LMFDB - Embedded newform 720.2.bm.h.109.9

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			109.9
Character	$\chi$	$=$	720.109
Dual form			720.2.bm.h.469.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.550383 + 1.30272i) q^{2} +(-1.39416 - 1.43399i) q^{4} +(2.23019 + 0.162008i) q^{5} -2.93661 q^{7} +(2.63541 - 1.02695i) q^{8} +O(q^{10})$	\(q+(-0.550383 + 1.30272i) q^{2} +(-1.39416 - 1.43399i) q^{4} +(2.23019 + 0.162008i) q^{5} -2.93661 q^{7} +(2.63541 - 1.02695i) q^{8} +(-1.43851 + 2.81615i) q^{10} +(0.663996 - 0.663996i) q^{11} +(-1.12767 + 1.12767i) q^{13} +(1.61626 - 3.82558i) q^{14} +(-0.112647 + 3.99841i) q^{16} +7.47528i q^{17} +(0.423555 + 0.423555i) q^{19} +(-2.87692 - 3.42393i) q^{20} +(0.499549 + 1.23045i) q^{22} +6.17642 q^{23} +(4.94751 + 0.722620i) q^{25} +(-0.848386 - 2.08968i) q^{26} +(4.09410 + 4.21107i) q^{28} +(2.95128 + 2.95128i) q^{29} +1.82581 q^{31} +(-5.14681 - 2.34740i) q^{32} +(-9.73820 - 4.11426i) q^{34} +(-6.54921 - 0.475756i) q^{35} +(5.53509 + 5.53509i) q^{37} +(-0.784891 + 0.318656i) q^{38} +(6.04383 - 1.86335i) q^{40} +12.3694i q^{41} +(-0.897614 - 0.897614i) q^{43} +(-1.87788 - 0.0264474i) q^{44} +(-3.39939 + 8.04614i) q^{46} -4.12733i q^{47} +1.62370 q^{49} +(-3.66439 + 6.04750i) q^{50} +(3.18921 + 0.0449157i) q^{52} +(0.146479 + 0.146479i) q^{53} +(1.58841 - 1.37327i) q^{55} +(-7.73917 + 3.01577i) q^{56} +(-5.46902 + 2.22036i) q^{58} +(7.72645 - 7.72645i) q^{59} +(-7.37519 - 7.37519i) q^{61} +(-1.00489 + 2.37851i) q^{62} +(5.89073 - 5.41289i) q^{64} +(-2.69760 + 2.33222i) q^{65} +(-8.68265 + 8.68265i) q^{67} +(10.7195 - 10.4217i) q^{68} +(4.22435 - 8.26994i) q^{70} +8.95735i q^{71} -0.174246 q^{73} +(-10.2571 + 4.16425i) q^{74} +(0.0168705 - 1.19788i) q^{76} +(-1.94990 + 1.94990i) q^{77} +3.06488 q^{79} +(-0.899001 + 8.89898i) q^{80} +(-16.1139 - 6.80790i) q^{82} +(-9.18751 + 9.18751i) q^{83} +(-1.21106 + 16.6713i) q^{85} +(1.66337 - 0.675308i) q^{86} +(1.06801 - 2.43179i) q^{88} -8.71473i q^{89} +(3.31152 - 3.31152i) q^{91} +(-8.61090 - 8.85691i) q^{92} +(5.37676 + 2.27161i) q^{94} +(0.875989 + 1.01323i) q^{95} -10.5481i q^{97} +(-0.893654 + 2.11522i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * 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} - 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	−0.550383	+	1.30272i	−0.389179	+	0.921162i
$2$	−0.550383	+	1.30272i	−0.389179	+	0.921162i
$3$		0			0
$3$		0			0
$4$	−1.39416	−	1.43399i	−0.697079	−	0.716994i
$5$	2.23019	+	0.162008i	0.997372	+	0.0724524i
$5$	2.23019	+	0.162008i	0.997372	+	0.0724524i
$6$		0			0
$7$	−2.93661			−1.10994			−0.554968	−	0.831872i	$-0.687269\pi$
$7$	−2.93661			−1.10994			−0.554968	+	0.831872i	$0.687269\pi$
$8$	2.63541	−	1.02695i	0.931757	−	0.363083i
$9$		0			0
$10$	−1.43851	+	2.81615i	−0.454897	+	0.890544i
$11$	0.663996	−	0.663996i	0.200202	−	0.200202i	−0.599884	−	0.800087i	$-0.704787\pi$
$11$	0.663996	−	0.663996i	0.200202	−	0.200202i	0.800087	+	0.599884i	$0.204787\pi$
$12$		0			0
$13$	−1.12767	+	1.12767i	−0.312758	+	0.312758i	−0.845977	−	0.533219i	$-0.820982\pi$
$13$	−1.12767	+	1.12767i	−0.312758	+	0.312758i	0.533219	+	0.845977i	$0.320982\pi$
$14$	1.61626	−	3.82558i	0.431964	−	1.02243i
$15$		0			0
$16$	−0.112647	+	3.99841i	−0.0281618	+	0.999603i
$17$			7.47528i			1.81302i	0.422182	+	0.906511i	$0.361264\pi$
$17$			7.47528i			1.81302i	−0.422182	+	0.906511i	$0.638736\pi$
$18$		0			0
$19$	0.423555	+	0.423555i	0.0971702	+	0.0971702i	0.754021	−	0.656851i	$-0.228112\pi$
$19$	0.423555	+	0.423555i	0.0971702	+	0.0971702i	−0.656851	+	0.754021i	$0.728112\pi$
$20$	−2.87692	−	3.42393i	−0.643299	−	0.765615i
$21$		0			0
$22$	0.499549	+	1.23045i	0.106504	+	0.262333i
$23$	6.17642			1.28787			0.643936	−	0.765079i	$-0.277300\pi$
$23$	6.17642			1.28787			0.643936	+	0.765079i	$0.277300\pi$
$24$		0			0
$25$	4.94751	+	0.722620i	0.989501	+	0.144524i
$26$	−0.848386	−	2.08968i	−0.166382	−	0.409820i
$27$		0			0
$28$	4.09410	+	4.21107i	0.773713	+	0.795817i
$29$	2.95128	+	2.95128i	0.548038	+	0.548038i	0.925873	−	0.377835i	$-0.123331\pi$
$29$	2.95128	+	2.95128i	0.548038	+	0.548038i	−0.377835	+	0.925873i	$0.623331\pi$
$30$		0			0
$31$	1.82581			0.327924			0.163962	−	0.986467i	$-0.447572\pi$
$31$	1.82581			0.327924			0.163962	+	0.986467i	$0.447572\pi$
$32$	−5.14681	−	2.34740i	−0.909837	−	0.414966i
$33$		0			0
$34$	−9.73820	−	4.11426i	−1.67009	−	0.705591i
$35$	−6.54921	−	0.475756i	−1.10702	−	0.0804175i
$36$		0			0
$37$	5.53509	+	5.53509i	0.909963	+	0.909963i	0.996269	−	0.0863055i	$-0.0275061\pi$
$37$	5.53509	+	5.53509i	0.909963	+	0.909963i	−0.0863055	+	0.996269i	$0.527506\pi$
$38$	−0.784891	+	0.318656i	−0.127326	+	0.0516929i
$39$		0			0
$40$	6.04383	−	1.86335i	0.955614	−	0.294621i
$41$			12.3694i			1.93178i	0.258959	+	0.965888i	$0.416620\pi$
$41$			12.3694i			1.93178i	−0.258959	+	0.965888i	$0.583380\pi$
$42$		0			0
$43$	−0.897614	−	0.897614i	−0.136885	−	0.136885i	0.635344	−	0.772229i	$-0.280858\pi$
$43$	−0.897614	−	0.897614i	−0.136885	−	0.136885i	−0.772229	+	0.635344i	$0.780858\pi$
$44$	−1.87788	−	0.0264474i	−0.283101	−	0.00398710i
$45$		0			0
$46$	−3.39939	+	8.04614i	−0.501213	+	1.18634i
$47$		−	4.12733i		−	0.602033i	−0.953619	−	0.301017i	$-0.902674\pi$
$47$		−	4.12733i		−	0.602033i	0.953619	−	0.301017i	$-0.0973260\pi$
$48$		0			0
$49$	1.62370			0.231956
$50$	−3.66439	+	6.04750i	−0.518223	+	0.855245i
$51$		0			0
$52$	3.18921	+	0.0449157i	0.442263	+	0.00622869i
$53$	0.146479	+	0.146479i	0.0201204	+	0.0201204i	0.717095	−	0.696975i	$-0.245471\pi$
$53$	0.146479	+	0.146479i	0.0201204	+	0.0201204i	−0.696975	+	0.717095i	$0.745471\pi$
$54$		0			0
$55$	1.58841	−	1.37327i	0.214181	−	0.185171i
$56$	−7.73917	+	3.01577i	−1.03419	+	0.402999i
$57$		0			0
$58$	−5.46902	+	2.22036i	−0.718117	+	0.291547i
$59$	7.72645	−	7.72645i	1.00590	−	1.00590i	0.00591515	−	0.999983i	$-0.498117\pi$
$59$	7.72645	−	7.72645i	1.00590	−	1.00590i	0.999983	−	0.00591515i	$-0.00188286\pi$
$60$		0			0
$61$	−7.37519	−	7.37519i	−0.944297	−	0.944297i	0.0542318	−	0.998528i	$-0.482729\pi$
$61$	−7.37519	−	7.37519i	−0.944297	−	0.944297i	−0.998528	+	0.0542318i	$0.982729\pi$
$62$	−1.00489	+	2.37851i	−0.127621	+	0.302071i
$63$		0			0
$64$	5.89073	−	5.41289i	0.736341	−	0.676611i
$65$	−2.69760	+	2.33222i	−0.334597	+	0.289276i
$66$		0			0
$67$	−8.68265	+	8.68265i	−1.06075	+	1.06075i	−0.0627239	+	0.998031i	$0.519979\pi$
$67$	−8.68265	+	8.68265i	−1.06075	+	1.06075i	−0.998031	+	0.0627239i	$0.980021\pi$
$68$	10.7195	−	10.4217i	1.29993	−	1.26382i
$69$		0			0
$70$	4.22435	−	8.26994i	0.504906	−	0.988446i
$71$			8.95735i			1.06304i	0.847045	+	0.531521i	$0.178379\pi$
$71$			8.95735i			1.06304i	−0.847045	+	0.531521i	$0.821621\pi$
$72$		0			0
$73$	−0.174246			−0.0203940			−0.0101970	−	0.999948i	$-0.503246\pi$
$73$	−0.174246			−0.0203940			−0.0101970	+	0.999948i	$0.503246\pi$
$74$	−10.2571	+	4.16425i	−1.19236	+	0.484085i
$75$		0			0
$76$	0.0168705	−	1.19788i	0.00193518	−	0.137406i
$77$	−1.94990	+	1.94990i	−0.222212	+	0.222212i
$78$		0			0
$79$	3.06488			0.344826			0.172413	−	0.985025i	$-0.444844\pi$
$79$	3.06488			0.344826			0.172413	+	0.985025i	$0.444844\pi$
$80$	−0.899001	+	8.89898i	−0.100511	+	0.994936i
$81$		0			0
$82$	−16.1139	−	6.80790i	−1.77948	−	0.751807i
$83$	−9.18751	+	9.18751i	−1.00846	+	1.00846i	−0.00849620	+	0.999964i	$0.502704\pi$
