LMFDB - Embedded newform 720.2.bm.g.469.3

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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			469.3
Character	$\chi$	$=$	720.469
Dual form			720.2.bm.g.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29731 + 0.563016i) q^{2} +(1.36603 - 1.46081i) q^{4} +(-0.496304 - 2.18029i) q^{5} -0.862231 q^{7} +(-0.949697 + 2.66422i) q^{8} +(1.87140 + 2.54909i) q^{10} +(-4.00287 - 4.00287i) q^{11} +(1.17783 + 1.17783i) q^{13} +(1.11858 - 0.485450i) q^{14} +(-0.267949 - 3.99102i) q^{16} +3.66487i q^{17} +(-0.732051 + 0.732051i) q^{19} +(-3.86297 - 2.25333i) q^{20} +(7.44665 + 2.93928i) q^{22} -4.97577 q^{23} +(-4.50736 + 2.16418i) q^{25} +(-2.19115 - 0.864873i) q^{26} +(-1.17783 + 1.25956i) q^{28} +(-0.253708 + 0.253708i) q^{29} +3.39471 q^{31} +(2.59462 + 5.02672i) q^{32} +(-2.06338 - 4.75447i) q^{34} +(0.427929 + 1.87992i) q^{35} +(-5.48124 + 5.48124i) q^{37} +(0.537540 - 1.36185i) q^{38} +(6.28012 + 0.748355i) q^{40} +9.27201i q^{41} +(2.43739 - 2.43739i) q^{43} +(-11.3155 + 0.379423i) q^{44} +(6.45512 - 2.80144i) q^{46} +6.79703i q^{47} -6.25656 q^{49} +(4.62898 - 5.34533i) q^{50} +(3.32953 - 0.111644i) q^{52} +(2.86097 - 2.86097i) q^{53} +(-6.74080 + 10.7141i) q^{55} +(0.818858 - 2.29718i) q^{56} +(0.186296 - 0.471980i) q^{58} +(-3.30973 - 3.30973i) q^{59} +(-3.44854 + 3.44854i) q^{61} +(-4.40399 + 1.91128i) q^{62} +(-6.19615 - 5.06040i) q^{64} +(1.98345 - 3.15258i) q^{65} +(-8.23423 - 8.23423i) q^{67} +(5.35369 + 5.00631i) q^{68} +(-1.61358 - 2.19791i) q^{70} -12.4801i q^{71} -11.5338 q^{73} +(4.02484 - 10.1969i) q^{74} +(0.0693893 + 2.06939i) q^{76} +(3.45140 + 3.45140i) q^{77} +0.0873587 q^{79} +(-8.56860 + 2.56496i) q^{80} +(-5.22029 - 12.0287i) q^{82} +(-7.17205 - 7.17205i) q^{83} +(7.99050 - 1.81889i) q^{85} +(-1.78976 + 4.53434i) q^{86} +(14.4661 - 6.86302i) q^{88} +5.86061i q^{89} +(-1.01556 - 1.01556i) q^{91} +(-6.79703 + 7.26867i) q^{92} +(-3.82684 - 8.81785i) q^{94} +(1.95941 + 1.23277i) q^{95} -15.8373i q^{97} +(8.11669 - 3.52254i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 24 q^{10} - 64 q^{16} + 32 q^{19} + 32 q^{31} - 72 q^{40} - 32 q^{46} + 128 q^{49} - 32 q^{64} - 104 q^{70} - 32 q^{76} + 224 q^{79} - 48 q^{85} - 32 q^{91} - 48 q^{94}+O(q^{100}) $ 32 * q + 16 * q^4 - 24 * q^10 - 64 * q^16 + 32 * q^19 + 32 * q^31 - 72 * q^40 - 32 * q^46 + 128 * q^49 - 32 * q^64 - 104 * q^70 - 32 * q^76 + 224 * q^79 - 48 * q^85 - 32 * q^91 - 48 * q^94

Character values

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

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

