667937\pi$
$881$	−29.8866			−1.00691			−0.503453	+	0.864023i	$0.667937\pi$
$882$		0			0
$883$	−16.5411	+	16.5411i	−0.556653	+	0.556653i	−0.928353	−	0.371700i	$-0.878775\pi$
$883$	−16.5411	+	16.5411i	−0.556653	+	0.556653i	0.371700	+	0.928353i	$0.378775\pi$
$884$	1.54879	+	0.466142i	0.0520914	+	0.0156781i
$885$		0			0
$886$	−16.0494	+	26.8430i	−0.539190	+	0.901807i
$887$	36.8915			1.23870			0.619348	−	0.785116i	$-0.287397\pi$
$887$	36.8915			1.23870			0.619348	+	0.785116i	$0.287397\pi$
$888$		0			0
$889$			41.9625i			1.40738i
$890$	−1.83266	−	0.0135495i	−0.0614309	−	0.000454182i
$891$		0			0
$892$	7.93406	+	14.7662i	0.265652	+	0.494409i
$893$	9.03432	−	9.03432i	0.302322	−	0.302322i
$894$		0			0
$895$	26.9700	+	45.8746i	0.901508	+	1.53342i
$896$	−50.4828	+	7.88179i	−1.68651	+	0.263312i
$897$		0			0
$898$	−7.66575	−	30.4627i	−0.255809	−	1.01655i
$899$	−6.53766	−	6.53766i	−0.218043	−	0.218043i
$900$		0			0
$901$	16.4638	−	16.4638i	0.548487	−	0.548487i
$902$	11.8499	−	19.8192i	0.394558	−	0.659908i
$903$		0			0
$904$	2.14151	−	1.95372i	0.0712257	−	0.0649799i
$905$	28.3520	−	16.6683i	0.942452	−	0.554074i
$906$		0			0
$907$	19.6564	+	19.6564i	0.652679	+	0.652679i	0.953637	−	0.300958i	$-0.0973064\pi$
$907$	19.6564	+	19.6564i	0.652679	+	0.652679i	−0.300958	+	0.953637i	$0.597306\pi$
$908$	5.49064	−	18.2430i	0.182213	−	0.605416i
$909$		0			0
$910$	1.61057	+	1.63456i	0.0533898	+	0.0541851i
$911$	10.4327			0.345650			0.172825	−	0.984953i	$-0.444711\pi$
$911$	10.4327			0.345650			0.172825	+	0.984953i	$0.444711\pi$
$912$		0			0
$913$		−	43.9749i		−	1.45536i
$914$	−9.82730	−	39.0525i	−0.325058	−	1.29174i
$915$		0			0
$916$	11.1489	−	37.0429i	0.368370	−	1.22393i
$917$	20.4924	+	20.4924i	0.676719	+	0.676719i
$918$		0			0
$919$		−	21.6666i		−	0.714715i	−0.933968	−	0.357357i	$-0.883678\pi$
$919$		−	21.6666i		−	0.714715i	0.933968	−	0.357357i	$-0.116322\pi$
$920$	23.6331	+	44.7748i	0.779161	+	1.47618i
$921$		0			0
$922$	23.3778	−	39.0998i	0.769905	−	1.28768i
$923$	−0.0721827	−	0.0721827i	−0.00237592	−	0.00237592i
$924$		0			0
$925$	3.16712	+	11.1160i	0.104134	+	0.365490i
$926$	−33.7109	+	8.48314i	−1.10781	+	0.278773i
$927$		0			0
$928$	3.51932	+	7.33743i	0.115527	+	0.240863i
$929$	−6.46931			−0.212251			−0.106126	−	0.994353i	$-0.533845\pi$
$929$	−6.46931			−0.212251			−0.106126	+	0.994353i	$0.533845\pi$
$930$		0			0
$931$	−13.2951	−	13.2951i	−0.435728	−	0.435728i
$932$	−2.86716	+	1.54056i	−0.0939168	+	0.0504626i
$933$		0			0