$83$	−9.18751	+	9.18751i	−1.00846	+	1.00846i	−0.999964	+	0.00849620i	$0.997296\pi$
$84$		0			0
$85$	−1.21106	+	16.6713i	−0.131358	+	1.80826i
$86$	1.66337	−	0.675308i	0.179366	−	0.0728204i
$87$		0			0
$88$	1.06801	−	2.43179i	0.113850	−	0.259230i
$89$		−	8.71473i		−	0.923760i	−0.886942	−	0.461880i	$-0.847175\pi$
$89$		−	8.71473i		−	0.923760i	0.886942	−	0.461880i	$-0.152825\pi$
$90$		0			0
$91$	3.31152	−	3.31152i	0.347142	−	0.347142i
$92$	−8.61090	−	8.85691i	−0.897749	−	0.923397i
$93$		0			0
$94$	5.37676	+	2.27161i	0.554570	+	0.234299i
$95$	0.875989	+	1.01323i	0.0898746	+	0.103955i
$96$		0			0
$97$		−	10.5481i		−	1.07100i	−0.844535	−	0.535500i	$-0.820123\pi$
$97$		−	10.5481i		−	1.07100i	0.844535	−	0.535500i	$-0.179877\pi$
$98$	−0.893654	+	2.11522i	−0.0902727	+	0.213669i
$99$		0			0
$100$	−5.86138	−	8.10211i	−0.586138	−	0.810211i
$101$	9.65550	−	9.65550i	0.960758	−	0.960758i	−0.0385005	−	0.999259i	$-0.512258\pi$
$101$	9.65550	−	9.65550i	0.960758	−	0.960758i	0.999259	+	0.0385005i	$0.0122581\pi$
$102$		0			0
$103$	−14.5564			−1.43428			−0.717141	−	0.696928i	$-0.754550\pi$
$103$	−14.5564			−1.43428			−0.717141	+	0.696928i	$0.754550\pi$
$104$	−1.81380	+	4.12992i	−0.177857	+	0.404972i
$105$		0			0
$106$	−0.271440	+	0.110201i	−0.0263646	+	0.0107037i
$107$	−5.86260	−	5.86260i	−0.566759	−	0.566759i	0.364460	−	0.931219i	$-0.381253\pi$
$107$	−5.86260	−	5.86260i	−0.566759	−	0.566759i	−0.931219	+	0.364460i	$0.881253\pi$
$108$		0			0
$109$	4.91625	+	4.91625i	0.470891	+	0.470891i	0.902203	−	0.431312i	$-0.141949\pi$
$109$	4.91625	+	4.91625i	0.470891	+	0.470891i	−0.431312	+	0.902203i	$0.641949\pi$
$110$	0.914746	+	2.82508i	0.0872176	+	0.269360i
$111$		0			0
$112$	0.330801	−	11.7418i	0.0312577	−	1.10950i
$113$		−	12.8334i		−	1.20726i	−0.797263	−	0.603632i	$-0.793720\pi$
$113$		−	12.8334i		−	1.20726i	0.797263	−	0.603632i	$-0.206280\pi$
$114$		0			0
$115$	13.7746	+	1.00063i	1.28449	+	0.0933094i
$116$	0.117551	−	8.34664i	0.0109144	−	0.774966i
$117$		0			0
$118$	5.81289	+	14.3179i	0.535120	+	1.31807i
$119$		−	21.9520i		−	2.01234i
$120$		0			0
$121$			10.1182i			0.919838i
$122$	13.6670	−	5.54863i	1.23735	−	0.502349i
$123$		0			0
$124$	−2.54546	−	2.61818i	−0.228589	−	0.235120i
$125$	10.9168	+	2.41312i	0.976430	+	0.215836i
$126$		0			0
$127$		−	1.07042i		−	0.0949847i	−0.998872	−	0.0474924i	$-0.984877\pi$
$127$		−	1.07042i		−	0.0949847i	0.998872	−	0.0474924i	$-0.0151230\pi$
$128$	3.80932	+	10.6531i	0.336699	+	0.941612i
$129$		0			0
$130$	−1.55352	−	4.79784i	−0.136252	−	0.420798i
$131$	10.9024	+	10.9024i	0.952545	+	0.952545i	0.998924	−	0.0463789i	$-0.0147682\pi$
$131$	10.9024	+	10.9024i	0.952545	+	0.952545i	−0.0463789	+	0.998924i	$0.514768\pi$
$132$		0			0
$133$	−1.24382	−	1.24382i	−0.107853	−	0.107853i
$134$	−6.53228	−	16.0898i	−0.564303	−	1.38995i
$135$		0			0
$136$	7.67678	+	19.7004i	0.658278	+	1.68930i
$137$	−10.0549			−0.859046			−0.429523	−	0.903056i	$-0.641318\pi$
$137$	−10.0549			−0.859046			−0.429523	+	0.903056i	$0.641318\pi$
$138$		0			0
$139$	2.90773	−	2.90773i	0.246630	−	0.246630i	−0.572956	−	0.819586i	$-0.694203\pi$
$139$	2.90773	−	2.90773i	0.246630	−	0.246630i	0.819586	+	0.572956i	$0.194203\pi$
$140$	8.44840	+	10.0548i	0.714020	+	0.849783i
$141$		0			0
$142$	−11.6689	−	4.92997i	−0.979234	−	0.413714i
$143$			1.49753i			0.125230i
$144$		0			0
$145$	6.10378	+	7.06004i	0.506891	+	0.586305i
$146$	0.0959021	−	0.226994i	0.00793691	−	0.0187862i
$147$		0			0
$148$	0.220467	−	15.6540i	0.0181222	−	1.28675i
$149$	1.26131	−	1.26131i	0.103331	−	0.103331i	−0.653551	−	0.756882i	$-0.726722\pi$
$149$	1.26131	−	1.26131i	0.103331	−	0.103331i	0.756882	+	0.653551i	$0.226722\pi$
$150$		0			0
$151$		−	20.4739i		−	1.66614i	−0.553169	−	0.833069i	$-0.686582\pi$
$151$		−	20.4739i		−	1.66614i	0.553169	−	0.833069i	$-0.313418\pi$
$152$	1.55121	+	0.681268i	0.125820	+	0.0552581i
$153$		0			0
$154$	−1.46698	−	3.61336i	−0.118213	−	0.291173i
$155$	4.07190	+	0.295796i	0.327063	+	0.0237589i
$156$		0			0
$157$	8.13344	−	8.13344i	0.649119	−	0.649119i	−0.303661	−	0.952780i	$-0.598209\pi$
$157$	8.13344	−	8.13344i	0.649119	−	0.649119i	0.952780	+	0.303661i	$0.0982091\pi$
$158$	−1.68686	+	3.99269i	−0.134199	+	0.317641i
$159$		0			0
$160$	−11.0981	−	6.06899i	−0.877380	−	0.479796i
$161$	−18.1377			−1.42945
$162$		0			0
$163$	4.08947	−	4.08947i	0.320312	−	0.320312i	−0.528575	−	0.848887i	$-0.677273\pi$
$163$	4.08947	−	4.08947i	0.320312	−	0.320312i	0.848887	+	0.528575i	$0.177273\pi$
$164$	17.7376	−	17.2449i	1.38507	−	1.34660i
$165$		0			0
$166$	−6.91211	−	17.0254i	−0.536483	−	1.32143i
$167$	9.52867			0.737350			0.368675	−	0.929558i	$-0.379811\pi$
$167$	9.52867			0.737350			0.368675	+	0.929558i	$0.379811\pi$
$168$		0			0
$169$			10.4567i			0.804364i
$170$	−21.0515	−	10.7533i	−1.61458	−	0.824738i
$171$		0			0
$172$	−0.0357526	+	2.53858i	−0.00272611	+	0.193565i
$173$	6.18234	−	6.18234i	0.470035	−	0.470035i	−0.431891	−	0.901926i	$-0.642153\pi$
$173$	6.18234	−	6.18234i	0.470035	−	0.470035i	0.901926	+	0.431891i	$0.142153\pi$
$174$		0			0
$175$	−14.5289	−	2.12205i	−1.09828	−	0.160412i
$176$	2.58013	+	2.72973i	0.194485	+	0.205761i
$177$		0			0
$178$	11.3529	+	4.79644i	0.850933	+	0.359508i
$179$	10.3548	+	10.3548i	0.773954	+	0.773954i	0.978795	−	0.204841i	$-0.0656678\pi$
$179$	10.3548	+	10.3548i	0.773954	+	0.773954i	−0.204841	+	0.978795i	$0.565668\pi$
$180$		0			0
$181$	5.98013	−	5.98013i	0.444500	−	0.444500i	−0.449021	−	0.893521i	$-0.648227\pi$
$181$	5.98013	−	5.98013i	0.444500	−	0.444500i	0.893521	+	0.449021i	$0.148227\pi$
$182$	2.49138	+	6.13659i	0.184673	+	0.454874i
$183$		0			0
$184$	16.2774	−	6.34290i	1.19998	−	0.467605i
$185$	11.4476	+	13.2410i	0.841643	+	0.973501i
$186$		0			0
$187$	4.96356	+	4.96356i	0.362971	+	0.362971i
$188$	−5.91855	+	5.75415i	−0.431655	+	0.419665i
$189$		0			0
$190$	−1.80208	+	0.583505i	−0.130737	+	0.0423319i
$191$	0.404932			0.0292998			0.0146499	−	0.999893i	$-0.495337\pi$
$191$	0.404932			0.0292998			0.0146499	+	0.999893i	$0.495337\pi$
$192$		0			0
$193$		−	6.48969i		−	0.467138i	−0.972340	−	0.233569i	$-0.924959\pi$
$193$		−	6.48969i		−	0.467138i	0.972340	−	0.233569i	$-0.0750405\pi$
$194$	13.7412	+	5.80550i	0.986564	+	0.416811i
$195$		0			0
$196$	−2.26369	−	2.32836i	−0.161692	−	0.166311i
$197$	18.4425	+	18.4425i	1.31397	+	1.31397i	0.918460	+	0.395514i	$0.129434\pi$
$197$	18.4425	+	18.4425i	1.31397	+	1.31397i	0.395514	+	0.918460i	$0.370566\pi$
$198$		0			0
$199$		−	13.4696i		−	0.954833i	−0.878677	−	0.477417i	$-0.841573\pi$
$199$		−	13.4696i		−	0.954833i	0.878677	−	0.477417i	$-0.158427\pi$
$200$	13.7808	−	3.17647i	0.974449	−	0.224610i
$201$		0			0
$202$	7.26419	+	17.8926i	0.511107	+	1.25892i
$203$	−8.66676	−	8.66676i	−0.608287	−	0.608287i
$204$		0			0
$205$	−2.00395	+	27.5861i	−0.139962	+	1.92670i
$206$	8.01157	−	18.9629i	0.558193	−	1.32121i
$207$		0			0
$208$	−4.38185	−	4.63591i	−0.303827	−	0.321442i
$209$	0.562478			0.0389074
$210$		0			0
$211$	6.07749	+	6.07749i	0.418392	+	0.418392i	0.884649	−	0.466257i	$-0.154398\pi$
$211$	6.07749	+	6.07749i	0.418392	+	0.418392i	−0.466257	+	0.884649i	$0.654398\pi$
$212$	0.00583434	−	0.414263i	0.000400704	−	0.0284517i
$213$		0			0
$214$	10.8640	−	4.41065i	0.742647	−	0.301506i
$215$	−1.85643	−	2.14727i	−0.126607	−	0.146443i
$216$		0			0
$217$	−5.36168			−0.363975
$218$	−9.11032	+	3.69868i	−0.617028	+	0.250506i
$219$		0			0