Coefficient data

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

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

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

$2$	−1.29731	+	0.563016i	−0.917337	+	0.398113i
$2$	−1.29731	+	0.563016i	−0.917337	+	0.398113i
$3$		0			0
$3$		0			0
$4$	1.36603	−	1.46081i	0.683013	−	0.730406i
$5$	−0.496304	−	2.18029i	−0.221954	−	0.975057i
$5$	−0.496304	−	2.18029i	−0.221954	−	0.975057i
$6$		0			0
$7$	−0.862231			−0.325893			−0.162946	−	0.986635i	$-0.552100\pi$
$7$	−0.862231			−0.325893			−0.162946	+	0.986635i	$0.552100\pi$
$8$	−0.949697	+	2.66422i	−0.335768	+	0.941945i
$9$		0			0
$10$	1.87140	+	2.54909i	0.591789	+	0.806093i
$11$	−4.00287	−	4.00287i	−1.20691	−	1.20691i	−0.972022	−	0.234889i	$-0.924527\pi$
$11$	−4.00287	−	4.00287i	−1.20691	−	1.20691i	−0.234889	−	0.972022i	$-0.575473\pi$
$12$		0			0
$13$	1.17783	+	1.17783i	0.326671	+	0.326671i	0.851319	−	0.524648i	$-0.175803\pi$
$13$	1.17783	+	1.17783i	0.326671	+	0.326671i	−0.524648	+	0.851319i	$0.675803\pi$
$14$	1.11858	−	0.485450i	0.298953	−	0.129742i
$15$		0			0
$16$	−0.267949	−	3.99102i	−0.0669873	−	0.997754i
$17$			3.66487i			0.888862i	0.895813	+	0.444431i	$0.146594\pi$
$17$			3.66487i			0.888862i	−0.895813	+	0.444431i	$0.853406\pi$
$18$		0			0
$19$	−0.732051	+	0.732051i	−0.167944	+	0.167944i	−0.786075	−	0.618131i	$-0.787890\pi$
$19$	−0.732051	+	0.732051i	−0.167944	+	0.167944i	0.618131	+	0.786075i	$0.287890\pi$
$20$	−3.86297	−	2.25333i	−0.863785	−	0.503860i
$21$		0			0
$22$	7.44665	+	2.93928i	1.58763	+	0.626657i
$23$	−4.97577			−1.03752			−0.518760	−	0.854920i	$-0.673606\pi$
$23$	−4.97577			−1.03752			−0.518760	+	0.854920i	$0.673606\pi$
$24$		0			0
$25$	−4.50736	+	2.16418i	−0.901473	+	0.432835i
$26$	−2.19115	−	0.864873i	−0.429719	−	0.169616i
$27$		0			0
$28$	−1.17783	+	1.25956i	−0.222589	+	0.238034i
$29$	−0.253708	+	0.253708i	−0.0471124	+	0.0471124i	−0.730271	−	0.683158i	$-0.760606\pi$
$29$	−0.253708	+	0.253708i	−0.0471124	+	0.0471124i	0.683158	+	0.730271i	$0.260606\pi$
$30$		0			0
$31$	3.39471			0.609708			0.304854	−	0.952399i	$-0.401392\pi$
$31$	3.39471			0.609708			0.304854	+	0.952399i	$0.401392\pi$
$32$	2.59462	+	5.02672i	0.458668	+	0.888608i
$33$		0			0
$34$	−2.06338	−	4.75447i	−0.353867	−	0.815385i
$35$	0.427929	+	1.87992i	0.0723332	+	0.317764i
$36$		0			0
$37$	−5.48124	+	5.48124i	−0.901110	+	0.901110i	−0.995532	−	0.0944220i	$-0.969900\pi$
$37$	−5.48124	+	5.48124i	−0.901110	+	0.901110i	0.0944220	+	0.995532i	$0.469900\pi$
$38$	0.537540	−	1.36185i	0.0872005	−	0.220922i
$39$		0			0
$40$	6.28012	+	0.748355i	0.992975	+	0.118325i