$934$	−26.9223	−	16.0968i	−0.880925	−	0.526704i
$935$	−27.7482	−	47.1983i	−0.907463	−	1.54355i
$936$		0			0
$937$	20.4235			0.667208			0.333604	−	0.942713i	$-0.391735\pi$
$937$	20.4235			0.667208			0.333604	+	0.942713i	$0.391735\pi$
$938$	−14.5463	−	8.69724i	−0.474955	−	0.283975i
$939$		0			0
$940$	9.64209	+	39.5497i	0.314490	+	1.28997i
$941$	28.2871	+	28.2871i	0.922134	+	0.922134i	0.997180	−	0.0750464i	$-0.0239105\pi$
$941$	28.2871	+	28.2871i	0.922134	+	0.922134i	−0.0750464	+	0.997180i	$0.523910\pi$
$942$		0			0
$943$		−	26.8680i		−	0.874943i
$944$	−5.98648	−	29.4262i	−0.194843	−	0.957742i
$945$		0			0
$946$	13.4913	+	53.6129i	0.438641	+	1.74311i
$947$	8.81881	−	8.81881i	0.286573	−	0.286573i	−0.549151	−	0.835723i	$-0.685049\pi$
$947$	8.81881	−	8.81881i	0.286573	−	0.286573i	0.835723	+	0.549151i	$0.185049\pi$
$948$		0			0
$949$	−0.697849	+	0.697849i	−0.0226531	+	0.0226531i
$950$	8.59286	−	4.96668i	0.278789	−	0.161140i
$951$		0			0
$952$	47.4947	−	43.3298i	1.53931	−	1.40433i
$953$	43.7042			1.41572			0.707858	−	0.706354i	$-0.249661\pi$
$953$	43.7042			1.41572			0.707858	+	0.706354i	$0.249661\pi$
$954$		0			0
$955$	45.0719	+	11.6970i	1.45849	+	0.378508i
$956$	−22.3586	+	12.0135i	−0.723127	+	0.388545i
$957$		0			0
$958$	3.26462	+	12.9732i	0.105475	+	0.419145i
$959$	−2.02703			−0.0654564
$960$		0			0
$961$	10.3059			0.332449
$962$	−0.128190	−	0.509411i	−0.00413301	−	0.0164241i
$963$		0			0
$964$	−37.1795	+	19.9770i	−1.19747	+	0.643416i
$965$	−3.27206	+	12.6081i	−0.105331	+	0.405870i
$966$		0			0
$967$	−24.4130			−0.785068			−0.392534	−	0.919738i	$-0.628401\pi$
$967$	−24.4130			−0.785068			−0.392534	+	0.919738i	$0.628401\pi$
$968$	−26.4684	+	24.1473i	−0.850725	+	0.776125i
$969$		0			0
$970$	−48.3085	−	0.357162i	−1.55109	−	0.0114678i
$971$	3.61271	−	3.61271i	0.115937	−	0.115937i	−0.646758	−	0.762695i	$-0.723876\pi$
$971$	3.61271	−	3.61271i	0.115937	−	0.115937i	0.762695	+	0.646758i	$0.223876\pi$
$972$		0			0
$973$	−23.1529	+	23.1529i	−0.742247	+	0.742247i
$974$	3.43723	+	13.6591i	0.110136	+	0.437666i
$975$		0			0
$976$	−32.5662	+	6.62527i	−1.04242	+	0.212070i
$977$		−	52.1693i		−	1.66904i	−0.550975	−	0.834522i	$-0.685744\pi$
$977$		−	52.1693i		−	1.66904i	0.550975	−	0.834522i	$-0.314256\pi$
$978$		0			0
$979$	−1.99367	−	1.99367i	−0.0637179	−	0.0637179i
$980$	58.2021	−	14.1895i	1.85920	−	0.453266i
$981$		0			0
$982$	−7.47026	−	4.46646i	−0.238386	−	0.142531i
$983$	43.2396			1.37913			0.689564	−	0.724225i	$-0.257802\pi$