$220$	−4.18374	−	0.363215i	−0.282068	−	0.0244879i
$221$	−8.42963	−	8.42963i	−0.567038	−	0.567038i
$222$		0			0
$223$		−	22.0794i		−	1.47855i	−0.673405	−	0.739273i	$-0.735169\pi$
$223$		−	22.0794i		−	1.47855i	0.673405	−	0.739273i	$-0.264831\pi$
$224$	15.1142	+	6.89342i	1.00986	+	0.460586i
$225$		0			0
$226$	16.7183	+	7.06328i	1.11209	+	0.469842i
$227$	−5.55919	+	5.55919i	−0.368977	+	0.368977i	−0.867104	−	0.498127i	$-0.834021\pi$
$227$	−5.55919	+	5.55919i	−0.368977	+	0.368977i	0.498127	+	0.867104i	$0.334021\pi$
$228$		0			0
$229$	11.8223	−	11.8223i	0.781242	−	0.781242i	−0.198798	−	0.980040i	$-0.563704\pi$
$229$	11.8223	−	11.8223i	0.781242	−	0.781242i	0.980040	+	0.198798i	$0.0637038\pi$
$230$	−8.88484	+	17.3937i	−0.585849	+	1.14691i
$231$		0			0
$232$	10.8086	+	4.74698i	0.709622	+	0.311655i
$233$	−8.92024			−0.584385			−0.292192	−	0.956360i	$-0.594385\pi$
$233$	−8.92024			−0.584385			−0.292192	+	0.956360i	$0.594385\pi$
$234$		0			0
$235$	0.668663	−	9.20474i	0.0436188	−	0.600451i
$236$	−21.8515	−	0.307750i	−1.42241	−	0.0200328i
$237$		0			0
$238$	28.5973	+	12.0820i	1.85369	+	0.783160i
$239$	−22.9320			−1.48335			−0.741673	−	0.670762i	$-0.765967\pi$
$239$	−22.9320			−1.48335			−0.741673	+	0.670762i	$0.765967\pi$
$240$		0			0
$241$	−6.48232			−0.417563			−0.208781	−	0.977962i	$-0.566950\pi$
$241$	−6.48232			−0.417563			−0.208781	+	0.977962i	$0.566950\pi$
$242$	−13.1812	−	5.56889i	−0.847320	−	0.357982i
$243$		0			0
$244$	−0.293759	+	20.8581i	−0.0188060	+	1.33530i
$245$	3.62115	+	0.263052i	0.231347	+	0.0168058i
$246$		0			0
$247$	−0.955258			−0.0607816
$248$	4.81174	−	1.87502i	0.305546	−	0.119064i
$249$		0			0
$250$	−9.15204	+	12.8934i	−0.578826	+	0.815451i
$251$	−14.4218	+	14.4218i	−0.910293	+	0.910293i	−0.996295	−	0.0860018i	$-0.972591\pi$
$251$	−14.4218	+	14.4218i	−0.910293	+	0.910293i	0.0860018	+	0.996295i	$0.472591\pi$
$252$		0			0
$253$	4.10112	−	4.10112i	0.257835	−	0.257835i
$254$	1.39446	+	0.589143i	0.0874963	+	0.0369661i
$255$		0			0
$256$	−15.9746	−	0.900819i	−0.998414	−	0.0563012i
$257$		−	0.193739i		−	0.0120851i	−0.999982	−	0.00604256i	$-0.998077\pi$
$257$		−	0.193739i		−	0.0120851i	0.999982	−	0.00604256i	$-0.00192342\pi$
$258$		0			0
$259$	−16.2544	−	16.2544i	−1.01000	−	1.01000i
$260$	7.10526	+	0.616849i	0.440650	+	0.0382554i
$261$		0			0
$262$	−20.2032	+	8.20226i	−1.24816	+	0.506738i
$263$	−16.5708			−1.02180			−0.510900	−	0.859640i	$-0.670688\pi$
$263$	−16.5708			−1.02180			−0.510900	+	0.859640i	$0.670688\pi$
$264$		0			0
$265$	0.302944	+	0.350406i	0.0186097	+	0.0215253i
$266$	2.30492	−	0.935770i	0.141324	−	0.0573757i
$267$		0			0
$268$	24.5558	+	0.345836i	1.49999	+	0.0211253i
$269$	−7.09381	−	7.09381i	−0.432517	−	0.432517i	0.456967	−	0.889484i	$-0.348936\pi$
$269$	−7.09381	−	7.09381i	−0.432517	−	0.432517i	−0.889484	+	0.456967i	$0.848936\pi$
$270$		0			0
$271$	2.62278			0.159323			0.0796613	−	0.996822i	$-0.474616\pi$
$271$	2.62278			0.159323			0.0796613	+	0.996822i	$0.474616\pi$
$272$	−29.8893	−	0.842068i	−1.81230	−	0.0510579i
$273$		0			0
$274$	5.53403	−	13.0987i	0.334323	−	0.791320i
$275$	3.76494	−	2.80531i	0.227035	−	0.169166i
$276$		0			0
$277$	7.97533	+	7.97533i	0.479191	+	0.479191i	0.904873	−	0.425682i	$-0.139966\pi$
$277$	7.97533	+	7.97533i	0.479191	+	0.479191i	−0.425682	+	0.904873i	$0.639966\pi$
$278$	2.18759	+	5.38832i	0.131203	+	0.323170i
$279$		0			0
$280$	−17.7484	+	5.47193i	−1.06067	+	0.327010i
$281$		−	9.97850i		−	0.595267i	−0.954680	−	0.297634i	$-0.903803\pi$
$281$		−	9.97850i		−	0.595267i	0.954680	−	0.297634i	$-0.0961974\pi$
$282$		0			0
$283$	−20.4056	−	20.4056i	−1.21299	−	1.21299i	−0.970040	−	0.242946i	$-0.921886\pi$
$283$	−20.4056	−	20.4056i	−1.21299	−	1.21299i	−0.242946	−	0.970040i	$-0.578114\pi$
$284$	12.8447	−	12.4880i	0.762195	−	0.741024i
$285$		0			0
$286$	−1.95087	−	0.824216i	−0.115357	−	0.0487369i
$287$		−	36.3242i		−	2.14415i
$288$		0			0
$289$	−38.8798			−2.28705
$290$	−12.5567	+	4.06579i	−0.737353	+	0.238751i
$291$		0			0
$292$	0.242927	+	0.249867i	0.0142162	+	0.0146224i
$293$	4.65889	+	4.65889i	0.272175	+	0.272175i	0.829975	−	0.557800i	$-0.188354\pi$
$293$	4.65889	+	4.65889i	0.272175	+	0.272175i	−0.557800	+	0.829975i	$0.688354\pi$
$294$		0			0
$295$	18.4832	−	15.9797i	1.07613	−	0.930374i
$296$	20.2715	+	8.90292i	1.17826	+	0.517472i
$297$		0			0
$298$	0.948931	+	2.33734i	0.0549701	+	0.135398i
$299$	−6.96494	+	6.96494i	−0.402793	+	0.402793i
$300$		0			0
$301$	2.63594	+	2.63594i	0.151933	+	0.151933i
$302$	26.6717	+	11.2685i	1.53478	+	0.648427i
$303$		0			0
$304$	−1.74126	+	1.64584i	−0.0998681	+	0.0943952i
$305$	−15.2532	−	17.6429i	−0.873398	−	1.01023i
$306$		0			0
$307$	−9.05487	+	9.05487i	−0.516789	+	0.516789i	−0.916598	−	0.399810i	$-0.869076\pi$
$307$	−9.05487	+	9.05487i	−0.516789	+	0.516789i	0.399810	+	0.916598i	$0.369076\pi$
$308$	5.51460	+	0.0776659i	0.314224	+	0.00442542i
$309$		0			0
$310$	−2.62644	+	5.14174i	−0.149172	+	0.292031i
$311$			3.39349i			0.192427i	0.995361	+	0.0962137i	$0.0306732\pi$
$311$			3.39349i			0.192427i	−0.995361	+	0.0962137i	$0.969327\pi$
$312$		0			0
$313$	−10.8943			−0.615784			−0.307892	−	0.951421i	$-0.599624\pi$
$313$	−10.8943			−0.615784			−0.307892	+	0.951421i	$0.599624\pi$
$314$	6.11909	+	15.0721i	0.345320	+	0.850567i
$315$		0			0
$316$	−4.27293	−	4.39501i	−0.240371	−	0.247239i
$317$	3.45776	−	3.45776i	0.194207	−	0.194207i	−0.603304	−	0.797511i	$-0.706149\pi$
$317$	3.45776	−	3.45776i	0.194207	−	0.194207i	0.797511	+	0.603304i	$0.206149\pi$
$318$		0			0
$319$	3.91927			0.219437
$320$	14.0144	−	11.1174i	0.783428	−	0.621483i
$321$		0			0
$322$	9.98270	−	23.6284i	0.556314	−	1.31676i
$323$	−3.16619	+	3.16619i	−0.176172	+	0.176172i
$324$		0			0
$325$	−6.39401	+	4.76426i	−0.354676	+	0.264274i
$326$	3.07666	+	7.57820i	0.170400	+	0.419718i
$327$		0			0
$328$	12.7028	+	32.5984i	0.701396	+	1.79995i
$329$			12.1204i			0.668218i
$330$		0			0
$331$	−24.9246	+	24.9246i	−1.36998	+	1.36998i	−0.509526	+	0.860455i	$0.670179\pi$
$331$	−24.9246	+	24.9246i	−1.36998	+	1.36998i	−0.860455	+	0.509526i	$0.829821\pi$
$332$	25.9836	+	0.365945i	1.42604	+	0.0200838i
$333$		0			0
$334$	−5.24441	+	12.4132i	−0.286961	+	0.679219i
$335$	−20.7706	+	17.9573i	−1.13482	+	0.981113i
$336$		0			0
$337$			9.62502i			0.524308i	0.965026	+	0.262154i	$0.0844329\pi$
$337$			9.62502i			0.524308i	−0.965026	+	0.262154i	$0.915567\pi$
$338$	−13.6222	−	5.75521i	−0.740950	−	0.313042i
$339$		0			0
$340$	25.5949	−	21.5058i	1.38808	−	1.16632i
$341$	1.21233	−	1.21233i	0.0656512	−	0.0656512i
$342$		0			0
$343$	15.7881			0.852479
$344$	−3.28739	−	1.44377i	−0.177244	−	0.0778428i
$345$		0			0
$346$	4.65121	+	11.4565i	0.250050	+	0.615906i
$347$	15.9302	+	15.9302i	0.855178	+	0.855178i	0.990765	−	0.135588i	$-0.0432923\pi$
$347$	15.9302	+	15.9302i	0.855178	+	0.855178i	−0.135588	+	0.990765i	$0.543292\pi$
$348$		0			0
$349$	−4.56134	−	4.56134i	−0.244163	−	0.244163i	0.574407	−	0.818570i	$-0.305233\pi$
$349$	−4.56134	−	4.56134i	−0.244163	−	0.244163i	−0.818570	+	0.574407i	$0.805233\pi$
$350$	10.7609	−	17.7592i	0.575194	−	0.949267i
$351$		0			0
$352$	−4.97613	+	1.85880i	−0.265229	+	0.0990742i
$353$		−	14.1314i		−	0.752141i	−0.926591	−	0.376070i	$-0.877275\pi$
$353$		−	14.1314i		−	0.752141i	0.926591	−	0.376070i	$-0.122725\pi$
$354$		0			0
$355$	−1.45117	+	19.9766i	−0.0770199	+	1.06025i