$41$			9.27201i			1.44804i	0.689777	+	0.724022i	$0.257709\pi$
$41$			9.27201i			1.44804i	−0.689777	+	0.724022i	$0.742291\pi$
$42$		0			0
$43$	2.43739	−	2.43739i	0.371698	−	0.371698i	−0.496397	−	0.868096i	$-0.665344\pi$
$43$	2.43739	−	2.43739i	0.371698	−	0.371698i	0.868096	+	0.496397i	$0.165344\pi$
$44$	−11.3155	+	0.379423i	−1.70587	+	0.0572001i
$45$		0			0
$46$	6.45512	−	2.80144i	0.951755	−	0.413050i
$47$			6.79703i			0.991449i	0.868480	+	0.495724i	$0.165097\pi$
$47$			6.79703i			0.991449i	−0.868480	+	0.495724i	$0.834903\pi$
$48$		0			0
$49$	−6.25656			−0.893794
$50$	4.62898	−	5.34533i	0.654637	−	0.755943i
$51$		0			0
$52$	3.32953	−	0.111644i	0.461723	−	0.0154822i
$53$	2.86097	−	2.86097i	0.392985	−	0.392985i	−0.482765	−	0.875750i	$-0.660367\pi$
$53$	2.86097	−	2.86097i	0.392985	−	0.392985i	0.875750	+	0.482765i	$0.160367\pi$
$54$		0			0
$55$	−6.74080	+	10.7141i	−0.908929	+	1.44469i
$56$	0.818858	−	2.29718i	0.109425	−	0.306973i
$57$		0			0
$58$	0.186296	−	0.471980i	0.0244619	−	0.0619740i
$59$	−3.30973	−	3.30973i	−0.430890	−	0.430890i	0.458041	−	0.888931i	$-0.348551\pi$
$59$	−3.30973	−	3.30973i	−0.430890	−	0.430890i	−0.888931	+	0.458041i	$0.848551\pi$
$60$		0			0
$61$	−3.44854	+	3.44854i	−0.441540	+	0.441540i	−0.892529	−	0.450989i	$-0.851071\pi$
$61$	−3.44854	+	3.44854i	−0.441540	+	0.441540i	0.450989	+	0.892529i	$0.351071\pi$
$62$	−4.40399	+	1.91128i	−0.559308	+	0.242733i
$63$		0			0
$64$	−6.19615	−	5.06040i	−0.774519	−	0.632551i
$65$	1.98345	−	3.15258i	0.246017	−	0.391029i
$66$		0			0
$67$	−8.23423	−	8.23423i	−1.00597	−	1.00597i	−0.999982	−	0.00598890i	$-0.998094\pi$
$67$	−8.23423	−	8.23423i	−1.00597	−	1.00597i	−0.00598890	−	0.999982i	$-0.501906\pi$
$68$	5.35369	+	5.00631i	0.649230	+	0.607104i
$69$		0			0
$70$	−1.61358	−	2.19791i	−0.192860	−	0.262700i
$71$		−	12.4801i		−	1.48111i	−0.671995	−	0.740556i	$-0.734562\pi$
$71$		−	12.4801i		−	1.48111i	0.671995	−	0.740556i	$-0.265438\pi$
$72$		0			0
$73$	−11.5338			−1.34993			−0.674967	−	0.737848i	$-0.735842\pi$
$73$	−11.5338			−1.34993			−0.674967	+	0.737848i	$0.735842\pi$
$74$	4.02484	−	10.1969i	0.467878	−	1.18536i
$75$		0			0
$76$	0.0693893	+	2.06939i	0.00795950	+	0.237375i
$77$	3.45140	+	3.45140i	0.393324	+	0.393324i
$78$		0			0
$79$	0.0873587			0.00982862			0.00491431	−	0.999988i	$-0.498436\pi$
$79$	0.0873587			0.00982862			0.00491431	+	0.999988i	$0.498436\pi$
$80$	−8.56860	+	2.56496i	−0.957999	+	0.286772i
$81$		0			0
$82$	−5.22029	−	12.0287i	−0.576485	−	1.32834i
$83$	−7.17205	−	7.17205i	−0.787235	−	0.787235i	0.193805	−	0.981040i	$-0.437917\pi$
$83$	−7.17205	−	7.17205i	−0.787235	−	0.787235i	−0.981040	+	0.193805i	$0.937917\pi$