$983$	43.2396			1.37913			0.689564	+	0.724225i	$0.257802\pi$
$984$		0			0
$985$	−17.7345	−	30.1656i	−0.565069	−	0.961155i
$986$	−8.78841	−	5.25458i	−0.279880	−	0.167340i
$987$		0			0
$988$	−0.397337	+	0.213494i	−0.0126410	+	0.00679214i
$989$	45.4851	+	45.4851i	1.44634	+	1.44634i
$990$		0			0
$991$	−48.9048			−1.55351			−0.776756	−	0.629802i	$-0.783136\pi$
$991$	−48.9048			−1.55351			−0.776756	+	0.629802i	$0.783136\pi$
$992$	−34.2973	−	12.0617i	−1.08894	−	0.382960i
$993$		0			0
$994$	−3.93493	+	0.990200i	−0.124808	+	0.0314072i
$995$	−3.95751	+	15.2494i	−0.125462	+	0.483438i
$996$		0			0
$997$	41.0281	+	41.0281i	1.29937	+	1.29937i	0.928806	+	0.370565i	$0.120836\pi$
$997$	41.0281	+	41.0281i	1.29937	+	1.29937i	0.370565	+	0.928806i	$0.379164\pi$
$998$	−3.17606	+	5.31203i	−0.100536	+	0.168149i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bm.h.109.13		48
3.2	odd	2		240.2.bl.a.109.12	✓	48
5.4	even	2	inner	720.2.bm.h.109.12		48
12.11	even	2		960.2.bl.a.529.12		48
15.14	odd	2		240.2.bl.a.109.13	yes	48
16.5	even	4	inner	720.2.bm.h.469.12		48
24.5	odd	2		1920.2.bl.a.289.12		48
24.11	even	2		1920.2.bl.b.289.13		48
48.5	odd	4		240.2.bl.a.229.13	yes	48
48.11	even	4		960.2.bl.a.49.18		48
48.29	odd	4		1920.2.bl.a.1249.13		48
48.35	even	4		1920.2.bl.b.1249.12		48
60.59	even	2		960.2.bl.a.529.18		48
80.69	even	4	inner	720.2.bm.h.469.13		48
120.29	odd	2		1920.2.bl.a.289.13		48
120.59	even	2		1920.2.bl.b.289.12		48
240.29	odd	4		1920.2.bl.a.1249.12		48
240.59	even	4		960.2.bl.a.49.12		48
240.149	odd	4		240.2.bl.a.229.12	yes	48
240.179	even	4		1920.2.bl.b.1249.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.12	✓	48	3.2	odd	2
240.2.bl.a.109.13	yes	48	15.14	odd	2
240.2.bl.a.229.12	yes	48	240.149	odd	4
240.2.bl.a.229.13	yes	48	48.5	odd	4
720.2.bm.h.109.12		48	5.4	even	2	inner
720.2.bm.h.109.13		48	1.1	even	1	trivial
720.2.bm.h.469.12		48	16.5	even	4	inner
720.2.bm.h.469.13		48	80.69	even	4	inner
960.2.bl.a.49.12		48	240.59	even	4
960.2.bl.a.49.18		48	48.11	even	4
960.2.bl.a.529.12		48	12.11	even	2
960.2.bl.a.529.18		48	60.59	even	2
1920.2.bl.a.289.12		48	24.5	odd	2
1920.2.bl.a.289.13		48	120.29	odd	2
1920.2.bl.a.1249.12		48	240.29	odd	4
1920.2.bl.a.1249.13		48	48.29	odd	4
1920.2.bl.b.289.12		48	120.59	even	2
1920.2.bl.b.289.13		48	24.11	even	2
1920.2.bl.b.1249.12		48	48.35	even	4
1920.2.bl.b.1249.13		48	240.179	even	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)