$356$	−12.4968	+	12.1497i	−0.662331	+	0.643934i
$357$		0			0
$358$	−19.1885	+	7.79030i	−1.01414	+	0.411730i
$359$		−	25.2588i		−	1.33311i	−0.745456	−	0.666555i	$-0.767768\pi$
$359$		−	25.2588i		−	1.33311i	0.745456	−	0.666555i	$-0.232232\pi$
$360$		0			0
$361$		−	18.6412i		−	0.981116i
$362$	4.49907	+	11.0818i	0.236466	+	0.582446i
$363$		0			0
$364$	−9.36547	−	0.131900i	−0.490884	−	0.00691345i
$365$	−0.388602	−	0.0282294i	−0.0203404	−	0.00147759i
$366$		0			0
$367$			3.01381i			0.157320i	0.996902	+	0.0786598i	$0.0250641\pi$
$367$			3.01381i			0.157320i	−0.996902	+	0.0786598i	$0.974936\pi$
$368$	−0.695755	+	24.6959i	−0.0362688	+	1.28736i
$369$		0			0
$370$	−23.5499	+	7.62535i	−1.22430	+	0.396423i
$371$	−0.430151	−	0.430151i	−0.0223323	−	0.0223323i
$372$		0			0
$373$	−13.1060	−	13.1060i	−0.678604	−	0.678604i	0.281080	−	0.959684i	$-0.409307\pi$
$373$	−13.1060	−	13.1060i	−0.678604	−	0.678604i	−0.959684	+	0.281080i	$0.909307\pi$
$374$	−9.19798	+	3.73427i	−0.475616	+	0.193094i
$375$		0			0
$376$	−4.23858	−	10.8772i	−0.218588	−	0.560949i
$377$	−6.65611			−0.342807
$378$		0			0
$379$	8.34584	−	8.34584i	0.428697	−	0.428697i	−0.459487	−	0.888184i	$-0.651967\pi$
$379$	8.34584	−	8.34584i	0.428697	−	0.428697i	0.888184	+	0.459487i	$0.151967\pi$
$380$	0.231690	−	2.66876i	0.0118855	−	0.136904i
$381$		0			0
$382$	−0.222867	+	0.527513i	−0.0114029	+	0.0269899i
$383$		−	25.5695i		−	1.30654i	−0.757124	−	0.653271i	$-0.773396\pi$
$383$		−	25.5695i		−	1.30654i	0.757124	−	0.653271i	$-0.226604\pi$
$384$		0			0
$385$	−4.66455	+	4.03275i	−0.237727	+	0.205528i
$386$	8.45425	+	3.57181i	0.430310	+	0.181801i
$387$		0			0
$388$	−15.1259	+	14.7057i	−0.767900	+	0.746571i
$389$	−4.31954	+	4.31954i	−0.219009	+	0.219009i	−0.808081	−	0.589072i	$-0.799494\pi$
$389$	−4.31954	+	4.31954i	−0.219009	+	0.219009i	0.589072	+	0.808081i	$0.299494\pi$
$390$		0			0
$391$			46.1705i			2.33494i
$392$	4.27910	−	1.66746i	0.216127	−	0.0842195i
$393$		0			0
$394$	−34.1758	+	13.8750i	−1.72175	+	0.699011i
$395$	6.83528	+	0.496537i	0.343920	+	0.0249835i
$396$		0			0
$397$	23.5750	−	23.5750i	1.18319	−	1.18319i	0.204281	−	0.978912i	$-0.434515\pi$
$397$	23.5750	−	23.5750i	1.18319	−	1.18319i	0.978912	−	0.204281i	$-0.0654855\pi$
$398$	17.5471	+	7.41342i	0.879556	+	0.371601i
$399$		0			0
$400$	−3.44665	+	19.7008i	−0.172333	+	0.985039i
$401$	−17.1100			−0.854430			−0.427215	−	0.904150i	$-0.640505\pi$
$401$	−17.1100			−0.854430			−0.427215	+	0.904150i	$0.640505\pi$
$402$		0			0
$403$	−2.05890	+	2.05890i	−0.102561	+	0.102561i
$404$	−27.3072	−	0.384585i	−1.35858	−	0.0191338i
$405$		0			0
$406$	16.0604	−	6.52032i	0.797064	−	0.323598i
$407$	7.35056			0.364354
$408$		0			0
$409$			25.2659i			1.24932i	0.780897	+	0.624659i	$0.214762\pi$
$409$			25.2659i			1.24932i	−0.780897	+	0.624659i	$0.785238\pi$
$410$	−34.8341	−	17.7935i	−1.72033	−	0.878759i
$411$		0			0
$412$	20.2939	+	20.8737i	0.999807	+	1.02837i
$413$	−22.6896	+	22.6896i	−1.11648	+	1.11648i
$414$		0			0
$415$	−21.9784	+	19.0014i	−1.07888	+	0.932744i
$416$	8.45098	−	3.15680i	0.414343	−	0.154775i
$417$		0			0
$418$	−0.309578	+	0.732751i	−0.0151420	+	0.0358400i
$419$	15.7885	+	15.7885i	0.771317	+	0.771317i	0.978337	−	0.207020i	$-0.0663765\pi$
$419$	15.7885	+	15.7885i	0.771317	+	0.771317i	−0.207020	+	0.978337i	$0.566376\pi$
$420$		0			0
$421$	−4.64861	+	4.64861i	−0.226559	+	0.226559i	−0.811254	−	0.584694i	$-0.801214\pi$
$421$	−4.64861	+	4.64861i	−0.226559	+	0.226559i	0.584694	+	0.811254i	$0.301214\pi$
$422$	−11.2622	+	4.57232i	−0.548236	+	0.222577i
$423$		0			0
$424$	0.536457	+	0.235604i	0.0260527	+	0.0114419i
$425$	−5.40179	+	36.9840i	−0.262025	+	1.79399i
$426$		0			0
$427$	21.6581	+	21.6581i	1.04811	+	1.04811i
$428$	−0.233511	+	16.5803i	−0.0112872	+	0.801438i
$429$		0			0
$430$	3.81904	−	1.23659i	0.184170	−	0.0596335i
$431$	28.6320			1.37915			0.689577	−	0.724213i	$-0.257797\pi$
$431$	28.6320			1.37915			0.689577	+	0.724213i	$0.257797\pi$
$432$		0			0
$433$			6.14954i			0.295528i	0.989023	+	0.147764i	$0.0472076\pi$
$433$			6.14954i			0.295528i	−0.989023	+	0.147764i	$0.952792\pi$
$434$	2.95098	−	6.98477i	0.141651	−	0.335280i
$435$		0			0
$436$	0.195818	−	13.9039i	0.00937797	−	0.665875i
$437$	2.61605	+	2.61605i	0.125143	+	0.125143i
$438$		0			0
$439$			37.8541i			1.80668i	0.428926	+	0.903340i	$0.358892\pi$
$439$			37.8541i			1.80668i	−0.428926	+	0.903340i	$0.641108\pi$
$440$	2.77583	−	5.25034i	0.132332	−	0.250300i
$441$		0			0
$442$	15.6210	−	6.34192i	0.743013	−	0.301654i
$443$	−3.41746	−	3.41746i	−0.162368	−	0.162368i	0.621247	−	0.783615i	$-0.286627\pi$
$443$	−3.41746	−	3.41746i	−0.162368	−	0.162368i	−0.783615	+	0.621247i	$0.786627\pi$
$444$		0			0
$445$	1.41186	−	19.4355i	0.0669286	−	0.921332i
$446$	28.7633	+	12.1521i	1.36198	+	0.575420i
$447$		0			0
$448$	−17.2988	+	15.8955i	−0.817291	+	0.750994i
$449$	31.6935			1.49571			0.747855	−	0.663862i	$-0.231084\pi$
$449$	31.6935			1.49571			0.747855	+	0.663862i	$0.231084\pi$
$450$		0			0
$451$	8.21324	+	8.21324i	0.386746	+	0.386746i
$452$	−18.4029	+	17.8918i	−0.865601	+	0.841558i
$453$		0			0
$454$	−4.18239	−	10.3018i	−0.196289	−	0.483485i
$455$	7.92182	−	6.84883i	0.371381	−	0.321078i
$456$		0			0
$457$	7.26208			0.339706			0.169853	−	0.985469i	$-0.445671\pi$
$457$	7.26208			0.339706			0.169853	+	0.985469i	$0.445671\pi$
$458$	8.89439	+	21.9080i	0.415607	+	1.02369i
$459$		0			0
$460$	−17.7691	−	21.1477i	−0.828487	−	0.986014i
$461$	−16.1568	−	16.1568i	−0.752499	−	0.752499i	0.222446	−	0.974945i	$-0.428596\pi$
$461$	−16.1568	−	16.1568i	−0.752499	−	0.752499i	−0.974945	+	0.222446i	$0.928596\pi$
$462$		0			0
$463$			13.4637i			0.625710i	0.949801	+	0.312855i	$0.101285\pi$
$463$			13.4637i			0.625710i	−0.949801	+	0.312855i	$0.898715\pi$
$464$	−12.1329	+	11.4680i	−0.563255	+	0.532387i
$465$		0			0
$466$	4.90955	−	11.6206i	0.227430	−	0.538313i
$467$	10.5630	−	10.5630i	0.488795	−	0.488795i	−0.419131	−	0.907926i	$-0.637665\pi$
$467$	10.5630	−	10.5630i	0.488795	−	0.488795i	0.907926	+	0.419131i	$0.137665\pi$
$468$		0			0
$469$	25.4976	−	25.4976i	1.17737	−	1.17737i
$470$	11.6232	+	5.93721i	0.536137	+	0.273863i
$471$		0			0
$472$	12.4276	−	28.2970i	0.572027	−	1.30248i
$473$	−1.19202			−0.0548093
$474$		0			0
$475$	1.78947	+	2.40161i	0.0821066	+	0.110193i
$476$	−31.4789	+	30.6046i	−1.44283	+	1.40276i
$477$		0			0
$478$	12.6214	−	29.8739i	0.577287	−	1.36640i
$479$	−34.2747			−1.56605			−0.783026	−	0.621989i	$-0.786325\pi$
$479$	−34.2747			−1.56605			−0.783026	+	0.621989i	$0.786325\pi$
$480$		0			0
$481$	−12.4835			−0.569197
$482$	3.56776	−	8.44465i	0.162507	−	0.384643i
$483$		0			0
$484$	14.5094	−	14.1064i	0.659519	−	0.641200i
$485$	1.70888	−	23.5243i	0.0775964	−	1.06818i
$486$		0			0
$487$	33.4994			1.51800			0.759002	−	0.651088i	$-0.225687\pi$
$487$	33.4994			1.51800			0.759002	+	0.651088i	$0.225687\pi$
$488$	−27.0106	−	11.8626i	−1.22271	−	0.536996i
$489$		0			0
$490$	−2.33570	+	4.57257i	−0.105516	+	0.206567i
$491$	−0.491541	+	0.491541i	−0.0221829	+	0.0221829i	−0.718111	−	0.695928i	$-0.754993\pi$
$491$	−0.491541	+	0.491541i	−0.0221829	+	0.0221829i	0.695928	+	0.718111i	$0.254993\pi$
$492$		0			0
$493$	−22.0616	+	22.0616i	−0.993606	+	0.993606i
$494$	0.525757	−	1.24443i	0.0236549	−	0.0559897i
$495$		0			0
$496$	−0.205672	+	7.30033i	−0.00923493	+	0.327794i
$497$		−	26.3043i		−	1.17991i
$498$		0			0