$84$		0			0
$85$	7.99050	−	1.81889i	0.866691	−	0.197286i
$86$	−1.78976	+	4.53434i	−0.192995	+	0.488950i
$87$		0			0
$88$	14.4661	−	6.86302i	1.54209	−	0.731601i
$89$			5.86061i			0.621224i	0.950537	+	0.310612i	$0.100534\pi$
$89$			5.86061i			0.621224i	−0.950537	+	0.310612i	$0.899466\pi$
$90$		0			0
$91$	−1.01556	−	1.01556i	−0.106460	−	0.106460i
$92$	−6.79703	+	7.26867i	−0.708639	+	0.757811i
$93$		0			0
$94$	−3.82684	−	8.81785i	−0.394708	−	0.909492i
$95$	1.95941	+	1.23277i	0.201031	+	0.126479i
$96$		0			0
$97$		−	15.8373i		−	1.60803i	−0.594609	−	0.804015i	$-0.702693\pi$
$97$		−	15.8373i		−	1.60803i	0.594609	−	0.804015i	$-0.297307\pi$
$98$	8.11669	−	3.52254i	0.819910	−	0.355831i
$99$		0			0
$100$	−2.99572	+	9.54074i	−0.299572	+	0.954074i
$101$	8.53721	+	8.53721i	0.849484	+	0.849484i	0.990069	−	0.140584i	$-0.0448982\pi$
$101$	8.53721	+	8.53721i	0.849484	+	0.849484i	−0.140584	+	0.990069i	$0.544898\pi$
$102$		0			0
$103$	−14.1804			−1.39723			−0.698617	−	0.715496i	$-0.746201\pi$
$103$	−14.1804			−1.39723			−0.698617	+	0.715496i	$0.746201\pi$
$104$	−4.25658	+	2.01942i	−0.417392	+	0.198020i
$105$		0			0
$106$	−2.10080	+	5.32235i	−0.204047	+	0.516952i
$107$	−9.73420	+	9.73420i	−0.941041	+	0.941041i	−0.998356	−	0.0573151i	$-0.981746\pi$
$107$	−9.73420	+	9.73420i	−0.941041	+	0.941041i	0.0573151	+	0.998356i	$0.481746\pi$
$108$		0			0
$109$	10.7231	−	10.7231i	1.02708	−	1.02708i	0.0274606	−	0.999623i	$-0.491258\pi$
$109$	10.7231	−	10.7231i	1.02708	−	1.02708i	0.999623	−	0.0274606i	$-0.00874207\pi$
$110$	2.71270	−	17.6947i	0.258646	−	1.68712i
$111$		0			0
$112$	0.231034	+	3.44118i	0.0218307	+	0.325161i
$113$		−	14.0025i		−	1.31725i	−0.752473	−	0.658623i	$-0.771139\pi$
$113$		−	14.0025i		−	1.31725i	0.752473	−	0.658623i	$-0.228861\pi$
$114$		0			0
$115$	2.46949	+	10.8486i	0.230282	+	1.01164i
$116$	0.0240484	+	0.717192i	0.00223284	+	0.0665896i
$117$		0			0
$118$	6.15717	+	2.43031i	0.566814	+	0.223728i
$119$		−	3.15997i		−	0.289674i
$120$		0			0
$121$			21.0460i			1.91327i
$122$	2.53224	−	6.41541i	0.229258	−	0.580824i
$123$		0			0
$124$	4.63726	−	4.95904i	0.416439	−	0.445335i
$125$	6.95556	+	8.75329i	0.622125	+	0.782918i
$126$		0			0
$127$			22.0420i			1.95591i	0.208812	+	0.977956i	$0.433040\pi$
$127$			22.0420i			1.95591i	−0.208812	+	0.977956i	$0.566960\pi$
$128$	10.8874	+	3.07638i	0.962321	+	0.271916i
$129$		0			0
$130$	−0.798202	+	5.20659i	−0.0700070	+	0.456648i
$131$	0.609083	−	0.609083i	0.0532158	−	0.0532158i	−0.679998	−	0.733214i	$-0.738019\pi$
$131$	0.609083	−	0.609083i	0.0532158	−	0.0532158i	0.733214	+	0.679998i	$0.238019\pi$