\(f(q)\)	\(=\)	\(q+(0.345118 + 1.37146i) q^{2} +(-1.76179 + 0.946629i) q^{4} +(-2.16437 - 0.561697i) q^{5} +4.51614 q^{7} +(-1.90629 - 2.08952i) q^{8} +(0.0233792 - 3.16219i) q^{10} +(3.44000 - 3.44000i) q^{11} +(-0.113618 + 0.113618i) q^{13} +(1.55860 + 6.19370i) q^{14} +(2.20779 - 3.33552i) q^{16} +5.03305i q^{17} +(-0.992498 - 0.992498i) q^{19} +(4.34488 - 1.05927i) q^{20} +(5.90502 + 3.53061i) q^{22} +8.00517 q^{23} +(4.36899 + 2.43144i) q^{25} +(-0.195033 - 0.116610i) q^{26} +(-7.95648 + 4.27512i) q^{28} +(1.01722 + 1.01722i) q^{29} -6.42697 q^{31} +(5.33647 + 1.87673i) q^{32} +(-6.90261 + 1.73700i) q^{34} +(-9.77461 - 2.53670i) q^{35} +(1.63459 + 1.63459i) q^{37} +(1.01864 - 1.70370i) q^{38} +(2.95223 + 5.59324i) q^{40} -3.35633i q^{41} +(5.68196 + 5.68196i) q^{43} +(-2.80414 + 9.31696i) q^{44} +(2.76273 + 10.9787i) q^{46} +9.10261i q^{47} +13.3956 q^{49} +(-1.82679 + 6.83102i) q^{50} +(0.0926163 - 0.307724i) q^{52} +(-3.27113 - 3.27113i) q^{53} +(-9.37767 + 5.51320i) q^{55} +(-8.60906 - 9.43655i) q^{56} +(-1.04401 + 1.74614i) q^{58} +(5.30843 - 5.30843i) q^{59} +(-5.87487 - 5.87487i) q^{61} +(-2.21806 - 8.81431i) q^{62} +(-0.732149 + 7.96643i) q^{64} +(0.309729 - 0.182092i) q^{65} +(-1.87639 + 1.87639i) q^{67} +(-4.76443 - 8.86716i) q^{68} +(0.105584 - 14.2809i) q^{70} +0.635312i q^{71} +6.14208 q^{73} +(-1.67765 + 2.80590i) q^{74} +(2.68810 + 0.809042i) q^{76} +(15.5355 - 15.5355i) q^{77} +1.76500 q^{79} +(-6.65201 + 5.97919i) q^{80} +(4.60307 - 1.15833i) q^{82} +(6.39170 - 6.39170i) q^{83} +(2.82705 - 10.8934i) q^{85} +(-5.83162 + 9.75352i) q^{86} +(-13.7456 - 0.630310i) q^{88} -0.579554i q^{89} +(-0.513114 + 0.513114i) q^{91} +(-14.1034 + 7.57793i) q^{92} +(-12.4838 + 3.14148i) q^{94} +(1.59065 + 2.70562i) q^{95} -15.2769i q^{97} +(4.62305 + 18.3714i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{10} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 48 q^{31} - 28 q^{34} - 24 q^{35} - 16 q^{40} + 40 q^{44} - 4 q^{46} + 48 q^{49} + 32 q^{50} - 48 q^{56} + 32 q^{59} + 16 q^{61} + 48 q^{64}+ \cdots + 48 q^{95}+O(q^{100}) \) 48 * q + 12 * q^10 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 48 * q^31 - 28 * q^34 - 24 * q^35 - 16 * q^40 + 40 * q^44 - 4 * q^46 + 48 * q^49 + 32 * q^50 - 48 * q^56 + 32 * q^59 + 16 * q^61 + 48 * q^64 - 16 * q^65 - 40 * q^74 + 60 * q^76 - 96 * q^79 - 72 * q^80 - 16 * q^86 - 32 * q^91 + 44 * q^94 + 48 * q^95

Introduction

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