$499$	−0.863504	−	0.863504i	−0.0386557	−	0.0386557i	0.687515	−	0.726170i	$-0.258702\pi$
$499$	−0.863504	−	0.863504i	−0.0386557	−	0.0386557i	−0.726170	+	0.687515i	$0.758702\pi$
$500$	−11.7594	−	19.0189i	−0.525896	−	0.850549i
$501$		0			0
$502$	−10.8500	−	26.7250i	−0.484260	−	1.19279i
$503$	12.8335			0.572218			0.286109	−	0.958197i	$-0.407638\pi$
$503$	12.8335			0.572218			0.286109	+	0.958197i	$0.407638\pi$
$504$		0			0
$505$	23.0979	−	19.9693i	1.02784	−	0.888624i
$506$	3.08542	+	7.59979i	0.137164	+	0.337852i
$507$		0			0
$508$	−1.53498	+	1.49234i	−0.0681035	+	0.0662119i
$509$	12.6692	+	12.6692i	0.561554	+	0.561554i	0.929749	−	0.368194i	$-0.120024\pi$
$509$	12.6692	+	12.6692i	0.561554	+	0.561554i	−0.368194	+	0.929749i	$0.620024\pi$
$510$		0			0
$511$	0.511694			0.0226360
$512$	9.96567	−	20.3147i	0.440424	−	0.897790i
$513$		0			0
$514$	0.252388	+	0.106631i	0.0111324	+	0.00470328i
$515$	−32.4635	−	2.35825i	−1.43051	−	0.103917i
$516$		0			0
$517$	−2.74053	−	2.74053i	−0.120529	−	0.120529i
$518$	30.1211	−	12.2288i	1.32345	−	0.537303i
$519$		0			0
$520$	−4.71420	+	8.91667i	−0.206731	+	0.391022i
$521$		−	30.2561i		−	1.32554i	−0.748821	−	0.662772i	$-0.769380\pi$
$521$		−	30.2561i		−	1.32554i	0.748821	−	0.662772i	$-0.230620\pi$
$522$		0			0
$523$	−4.01063	−	4.01063i	−0.175373	−	0.175373i	0.613962	−	0.789335i	$-0.289575\pi$
$523$	−4.01063	−	4.01063i	−0.175373	−	0.175373i	−0.789335	+	0.613962i	$0.789575\pi$
$524$	0.434249	−	30.8335i	0.0189703	−	1.34697i
$525$		0			0
$526$	9.12029	−	21.5871i	0.397663	−	0.941243i
$527$			13.6484i			0.594534i
$528$		0			0
$529$	15.1481			0.658615
$530$	−0.623216	+	0.201794i	−0.0270708	+	0.00876539i
$531$		0			0
$532$	−0.0495421	+	3.51770i	−0.00214792	+	0.152512i
$533$	−13.9486	−	13.9486i	−0.604179	−	0.604179i
$534$		0			0
$535$	−12.1249	−	14.0245i	−0.524206	−	0.606332i
$536$	−13.9656	+	31.7990i	−0.603223	+	1.37351i
$537$		0			0
$538$	13.1456	−	5.33694i	0.566745	−	0.230092i
$539$	1.07813	−	1.07813i	0.0464382	−	0.0464382i
$540$		0			0
$541$	−5.53130	−	5.53130i	−0.237809	−	0.237809i	0.578133	−	0.815942i	$-0.303781\pi$
$541$	−5.53130	−	5.53130i	−0.237809	−	0.237809i	−0.815942	+	0.578133i	$0.803781\pi$
$542$	−1.44353	+	3.41675i	−0.0620051	+	0.146762i
$543$		0			0
$544$	17.5475	−	38.4739i	0.752343	−	1.64955i
$545$	10.1677	+	11.7607i	0.435537	+	0.503771i
$546$		0			0
$547$	−22.6141	+	22.6141i	−0.966908	+	0.966908i	−0.999470	−	0.0325622i	$-0.989633\pi$
$547$	−22.6141	+	22.6141i	−0.966908	+	0.966908i	0.0325622	+	0.999470i	$0.489633\pi$
$548$	14.0181	+	14.4186i	0.598823	+	0.615931i
$549$		0			0
$550$	1.58237	+	6.44866i	0.0674726	+	0.274972i
$551$			2.50006i			0.106506i
$552$		0			0
$553$	−9.00038			−0.382735
$554$	−14.7791	+	6.00013i	−0.627904	+	0.254921i
$555$		0			0
$556$	−8.22349	−	0.115817i	−0.348753	−	0.00491173i
$557$	−6.08239	+	6.08239i	−0.257719	+	0.257719i	−0.824126	−	0.566407i	$-0.808333\pi$
$557$	−6.08239	+	6.08239i	−0.257719	+	0.257719i	0.566407	+	0.824126i	$0.308333\pi$
$558$		0			0
$559$	2.02442			0.0856238
$560$	2.64002	−	26.1329i	0.111561	−	1.10431i
$561$		0			0
$562$	12.9992	+	5.49199i	0.548338	+	0.231666i
$563$	23.1946	−	23.1946i	0.977536	−	0.977536i	−0.0222176	−	0.999753i	$-0.507073\pi$
$563$	23.1946	−	23.1946i	0.977536	−	0.977536i	0.999753	+	0.0222176i	$0.00707265\pi$
$564$		0			0
$565$	2.07912	−	28.6209i	0.0874692	−	1.20409i
$566$	37.8136	−	15.3519i	1.58943	−	0.645288i
$567$		0			0
$568$	9.19879	+	23.6062i	0.385973	+	0.990496i
$569$		−	1.31584i		−	0.0551629i	−0.999620	−	0.0275815i	$-0.991219\pi$
$569$		−	1.31584i		−	0.0551629i	0.999620	−	0.0275815i	$-0.00878056\pi$
$570$		0			0
$571$	18.2083	−	18.2083i	0.761993	−	0.761993i	−0.214690	−	0.976682i	$-0.568874\pi$
$571$	18.2083	−	18.2083i	0.761993	−	0.761993i	0.976682	+	0.214690i	$0.0688740\pi$
$572$	2.14744	−	2.08780i	0.0897892	−	0.0872952i
$573$		0			0
$574$	47.3202	+	19.9922i	1.97511	+	0.834458i
$575$	30.5579	+	4.46320i	1.27435	+	0.186128i
$576$		0			0
$577$		−	8.13617i		−	0.338713i	−0.985555	−	0.169357i	$-0.945831\pi$
$577$		−	8.13617i		−	0.338713i	0.985555	−	0.169357i	$-0.0541689\pi$
$578$	21.3988	−	50.6495i	0.890072	−	2.10674i
$579$		0			0
$580$	1.61439	−	18.5956i	0.0670339	−	0.772139i
$581$	26.9802	−	26.9802i	1.11933	−	1.11933i
$582$		0			0
$583$	0.194522			0.00805629
$584$	−0.459210	+	0.178943i	−0.0190022	+	0.00740472i
$585$		0			0
$586$	−8.63339	+	3.50505i	−0.356642	+	0.144792i
$587$	13.4231	+	13.4231i	0.554030	+	0.554030i	0.927601	−	0.373572i	$-0.121867\pi$
$587$	13.4231	+	13.4231i	0.554030	+	0.554030i	−0.373572	+	0.927601i	$0.621867\pi$
$588$		0			0
$589$	0.773329	+	0.773329i	0.0318645	+	0.0318645i
$590$	10.6442	+	32.8734i	0.438217	+	1.35338i
$591$		0			0
$592$	−22.7551	+	21.5081i	−0.935229	+	0.883976i
$593$			17.9386i			0.736649i	0.929697	+	0.368324i	$0.120068\pi$
$593$			17.9386i			0.736649i	−0.929697	+	0.368324i	$0.879932\pi$
$594$		0			0
$595$	3.55641	−	48.9572i	0.145799	−	2.00705i
$596$	−3.56717	−	0.0502389i	−0.146117	−	0.00205787i
$597$		0			0
$598$	−5.23998	−	12.9067i	−0.214279	−	0.527796i
$599$			3.98863i			0.162971i	0.996675	+	0.0814855i	$0.0259664\pi$
$599$			3.98863i			0.162971i	−0.996675	+	0.0814855i	$0.974034\pi$
$600$		0			0
$601$		−	20.7775i		−	0.847532i	−0.905772	−	0.423766i	$-0.860708\pi$
$601$		−	20.7775i		−	0.847532i	0.905772	−	0.423766i	$-0.139292\pi$
$602$	−4.88468	+	1.98312i	−0.199085	+	0.0808259i
$603$		0			0
$604$	−29.3593	+	28.5438i	−1.19461	+	1.16143i
$605$	−1.63924	+	22.5656i	−0.0666445	+	0.917421i
$606$		0			0
$607$		−	46.0393i		−	1.86868i	−0.356384	−	0.934340i	$-0.615990\pi$
$607$		−	46.0393i		−	1.86868i	0.356384	−	0.934340i	$-0.384010\pi$
$608$	−1.18570	−	3.17421i	−0.0480866	−	0.128731i
$609$		0			0
$610$	31.3789	−	10.1603i	1.27050	−	0.411380i
$611$	4.65426	+	4.65426i	0.188291	+	0.188291i
$612$		0			0
$613$	−13.9783	−	13.9783i	−0.564580	−	0.564580i	0.366025	−	0.930605i	$-0.380718\pi$
$613$	−13.9783	−	13.9783i	−0.564580	−	0.564580i	−0.930605	+	0.366025i	$0.880718\pi$
$614$	−6.81231	−	16.7796i	−0.274923	−	0.677169i
$615$		0			0
$616$	−3.13632	+	7.14124i	−0.126366	+	0.287729i
$617$	−33.5135			−1.34920			−0.674601	−	0.738182i	$-0.735684\pi$
$617$	−33.5135			−1.34920			−0.674601	+	0.738182i	$0.735684\pi$
$618$		0			0
$619$	−4.64277	+	4.64277i	−0.186609	+	0.186609i	−0.794228	−	0.607620i	$-0.792125\pi$
$619$	−4.64277	+	4.64277i	−0.186609	+	0.186609i	0.607620	+	0.794228i	$0.292125\pi$
$620$	−5.25270	−	6.25144i	−0.210953	−	0.251064i
$621$		0			0
$622$	−4.42077	−	1.86772i	−0.177257	−	0.0748887i
$623$			25.5918i			1.02531i
$624$		0			0
$625$	23.9556	+	7.15033i	0.958226	+	0.286013i
$626$	5.99605	−	14.1923i	0.239650	−	0.567237i
$627$		0			0
$628$	−23.0025	−	0.323960i	−0.917902	−	0.0129274i
$629$	−41.3764	+	41.3764i	−1.64978	+	1.64978i
$630$		0			0
$631$			4.43412i			0.176519i	0.996097	+	0.0882597i	$0.0281305\pi$
$631$			4.43412i			0.176519i	−0.996097	+	0.0882597i	$0.971869\pi$
$632$	8.07721	−	3.14750i	0.321294	−	0.125201i
$633$		0			0
$634$	2.60140	+	6.40758i	0.103315	+	0.254478i
$635$	0.173418	−	2.38725i	0.00688187	−	0.0947351i
$636$		0			0
$637$	−1.83099	+	1.83099i	−0.0725464	+	0.0725464i
$638$	−2.15710	+	5.10571i	−0.0854004	+	0.202137i
$639$		0			0
$640$	6.76961	+	24.3757i	0.267593	+	0.963532i
$641$	29.2735			1.15623			0.578116	−	0.815954i	$-0.303788\pi$
$641$	29.2735			1.15623			0.578116	+	0.815954i	$0.303788\pi$