$132$		0			0
$133$	0.631197	−	0.631197i	0.0547317	−	0.0547317i
$134$	15.3183	+	6.04634i	1.32330	+	0.522324i
$135$		0			0
$136$	−9.76403	−	3.48052i	−0.837258	−	0.298452i
$137$	9.11228			0.778515			0.389257	−	0.921129i	$-0.372732\pi$
$137$	9.11228			0.778515			0.389257	+	0.921129i	$0.372732\pi$
$138$		0			0
$139$	−12.2476	−	12.2476i	−1.03883	−	1.03883i	−0.999215	−	0.0396103i	$-0.987388\pi$
$139$	−12.2476	−	12.2476i	−1.03883	−	1.03883i	−0.0396103	−	0.999215i	$-0.512612\pi$
$140$	3.33077	+	1.94289i	0.281501	+	0.164204i
$141$		0			0
$142$	7.02648	+	16.1905i	0.589649	+	1.35868i
$143$		−	9.42941i		−	0.788527i
$144$		0			0
$145$	0.679075	+	0.427242i	0.0563941	+	0.0354805i
$146$	14.9630	−	6.49374i	1.23834	−	0.537426i
$147$		0			0
$148$	0.519554	+	15.4946i	0.0427070	+	1.27365i
$149$	9.01830	+	9.01830i	0.738808	+	0.738808i	0.972347	−	0.233539i	$-0.0750308\pi$
$149$	9.01830	+	9.01830i	0.738808	+	0.738808i	−0.233539	+	0.972347i	$0.575031\pi$
$150$		0			0
$151$		−	1.79183i		−	0.145817i	−0.997339	−	0.0729086i	$-0.976772\pi$
$151$		−	1.79183i		−	0.145817i	0.997339	−	0.0729086i	$-0.0232281\pi$
$152$	−1.25512	−	2.64557i	−0.101804	−	0.214584i
$153$		0			0
$154$	−6.42073	−	2.53434i	−0.517397	−	0.204223i
$155$	−1.68481	−	7.40147i	−0.135327	−	0.594500i
$156$		0			0
$157$	10.3560	+	10.3560i	0.826500	+	0.826500i	0.987031	−	0.160531i	$-0.0513206\pi$
$157$	10.3560	+	10.3560i	0.826500	+	0.826500i	−0.160531	+	0.987031i	$0.551321\pi$
$158$	−0.113331	+	0.0491844i	−0.00901615	+	0.00391290i
$159$		0			0
$160$	9.67202	−	8.15182i	0.764640	−	0.644458i
$161$	4.29027			0.338120
$162$		0			0
$163$	2.80998	+	2.80998i	0.220095	+	0.220095i	0.808538	−	0.588444i	$-0.200259\pi$
$163$	2.80998	+	2.80998i	0.220095	+	0.220095i	−0.588444	+	0.808538i	$0.700259\pi$
$164$	13.5447	+	12.6658i	1.05766	+	0.989033i
$165$		0			0
$166$	13.3424	+	5.26639i	1.03557	+	0.408751i
$167$	8.08558			0.625681			0.312840	−	0.949806i	$-0.398719\pi$
$167$	8.08558			0.625681			0.312840	+	0.949806i	$0.398719\pi$
$168$		0			0
$169$		−	10.2254i		−	0.786572i
$170$	−9.34208	+	6.85844i	−0.716505	+	0.526018i
$171$		0			0
$172$	−0.231034	−	6.89010i	−0.0176162	−	0.525366i
$173$	−10.9281	−	10.9281i	−0.830846	−	0.830846i	0.156787	−	0.987632i	$-0.449886\pi$
$173$	−10.9281	−	10.9281i	−0.830846	−	0.830846i	−0.987632	+	0.156787i	$0.949886\pi$
$174$		0			0
$175$	3.88639	−	1.86602i	0.293784	−	0.141058i
$176$	−14.9030	+	17.0481i	−1.12335	+	1.28505i
$177$		0			0
$178$	−3.29962	−	7.60303i	−0.247317	−	0.569871i
$179$	9.17034	−	9.17034i	0.685424	−	0.685424i	−0.275793	−	0.961217i	$-0.588941\pi$