$642$		0			0
$643$	−5.69367	+	5.69367i	−0.224536	+	0.224536i	−0.810406	−	0.585869i	$-0.800753\pi$
$643$	−5.69367	+	5.69367i	−0.224536	+	0.224536i	0.585869	+	0.810406i	$0.300753\pi$
$644$	25.2869	+	26.0093i	0.996443	+	1.02491i
$645$		0			0
$646$	−2.38205	−	5.86728i	−0.0937203	−	0.230845i
$647$	2.78788			0.109603			0.0548015	−	0.998497i	$-0.482547\pi$
$647$	2.78788			0.109603			0.0548015	+	0.998497i	$0.482547\pi$
$648$		0			0
$649$		−	10.2607i		−	0.402766i
$650$	−2.68735	−	10.9518i	−0.105406	−	0.429564i
$651$		0			0
$652$	−11.5656	−	0.162886i	−0.452944	−	0.00637912i
$653$	19.9931	−	19.9931i	0.782389	−	0.782389i	−0.197844	−	0.980233i	$-0.563394\pi$
$653$	19.9931	−	19.9931i	0.782389	−	0.782389i	0.980233	+	0.197844i	$0.0633940\pi$
$654$		0			0
$655$	22.5481	+	26.0807i	0.881027	+	1.01906i
$656$	−49.4580	−	1.39338i	−1.93101	−	0.0544022i
$657$		0			0
$658$	−15.7895	−	6.67085i	−0.615537	−	0.260057i
$659$	6.26656	+	6.26656i	0.244110	+	0.244110i	0.818548	−	0.574438i	$-0.194779\pi$
$659$	6.26656	+	6.26656i	0.244110	+	0.244110i	−0.574438	+	0.818548i	$0.694779\pi$
$660$		0			0
$661$	−2.89073	+	2.89073i	−0.112436	+	0.112436i	−0.761087	−	0.648650i	$-0.775334\pi$
$661$	−2.89073	+	2.89073i	−0.112436	+	0.112436i	0.648650	+	0.761087i	$0.275334\pi$
$662$	−18.7517	−	46.1879i	−0.728806	−	1.79514i
$663$		0			0
$664$	−14.7777	+	33.6480i	−0.573484	+	1.30579i
$665$	−2.57244	−	2.97546i	−0.0997550	−	0.115383i
$666$		0			0
$667$	18.2283	+	18.2283i	0.705803	+	0.705803i
$668$	−13.2845	−	13.6640i	−0.513991	−	0.528676i
$669$		0			0
$670$	−11.9615	−	36.9417i	−0.462115	−	1.42718i
$671$	−9.79420			−0.378101
$672$		0			0
$673$		−	30.9133i		−	1.19162i	−0.803125	−	0.595810i	$-0.796831\pi$
$673$		−	30.9133i		−	1.19162i	0.803125	−	0.595810i	$-0.203169\pi$
$674$	−12.5387	−	5.29745i	−0.482973	−	0.204050i
$675$		0			0
$676$	14.9948	−	14.5783i	0.576725	−	0.560705i
$677$	5.28850	+	5.28850i	0.203253	+	0.203253i	0.801392	−	0.598139i	$-0.204093\pi$
$677$	5.28850	+	5.28850i	0.203253	+	0.203253i	−0.598139	+	0.801392i	$0.704093\pi$
$678$		0			0
$679$			30.9757i			1.18874i
$680$	13.9290	+	45.1794i	0.534155	+	1.73255i
$681$		0			0
$682$	0.912079	+	2.24657i	0.0349253	+	0.0860255i
$683$	10.6055	+	10.6055i	0.405809	+	0.405809i	0.880274	−	0.474465i	$-0.157359\pi$
$683$	10.6055	+	10.6055i	0.405809	+	0.405809i	−0.474465	+	0.880274i	$0.657359\pi$
$684$		0			0
$685$	−22.4243	−	1.62897i	−0.856788	−	0.0622399i
$686$	−8.68951	+	20.5675i	−0.331767	+	0.785271i
$687$		0			0
$688$	3.69015	−	3.48792i	0.140685	−	0.132976i
$689$	−0.330358			−0.0125856
$690$		0			0
$691$	32.1363	+	32.1363i	1.22252	+	1.22252i	0.966732	+	0.255790i	$0.0823357\pi$
$691$	32.1363	+	32.1363i	1.22252	+	1.22252i	0.255790	+	0.966732i	$0.417664\pi$
$692$	−17.4846	−	0.246247i	−0.664664	−	0.00936091i
$693$		0			0
$694$	−29.5203	+	11.9849i	−1.12057	+	0.454940i
$695$	6.95587	−	6.01372i	0.263851	−	0.228113i
$696$		0			0
$697$	−92.4648			−3.50235
$698$	8.45264	−	3.43167i	0.319937	−	0.129891i
$699$		0			0
$700$	17.2126	+	23.7928i	0.650575	+	0.899282i
$701$	−13.0526	−	13.0526i	−0.492989	−	0.492989i	0.416258	−	0.909247i	$-0.363341\pi$
$701$	−13.0526	−	13.0526i	−0.492989	−	0.492989i	−0.909247	+	0.416258i	$0.863341\pi$
$702$		0			0
$703$			4.68883i			0.176843i
$704$	0.317285	−	7.50556i	0.0119581	−	0.282876i
$705$		0			0
$706$	18.4093	+	7.77770i	0.692844	+	0.292718i
$707$	−28.3545	+	28.3545i	−1.06638	+	1.06638i
$708$		0			0
$709$	−7.03016	+	7.03016i	−0.264023	+	0.264023i	−0.826686	−	0.562663i	$-0.809777\pi$
$709$	−7.03016	+	7.03016i	−0.264023	+	0.264023i	0.562663	+	0.826686i	$0.309777\pi$
$710$	−25.2252	−	12.8852i	−0.946686	−	0.483574i
$711$		0			0
$712$	−8.94964	−	22.9669i	−0.335402	−	0.860720i
$713$	11.2769			0.422325
$714$		0			0
$715$	−0.242613	+	3.33978i	−0.00907321	+	0.124901i
$716$	0.412439	−	29.2849i	0.0154136	−	1.09443i
$717$		0			0
$718$	32.9052	+	13.9020i	1.22801	+	0.518819i
$719$	15.9753			0.595778			0.297889	−	0.954601i	$-0.403718\pi$
$719$	15.9753			0.595778			0.297889	+	0.954601i	$0.403718\pi$
$720$		0			0
$721$	42.7464			1.59196
$722$	24.2843	+	10.2598i	0.903767	+	0.381830i
$723$		0			0
$724$	−16.9127	−	0.238193i	−0.628555	−	0.00885236i
$725$	12.4688	+	16.7341i	0.463080	+	0.621489i
$726$		0			0
$727$	−9.60073			−0.356071			−0.178036	−	0.984024i	$-0.556974\pi$
$727$	−9.60073			−0.356071			−0.178036	+	0.984024i	$0.556974\pi$
$728$	5.32642	−	12.1280i	0.197410	−	0.449493i
$729$		0			0
$730$	0.250655	−	0.490703i	0.00927716	−	0.0181617i
$731$	6.70992	−	6.70992i	0.248175	−	0.248175i
$732$		0			0
$733$	5.23740	−	5.23740i	0.193448	−	0.193448i	−0.603736	−	0.797184i	$-0.706322\pi$
$733$	5.23740	−	5.23740i	0.193448	−	0.193448i	0.797184	+	0.603736i	$0.206322\pi$
$734$	−3.92615	−	1.65875i	−0.144917	−	0.0612255i
$735$		0			0
$736$	−31.7889	−	14.4986i	−1.17175	−	0.534424i
$737$			11.5305i			0.424731i
$738$		0			0
$739$	−18.0809	−	18.0809i	−0.665118	−	0.665118i	0.291464	−	0.956582i	$-0.405858\pi$
$739$	−18.0809	−	18.0809i	−0.665118	−	0.665118i	−0.956582	+	0.291464i	$0.905858\pi$
$740$	3.02777	−	34.8758i	0.111303	−	1.28206i
$741$		0			0
$742$	0.797114	−	0.323619i	0.0292630	−	0.0118804i
$743$	−5.96005			−0.218653			−0.109326	−	0.994006i	$-0.534869\pi$
$743$	−5.96005			−0.218653			−0.109326	+	0.994006i	$0.534869\pi$
$744$		0			0
$745$	3.01731	−	2.60862i	0.110546	−	0.0955725i
$746$	24.2868	−	9.86015i	0.889203	−	0.361006i
$747$		0			0
$748$	0.197702	−	14.0377i	0.00722870	−	0.513268i
$749$	17.2162	+	17.2162i	0.629065	+	0.629065i
$750$		0			0
$751$	−32.6552			−1.19160			−0.595802	−	0.803131i	$-0.703166\pi$
$751$	−32.6552			−1.19160			−0.595802	+	0.803131i	$0.703166\pi$
$752$	16.5028	+	0.464932i	0.601795	+	0.0169543i
$753$		0			0
$754$	3.66341	−	8.67105i	0.133413	−	0.315781i
$755$	3.31694	−	45.6606i	0.120716	−	1.66176i
$756$		0			0
$757$	34.0760	+	34.0760i	1.23851	+	1.23851i	0.960609	+	0.277903i	$0.0896395\pi$
$757$	34.0760	+	34.0760i	1.23851	+	1.23851i	0.277903	+	0.960609i	$0.410361\pi$
$758$	6.27889	+	15.4657i	0.228060	+	0.561740i
$759$		0			0
$760$	3.34913	+	1.77067i	0.121486	+	0.0642288i
$761$		−	29.5888i		−	1.07259i	−0.844030	−	0.536296i	$-0.819823\pi$
$761$		−	29.5888i		−	1.07259i	0.844030	−	0.536296i	$-0.180177\pi$
$762$		0			0
$763$	−14.4371	−	14.4371i	−0.522659	−	0.522659i
$764$	−0.564539	−	0.580668i	−0.0204243	−	0.0210078i
$765$		0			0
$766$	33.3099	+	14.0730i	1.20354	+	0.508479i
$767$			17.4257i			0.629206i
$768$		0			0
$769$	29.1544			1.05133			0.525667	−	0.850690i	$-0.323816\pi$
$769$	29.1544			1.05133			0.525667	+	0.850690i	$0.323816\pi$
$770$	−2.68626	−	8.29616i	−0.0968059	−	0.298973i
$771$		0			0
$772$	−9.30615	+	9.04766i	−0.334936	+	0.325632i
$773$	16.3728	+	16.3728i	0.588889	+	0.588889i	0.937331	−	0.348441i	$-0.113289\pi$
$773$	16.3728	+	16.3728i	0.588889	+	0.588889i	−0.348441	+	0.937331i	$0.613289\pi$
$774$		0			0
$775$	9.03318	+	1.31936i	0.324482	+	0.0473929i
$776$	−10.8324	−	27.7986i	−0.388862	−	0.997911i
$777$		0			0
$778$	−3.24975	−	8.00455i	−0.116509	−	0.286977i
$779$	−5.23912	+	5.23912i	−0.187711	+	0.187711i
$780$		0			0
$781$	5.94764	+	5.94764i	0.212823	+	0.212823i
$782$	−60.1472	−	25.4114i	−2.15086	−	0.908711i
$783$		0			0
$784$	−0.182904	+	6.49221i	−0.00653230	+	0.231864i
$785$	19.4568	−	16.8214i	0.694443	−	0.600383i
$786$		0			0
$787$	27.4334	−	27.4334i	0.977894	−	0.977894i	−0.0218667	−	0.999761i	$-0.506961\pi$
$787$	27.4334	−	27.4334i	0.977894	−	0.977894i	0.999761	+	0.0218667i	$0.00696095\pi$
$788$	0.734578	−	52.1581i	0.0261682	−	1.85806i
$789$		0			0
$790$	−4.40887	+	8.63117i	−0.156860	+	0.307083i
$791$			37.6867i			1.33999i
$792$		0			0
$793$	16.6335			0.590673
$794$	17.7363	+	43.6868i	0.629438	+	1.55039i
$795$		0			0
$796$	−19.3152	+	18.7787i	−0.684610	+	0.665594i
$797$	1.30833	−	1.30833i	0.0463434	−	0.0463434i	−0.683555	−	0.729899i	$-0.739567\pi$
$797$	1.30833	−	1.30833i	0.0463434	−	0.0463434i	0.729899	+	0.683555i	$0.239567\pi$
$798$		0			0
$799$	30.8530			1.09150
$800$	−23.7676	−	15.3330i	−0.840312	−	0.542103i
$801$		0			0
$802$	9.41702	−	22.2895i	0.332527	−	0.787069i
$803$	−0.115699	+	0.115699i	−0.00408292	+	0.00408292i
$804$		0			0
$805$	−40.4507	−	2.93847i	−1.42570	−	0.103567i
$806$	−1.54899	−	3.81535i	−0.0545607	−	0.134390i
$807$		0			0
$808$	15.5304	−	35.3619i	0.546357	−	1.24403i
$809$		−	5.40398i		−	0.189994i	−0.995478	−	0.0949970i	$-0.969716\pi$
$809$		−	5.40398i		−	0.189994i	0.995478	−	0.0949970i	$-0.0302841\pi$
$810$		0			0
$811$	5.63507	−	5.63507i	0.197874	−	0.197874i	−0.601214	−	0.799088i	$-0.705316\pi$
$811$	5.63507	−	5.63507i	0.197874	−	0.197874i	0.799088	+	0.601214i	$0.205316\pi$
$812$	−0.345203	+	24.5109i	−0.0121143	+	0.860163i
$813$		0			0
$814$	−4.04562	+	9.57572i	−0.141799	+	0.335629i
$815$	9.78282	−	8.45776i	0.342677	−	0.296262i
$816$		0			0
$817$		−	0.760378i		−	0.0266023i
$818$	−32.9144	−	13.9059i	−1.15083	−	0.486209i
$819$		0			0
$820$	42.3520	−	35.5858i	1.47900	−	1.24271i
$821$	11.6911	−	11.6911i	0.408022	−	0.408022i	−0.473027	−	0.881048i	$-0.656839\pi$
$821$	11.6911	−	11.6911i	0.408022	−	0.408022i	0.881048	+	0.473027i	$0.156839\pi$
$822$		0			0
$823$	−12.7721			−0.445207			−0.222604	−	0.974909i	$-0.571456\pi$
$823$	−12.7721			−0.445207			−0.222604	+	0.974909i	$0.571456\pi$
$824$	−38.3619	+	14.9487i	−1.33640	+	0.520764i
$825$		0			0
$826$	−17.0702	−	42.0461i	−0.593949	−	1.46297i
$827$	−0.00790410	−	0.00790410i	−0.000274852	−	0.000274852i	0.706969	−	0.707244i	$-0.250062\pi$
$827$	−0.00790410	−	0.00790410i	−0.000274852	−	0.000274852i	−0.707244	+	0.706969i	$0.750062\pi$
$828$		0			0
$829$	−2.93843	−	2.93843i	−0.102056	−	0.102056i	0.654235	−	0.756291i	$-0.272991\pi$
$829$	−2.93843	−	2.93843i	−0.102056	−	0.102056i	−0.756291	+	0.654235i	$0.772991\pi$
$830$	−12.6571	−	39.0897i	−0.439333	−	1.35682i
$831$		0			0
$832$	−0.538846	+	12.7467i	−0.0186811	+	0.441913i
$833$			12.1376i			0.420542i
$834$		0			0
$835$	21.2508	+	1.54372i	0.735413	+	0.0534228i
$836$	−0.784183	−	0.806587i	−0.0271215	−	0.0278964i
$837$		0			0
$838$	−29.2576	+	11.8782i	−1.01069	+	0.410327i
$839$			39.0990i			1.34985i	0.737888	+	0.674923i	$0.235823\pi$
$839$			39.0990i			1.34985i	−0.737888	+	0.674923i	$0.764177\pi$
$840$		0			0
$841$		−	11.5799i		−	0.399308i
$842$	−3.49732	−	8.61435i	−0.120526	−	0.296870i
$843$		0			0
$844$	0.242071	−	17.1880i	0.00833241	−	0.591636i
$845$	−1.69408	+	23.3205i	−0.0582781	+	0.802250i
$846$		0			0
$847$		−	29.7133i		−	1.02096i
$848$	−0.602182	+	0.569182i	−0.0206790	+	0.0195458i
$849$		0			0
$850$	−45.2067	−	27.3924i	−1.55058	−	0.939550i
$851$	34.1870	+	34.1870i	1.17192	+	1.17192i
$852$		0			0
$853$	−0.788780	−	0.788780i	−0.0270073	−	0.0270073i	0.693474	−	0.720481i	$-0.256079\pi$
$853$	−0.788780	−	0.788780i	−0.0270073	−	0.0270073i	−0.720481	+	0.693474i	$0.756079\pi$
$854$	−40.1346	+	16.2942i	−1.37338	+	0.557575i
$855$		0			0
$856$	−21.4709	−	9.42970i	−0.733862	−	0.322300i
$857$	45.0264			1.53807			0.769036	−	0.639206i	$-0.220737\pi$
$857$	45.0264			1.53807			0.769036	+	0.639206i	$0.220737\pi$
$858$		0			0
$859$	−21.5188	+	21.5188i	−0.734212	+	0.734212i	−0.971451	−	0.237239i	$-0.923757\pi$
$859$	−21.5188	+	21.5188i	−0.734212	+	0.734212i	0.237239	+	0.971451i	$0.423757\pi$
$860$	−0.491007	+	5.65574i	−0.0167432	+	0.192859i
$861$		0			0
$862$	−15.7585	+	37.2994i	−0.536738	+	1.27042i
$863$			8.30436i			0.282684i	0.989961	+	0.141342i	$0.0451417\pi$
$863$			8.30436i			0.282684i	−0.989961	+	0.141342i	$0.954858\pi$
$864$		0			0
$865$	14.7894	−	12.7862i	0.502855	−	0.434744i
$866$	−8.01113	−	3.38460i	−0.272229	−	0.115013i
$867$		0			0
$868$	7.47503	+	7.68859i	0.253719	+	0.260968i
$869$	2.03507	−	2.03507i	0.0690351	−	0.0690351i
$870$		0			0
$871$		−	19.5823i		−	0.663520i
$872$	18.0051	+	7.90755i	0.609729	+	0.267783i
$873$		0			0
$874$	−4.84781	+	1.96815i	−0.163980	+	0.0665738i
$875$	−32.0585	−	7.08639i	−1.08377	−	0.239564i
$876$		0			0
$877$	−17.6134	+	17.6134i	−0.594764	+	0.594764i	−0.938914	−	0.344151i	$-0.888167\pi$
$877$	−17.6134	+	17.6134i	−0.594764	+	0.594764i	0.344151	+	0.938914i	$0.388167\pi$
$878$	−49.3133	−	20.8343i	−1.66424	−	0.703122i
$879$		0			0
$880$	5.31195	+	6.50582i	0.179066	+	0.219311i
$881$	−32.5717			−1.09737			−0.548684	−	0.836030i	$-0.684871\pi$
$881$	−32.5717			−1.09737			−0.548684	+	0.836030i	$0.684871\pi$
$882$		0			0
$883$	11.6327	−	11.6327i	0.391472	−	0.391472i	−0.483740	−	0.875212i	$-0.660722\pi$
$883$	11.6327	−	11.6327i	0.391472	−	0.391472i	0.875212	+	0.483740i	$0.160722\pi$
$884$	−0.335758	+	23.8402i	−0.0112928	+	0.801833i
$885$		0			0
$886$	6.33290	−	2.57108i	0.212758	−	0.0863772i
$887$	−40.0203			−1.34375			−0.671875	−	0.740665i	$-0.734511\pi$
$887$	−40.0203			−1.34375			−0.671875	+	0.740665i	$0.734511\pi$
$888$		0			0
$889$			3.14342i			0.105427i
$890$	24.5420	+	12.5362i	0.822649	+	0.420216i
$891$		0			0
$892$	−31.6616	+	30.7822i	−1.06011	+	1.03066i
$893$	1.74815	−	1.74815i	0.0584997	−	0.0584997i
$894$		0			0
$895$	21.4156	+	24.7708i	0.715845	+	0.827995i
$896$	−11.1865	−	31.2841i	−0.373715	−	1.04513i
$897$		0			0
$898$	−17.4436	+	41.2878i	−0.582100	+	1.37779i
$899$	5.38846	+	5.38846i	0.179715	+	0.179715i
$900$		0			0
$901$	−1.09497	+	1.09497i	−0.0364787	+	0.0364787i
$902$	−15.2200	+	6.17912i	−0.506770	+	0.205742i
$903$		0			0
$904$	−13.1793	−	33.8212i	−0.438337	−	1.12488i
$905$	14.3057	−	12.3680i	0.475536	−	0.411126i
$906$		0			0
$907$	−5.81050	−	5.81050i	−0.192934	−	0.192934i	0.604028	−	0.796963i	$-0.293561\pi$
$907$	−5.81050	−	5.81050i	−0.192934	−	0.192934i	−0.796963	+	0.604028i	$0.793561\pi$
$908$	15.7222	+	0.221427i	0.521760	+	0.00734830i
$909$		0			0
$910$	4.56208	+	14.0894i	0.151231	+	0.467059i
$911$	−10.4809			−0.347248			−0.173624	−	0.984812i	$-0.555548\pi$
$911$	−10.4809			−0.347248			−0.173624	+	0.984812i	$0.555548\pi$
$912$		0			0
$913$			12.2009i			0.403792i
$914$	−3.99692	+	9.46045i	−0.132206	+	0.312924i
$915$		0			0
$916$	−33.4353	−	0.470892i	−1.10473	−	0.0155587i
$917$	−32.0161	−	32.0161i	−1.05726	−	1.05726i
$918$		0			0
$919$		−	51.8755i		−	1.71121i	−0.517626	−	0.855607i	$-0.673184\pi$
$919$		−	51.8755i		−	1.71121i	0.517626	−	0.855607i	$-0.326816\pi$
$920$	37.3292	−	11.5088i	1.23071	−	0.379434i
$921$		0			0
$922$	29.9403	−	12.1554i	0.986031	−	0.400317i
$923$	−10.1009	−	10.1009i	−0.332475	−	0.332475i
$924$		0			0
$925$	23.3851	+	31.3847i	0.768898	+	1.03192i
$926$	−17.5394	−	7.41017i	−0.576380	−	0.243513i
$927$		0			0
$928$	−8.26183	−	22.1175i	−0.271208	−	0.726043i
$929$	5.54673			0.181982			0.0909912	−	0.995852i	$-0.470996\pi$
$929$	5.54673			0.181982			0.0909912	+	0.995852i	$0.470996\pi$
$930$		0			0
$931$	0.687724	+	0.687724i	0.0225393	+	0.0225393i
$932$	12.4362	+	12.7915i	0.407362	+	0.419000i