$179$	9.17034	−	9.17034i	0.685424	−	0.685424i	0.961217	+	0.275793i	$0.0889406\pi$
$180$		0			0
$181$	6.86184	+	6.86184i	0.510037	+	0.510037i	0.914538	−	0.404501i	$-0.132555\pi$
$181$	6.86184	+	6.86184i	0.510037	+	0.510037i	−0.404501	+	0.914538i	$0.632555\pi$
$182$	1.88928	+	0.745721i	0.140042	+	0.0552765i
$183$		0			0
$184$	4.72547	−	13.2566i	0.348367	−	0.977286i
$185$	14.6711	+	9.23035i	1.07864	+	0.678629i
$186$		0			0
$187$	14.6700	−	14.6700i	1.07278	−	1.07278i
$188$	9.92919	+	9.28492i	0.724161	+	0.677172i
$189$		0			0
$190$	−3.23602	−	0.496103i	−0.234766	−	0.0359911i
$191$	−4.67766			−0.338463			−0.169232	−	0.985576i	$-0.554129\pi$
$191$	−4.67766			−0.338463			−0.169232	+	0.985576i	$0.554129\pi$
$192$		0			0
$193$		−	7.75234i		−	0.558025i	−0.960287	−	0.279013i	$-0.909993\pi$
$193$		−	7.75234i		−	0.558025i	0.960287	−	0.279013i	$-0.0900071\pi$
$194$	8.91663	+	20.5458i	0.640177	+	1.47510i
$195$		0			0
$196$	−8.54662	+	9.13966i	−0.610473	+	0.652833i
$197$	12.6883	−	12.6883i	0.904001	−	0.904001i	−0.0917783	−	0.995779i	$-0.529255\pi$
$197$	12.6883	−	12.6883i	0.904001	−	0.904001i	0.995779	+	0.0917783i	$0.0292551\pi$
$198$		0			0
$199$			1.94377i			0.137790i	0.997624	+	0.0688949i	$0.0219473\pi$
$199$			1.94377i			0.137790i	−0.997624	+	0.0688949i	$0.978053\pi$
$200$	−1.48522	−	14.0639i	−0.105021	−	0.994470i
$201$		0			0
$202$	−15.8820	−	6.26882i	−1.11745	−	0.441073i
$203$	0.218755	−	0.218755i	0.0153536	−	0.0153536i
$204$		0			0
$205$	20.2157	−	4.60173i	1.41193	−	0.321399i
$206$	18.3963	−	7.98378i	1.28173	−	0.556256i
$207$		0			0
$208$	4.38514	−	5.01634i	0.304055	−	0.347820i
$209$	5.86061			0.405387
$210$		0			0
$211$	8.48794	−	8.48794i	0.584334	−	0.584334i	−0.351757	−	0.936091i	$-0.614416\pi$
$211$	8.48794	−	8.48794i	0.584334	−	0.584334i	0.936091	+	0.351757i	$0.114416\pi$
$212$	−0.271185	−	8.08751i	−0.0186251	−	0.555453i
$213$		0			0
$214$	7.14776	−	18.1088i	0.488611	−	1.23789i
$215$	−6.52391	−	4.10454i	−0.444927	−	0.279927i
$216$		0			0
$217$	−2.92703			−0.198700
$218$	−7.87388	+	19.9484i	−0.533286	+	1.35108i
$219$		0			0
$220$	6.44317	+	24.4828i	0.434398	+	1.65063i
$221$	−4.31659	+	4.31659i	−0.290366	+	0.290366i
$222$		0			0
$223$			8.72387i			0.584193i	0.956389	+	0.292097i	$0.0943529\pi$
$223$			8.72387i			0.584193i	−0.956389	+	0.292097i	$0.905647\pi$
$224$	−2.23716	−	4.33420i	−0.149477	−	0.289591i
$225$		0			0
$226$	7.88364	+	18.1656i	0.524412	+	1.20836i
$227$	−2.84056	−	2.84056i	−0.188534	−	0.188534i	0.606528	−	0.795062i	$-0.292562\pi$
$227$	−2.84056	−	2.84056i	−0.188534	−	0.188534i	−0.795062	+	0.606528i	$0.792562\pi$
$228$		0			0
$229$	−15.6513	−	15.6513i	−1.03426	−	1.03426i	−0.999392	−	0.0348732i	$-0.988897\pi$