$933$		0			0
$934$	7.94691	+	19.5742i	0.260031	+	0.640489i
$935$	10.2655	+	11.8738i	0.335719	+	0.388315i
$936$		0			0
$937$	−9.31790			−0.304402			−0.152201	−	0.988350i	$-0.548636\pi$
$937$	−9.31790			−0.304402			−0.152201	+	0.988350i	$0.548636\pi$
$938$	19.1828	+	47.2496i	0.626340	+	1.54276i
$939$		0			0
$940$	−14.1317	+	11.8740i	−0.460926	+	0.387288i
$941$	−21.9832	−	21.9832i	−0.716630	−	0.716630i	0.251283	−	0.967914i	$-0.419147\pi$
$941$	−21.9832	−	21.9832i	−0.716630	−	0.716630i	−0.967914	+	0.251283i	$0.919147\pi$
$942$		0			0
$943$			76.3986i			2.48788i
$944$	30.0232	+	31.7639i	0.977171	+	1.03383i
$945$		0			0
$946$	0.656069	−	1.55287i	0.0213307	−	0.0504883i
$947$	−15.4966	+	15.4966i	−0.503572	+	0.503572i	−0.912546	−	0.408974i	$-0.865887\pi$
$947$	−15.4966	+	15.4966i	−0.503572	+	0.503572i	0.408974	+	0.912546i	$0.365887\pi$
$948$		0			0
$949$	0.196492	−	0.196492i	0.00637839	−	0.00637839i
$950$	−4.11352	+	1.00938i	−0.133460	+	0.0327485i
$951$		0			0
$952$	−22.5437	−	57.8524i	−0.730646	−	1.87501i
$953$	−5.72390			−0.185415			−0.0927076	−	0.995693i	$-0.529552\pi$
$953$	−5.72390			−0.185415			−0.0927076	+	0.995693i	$0.529552\pi$
$954$		0			0
$955$	0.903075	+	0.0656024i	0.0292228	+	0.00212284i
$956$	31.9708	+	32.8842i	1.03401	+	1.06355i
$957$		0			0
$958$	18.8642	−	44.6504i	0.609475	−	1.44259i
$959$	29.5273			0.953485
$960$		0			0
$961$	−27.6664			−0.892466
$962$	6.87069	−	16.2625i	0.221520	−	0.524323i
$963$		0			0
$964$	9.03738	+	9.29557i	0.291074	+	0.299390i
$965$	1.05139	−	14.4733i	0.0338453	−	0.465911i
$966$		0			0
$967$	−8.80514			−0.283154			−0.141577	−	0.989927i	$-0.545217\pi$
$967$	−8.80514			−0.283154			−0.141577	+	0.989927i	$0.545217\pi$
$968$	10.3910	+	26.6656i	0.333978	+	0.857065i
$969$		0			0
$970$	29.7051	+	15.1736i	0.953772	+	0.487194i
$971$	26.8032	−	26.8032i	0.860157	−	0.860157i	−0.131199	−	0.991356i	$-0.541883\pi$
$971$	26.8032	−	26.8032i	0.860157	−	0.860157i	0.991356	+	0.131199i	$0.0418828\pi$
$972$		0			0
$973$	−8.53888	+	8.53888i	−0.273744	+	0.273744i
$974$	−18.4375	+	43.6404i	−0.590776	+	1.39833i
$975$		0			0
$976$	30.3199	−	28.6583i	0.970515	−	0.917329i
$977$			36.2126i			1.15854i	0.815134	+	0.579272i	$0.196663\pi$
$977$			36.2126i			1.15854i	−0.815134	+	0.579272i	$0.803337\pi$
$978$		0			0
$979$	−5.78655	−	5.78655i	−0.184939	−	0.184939i
$980$	−4.67124	−	5.55943i	−0.149217	−	0.177589i
$981$		0			0
$982$	−0.369804	−	0.910875i	−0.0118009	−	0.0290672i
$983$	−15.7547			−0.502496			−0.251248	−	0.967923i	$-0.580841\pi$
$983$	−15.7547			−0.502496			−0.251248	+	0.967923i	$0.580841\pi$
$984$		0			0
$985$	38.1425	+	44.1182i	1.21532	+	1.40572i
$986$	−16.5978	−	40.8825i	−0.528581	−	1.30196i
$987$		0			0
$988$	1.33178	+	1.36983i	0.0423696	+	0.0435801i
$989$	−5.54404	−	5.54404i	−0.176290	−	0.176290i
$990$		0			0
$991$	12.5049			0.397230			0.198615	−	0.980078i	$-0.436356\pi$
$991$	12.5049			0.397230			0.198615	+	0.980078i	$0.436356\pi$
$992$	−9.39708	−	4.28590i	−0.298358	−	0.136078i
$993$		0			0
$994$	34.2671	+	14.4774i	1.08689	+	0.459196i
$995$	2.18219	−	30.0397i	0.0691799	−	0.952324i
$996$		0			0
$997$	−4.59749	−	4.59749i	−0.145604	−	0.145604i	0.630547	−	0.776151i	$-0.282831\pi$
$997$	−4.59749	−	4.59749i	−0.145604	−	0.145604i	−0.776151	+	0.630547i	$0.782831\pi$
$998$	1.60016	−	0.649646i	0.0506522	−	0.0205642i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bm.h.109.9		48
3.2	odd	2		240.2.bl.a.109.16	yes	48
5.4	even	2	inner	720.2.bm.h.109.16		48
12.11	even	2		960.2.bl.a.529.13		48
15.14	odd	2		240.2.bl.a.109.9	✓	48
16.5	even	4	inner	720.2.bm.h.469.16		48
24.5	odd	2		1920.2.bl.a.289.14		48
24.11	even	2		1920.2.bl.b.289.11		48
48.5	odd	4		240.2.bl.a.229.9	yes	48
48.11	even	4		960.2.bl.a.49.6		48
48.29	odd	4		1920.2.bl.a.1249.11		48
48.35	even	4		1920.2.bl.b.1249.14		48
60.59	even	2		960.2.bl.a.529.6		48
80.69	even	4	inner	720.2.bm.h.469.9		48
120.29	odd	2		1920.2.bl.a.289.11		48
120.59	even	2		1920.2.bl.b.289.14		48
240.29	odd	4		1920.2.bl.a.1249.14		48
240.59	even	4		960.2.bl.a.49.13		48
240.149	odd	4		240.2.bl.a.229.16	yes	48
240.179	even	4		1920.2.bl.b.1249.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.9	✓	48	15.14	odd	2
240.2.bl.a.109.16	yes	48	3.2	odd	2
240.2.bl.a.229.9	yes	48	48.5	odd	4
240.2.bl.a.229.16	yes	48	240.149	odd	4
720.2.bm.h.109.9		48	1.1	even	1	trivial
720.2.bm.h.109.16		48	5.4	even	2	inner
720.2.bm.h.469.9		48	80.69	even	4	inner
720.2.bm.h.469.16		48	16.5	even	4	inner
960.2.bl.a.49.6		48	48.11	even	4
960.2.bl.a.49.13		48	240.59	even	4
960.2.bl.a.529.6		48	60.59	even	2
960.2.bl.a.529.13		48	12.11	even	2
1920.2.bl.a.289.11		48	120.29	odd	2
1920.2.bl.a.289.14		48	24.5	odd	2
1920.2.bl.a.1249.11		48	48.29	odd	4
1920.2.bl.a.1249.14		48	240.29	odd	4
1920.2.bl.b.289.11		48	24.11	even	2
1920.2.bl.b.289.14		48	120.59	even	2
1920.2.bl.b.1249.11		48	240.179	even	4
1920.2.bl.b.1249.14		48	48.35	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)

\(f(q)\)	\(=\)	\(q+(-0.550383 + 1.30272i) q^{2} +(-1.39416 - 1.43399i) q^{4} +(2.23019 + 0.162008i) q^{5} -2.93661 q^{7} +(2.63541 - 1.02695i) q^{8} +O(q^{10})\)	\(q+(-0.550383 + 1.30272i) q^{2} +(-1.39416 - 1.43399i) q^{4} +(2.23019 + 0.162008i) q^{5} -2.93661 q^{7} +(2.63541 - 1.02695i) q^{8} +(-1.43851 + 2.81615i) q^{10} +(0.663996 - 0.663996i) q^{11} +(-1.12767 + 1.12767i) q^{13} +(1.61626 - 3.82558i) q^{14} +(-0.112647 + 3.99841i) q^{16} +7.47528i q^{17} +(0.423555 + 0.423555i) q^{19} +(-2.87692 - 3.42393i) q^{20} +(0.499549 + 1.23045i) q^{22} +6.17642 q^{23} +(4.94751 + 0.722620i) q^{25} +(-0.848386 - 2.08968i) q^{26} +(4.09410 + 4.21107i) q^{28} +(2.95128 + 2.95128i) q^{29} +1.82581 q^{31} +(-5.14681 - 2.34740i) q^{32} +(-9.73820 - 4.11426i) q^{34} +(-6.54921 - 0.475756i) q^{35} +(5.53509 + 5.53509i) q^{37} +(-0.784891 + 0.318656i) q^{38} +(6.04383 - 1.86335i) q^{40} +12.3694i q^{41} +(-0.897614 - 0.897614i) q^{43} +(-1.87788 - 0.0264474i) q^{44} +(-3.39939 + 8.04614i) q^{46} -4.12733i q^{47} +1.62370 q^{49} +(-3.66439 + 6.04750i) q^{50} +(3.18921 + 0.0449157i) q^{52} +(0.146479 + 0.146479i) q^{53} +(1.58841 - 1.37327i) q^{55} +(-7.73917 + 3.01577i) q^{56} +(-5.46902 + 2.22036i) q^{58} +(7.72645 - 7.72645i) q^{59} +(-7.37519 - 7.37519i) q^{61} +(-1.00489 + 2.37851i) q^{62} +(5.89073 - 5.41289i) q^{64} +(-2.69760 + 2.33222i) q^{65} +(-8.68265 + 8.68265i) q^{67} +(10.7195 - 10.4217i) q^{68} +(4.22435 - 8.26994i) q^{70} +8.95735i q^{71} -0.174246 q^{73} +(-10.2571 + 4.16425i) q^{74} +(0.0168705 - 1.19788i) q^{76} +(-1.94990 + 1.94990i) q^{77} +3.06488 q^{79} +(-0.899001 + 8.89898i) q^{80} +(-16.1139 - 6.80790i) q^{82} +(-9.18751 + 9.18751i) q^{83} +(-1.21106 + 16.6713i) q^{85} +(1.66337 - 0.675308i) q^{86} +(1.06801 - 2.43179i) q^{88} -8.71473i q^{89} +(3.31152 - 3.31152i) q^{91} +(-8.61090 - 8.85691i) q^{92} +(5.37676 + 2.27161i) q^{94} +(0.875989 + 1.01323i) q^{95} -10.5481i q^{97} +(-0.893654 + 2.11522i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 48 q^{31} - 28 q^{34} - 24 q^{35} - 16 q^{40} + 40 q^{44} - 4 q^{46} + 48 q^{49} + 32 q^{50} - 48 q^{56} + 32 q^{59} + 16 q^{61} + 48 q^{64} - 16 q^{65} - 40 q^{74} + 60 q^{76} - 96 q^{79} - 72 q^{80} - 16 q^{86} - 32 q^{91} + 44 q^{94} + 48 q^{95}+O(q^{100}) \) 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

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