$229$	−15.6513	−	15.6513i	−1.03426	−	1.03426i	−0.0348732	−	0.999392i	$-0.511103\pi$
$230$	−9.31166	−	12.6837i	−0.613993	−	0.836338i
$231$		0			0
$232$	−0.434989	−	0.916881i	−0.0285584	−	0.0601962i
$233$	−8.00603			−0.524492			−0.262246	−	0.965001i	$-0.584463\pi$
$233$	−8.00603			−0.524492			−0.262246	+	0.965001i	$0.584463\pi$
$234$		0			0
$235$	14.8195	−	3.37339i	0.966719	−	0.220056i
$236$	−9.35607	+	0.313721i	−0.609028	+	0.0204215i
$237$		0			0
$238$	1.77911	+	4.09946i	0.115323	+	0.265728i
$239$	−12.8515			−0.831296			−0.415648	−	0.909526i	$-0.636445\pi$
$239$	−12.8515			−0.831296			−0.415648	+	0.909526i	$0.636445\pi$
$240$		0			0
$241$	−25.1326			−1.61894			−0.809468	−	0.587164i	$-0.800244\pi$
$241$	−25.1326			−1.61894			−0.809468	+	0.587164i	$0.800244\pi$
$242$	−11.8492	−	27.3032i	−0.761697	−	1.75511i
$243$		0			0
$244$	0.326879	+	9.74846i	0.0209263	+	0.624081i
$245$	3.10515	+	13.6411i	0.198381	+	0.871500i
$246$		0			0
$247$	−1.72446			−0.109725
$248$	−3.22395	+	9.04427i	−0.204721	+	0.574311i
$249$		0			0
$250$	−13.9518	−	7.43964i	−0.882387	−	0.470524i
$251$	10.6223	+	10.6223i	0.670476	+	0.670476i	0.957826	−	0.287350i	$-0.0927743\pi$
$251$	10.6223	+	10.6223i	0.670476	+	0.670476i	−0.287350	+	0.957826i	$0.592774\pi$
$252$		0			0
$253$	19.9174	+	19.9174i	1.25219	+	1.25219i
$254$	−12.4100	−	28.5953i	−0.778673	−	1.79423i
$255$		0			0
$256$	−15.8564	+	2.13878i	−0.991025	+	0.133674i
$257$			25.2426i			1.57459i	0.616576	+	0.787295i	$0.288519\pi$
$257$			25.2426i			1.57459i	−0.616576	+	0.787295i	$0.711481\pi$
$258$		0			0
$259$	4.72610	−	4.72610i	0.293665	−	0.293665i
$260$	−1.89588	−	7.20396i	−0.117577	−	0.446770i
$261$		0			0
$262$	−0.447245	+	1.13309i	−0.0276309	+	0.0700027i
$263$	−29.1656			−1.79843			−0.899215	−	0.437506i	$-0.855862\pi$
$263$	−29.1656			−1.79843			−0.899215	+	0.437506i	$0.855862\pi$
$264$		0			0
$265$	−7.65768	−	4.81785i	−0.470408	−	0.295958i
$266$	−0.463484	+	1.17423i	−0.0284180	+	0.0719968i
$267$		0			0
$268$	−23.2768	+	0.780503i	−1.42186	+	0.0476768i
$269$	−9.01830	+	9.01830i	−0.549855	+	0.549855i	−0.926399	−	0.376544i	$-0.877113\pi$
$269$	−9.01830	+	9.01830i	−0.549855	+	0.549855i	0.376544	+	0.926399i	$0.377113\pi$
$270$		0			0
$271$	21.2020			1.28793			0.643966	−	0.765054i	$-0.277288\pi$
$271$	21.2020			1.28793			0.643966	+	0.765054i	$0.277288\pi$
$272$	14.6266	−	0.981999i	0.886865	−	0.0595424i
$273$		0			0
$274$	−11.8215	+	5.13036i	−0.714160	+	0.309937i
$275$	26.7053	+	9.37948i	1.61039	+	0.565604i
$276$		0			0
$277$	−0.546633	+	0.546633i	−0.0328440	+	0.0328440i	−0.723338	−	0.690494i	$-0.757393\pi$
$277$	−0.546633	+	0.546633i	−0.0328440	+	0.0328440i	0.690494	+	0.723338i	$0.257393\pi$
$278$	22.7845	+	8.99331i	1.36652	+	0.539383i
$279$		0			0
$280$	−5.41492	−	0.645255i	−0.323603	−	0.0385613i
$281$		−	20.8573i		−	1.24424i	−0.782922	−	0.622120i	$-0.786271\pi$
$281$		−	20.8573i		−	1.24424i	0.782922	−	0.622120i	$-0.213729\pi$
$282$		0			0
$283$	23.2768	−	23.2768i	1.38366	−	1.38366i	0.545652	−	0.838012i	$-0.316282\pi$
$283$	23.2768	−	23.2768i	1.38366	−	1.38366i	0.838012	−	0.545652i	$-0.183718\pi$
$284$	−18.2310	−	17.0481i	−1.08181	−	1.01162i
$285$		0			0
$286$	5.30891	+	12.2329i	0.313922	+	0.723344i
$287$		−	7.99462i		−	0.471907i
$288$		0			0
$289$	3.56873			0.209925
$290$	−1.12152	−	0.171935i	−0.0658576	−	0.0100964i
$291$		0			0
$292$	−15.7555	+	16.8488i	−0.922023	+	0.986001i
$293$	−6.89558	+	6.89558i	−0.402844	+	0.402844i	−0.879234	−	0.476390i	$-0.841945\pi$
$293$	−6.89558	+	6.89558i	−0.402844	+	0.402844i	0.476390	+	0.879234i	$0.341945\pi$
$294$		0			0
$295$	−5.57355	+	8.85881i	−0.324505	+	0.515780i
$296$	−9.39772	−	19.8088i	−0.546231	−	1.15136i
$297$		0			0
$298$	−16.7770	−	6.62208i	−0.971864	−	0.383607i
$299$	−5.86061	−	5.86061i	−0.338928	−	0.338928i
$300$		0			0
$301$	−2.10159	+	2.10159i	−0.121134	+	0.121134i
$302$	1.00883	+	2.32456i	0.0580517	+	0.133763i
$303$		0			0
$304$	3.11778	+	2.72547i	0.178817	+	0.156317i
$305$	9.23035	+	5.80731i	0.528529	+	0.332525i
$306$		0			0
$307$	10.3313	+	10.3313i	0.589637	+	0.589637i	0.937533	−	0.347896i	$-0.113104\pi$
$307$	10.3313	+	10.3313i	0.589637	+	0.589637i	−0.347896	+	0.937533i	$0.613104\pi$
$308$	9.75656	−	0.327150i	0.555931	−	0.0186411i
$309$		0			0
$310$	6.35287	+	8.65343i	0.360819	+	0.491482i
$311$			16.7703i			0.950959i	0.879727	+	0.475479i	$0.157725\pi$
$311$			16.7703i			0.950959i	−0.879727	+	0.475479i	$0.842275\pi$
$312$		0			0
$313$	3.04102			0.171888			0.0859442	−	0.996300i	$-0.472609\pi$
$313$	3.04102			0.171888			0.0859442	+	0.996300i	$0.472609\pi$
$314$	−19.2656	−	7.60436i	−1.08722	−	0.429139i
$315$		0			0
$316$	0.119334	−	0.127615i	0.00671307	−	0.00717889i
$317$	−13.9469	−	13.9469i	−0.783337	−	0.783337i	0.197056	−	0.980392i	$-0.436862\pi$
$317$	−13.9469	−	13.9469i	−0.783337	−	0.783337i	−0.980392	+	0.197056i	$0.936862\pi$
$318$		0			0
$319$	2.03112			0.113721
$320$	−7.95800	+	16.0209i	−0.444865	+	0.895597i
$321$		0			0
$322$	−5.56580	+	2.41549i	−0.310170	+	0.134610i
$323$	−2.68287	−	2.68287i	−0.149279	−	0.149279i
$324$		0			0
$325$	−7.85794	−	2.75988i	−0.435880	−	0.153090i
$326$	−5.22748	−	2.06335i	−0.289523	−	0.114278i
$327$		0			0
$328$	−24.7027	−	8.80559i	−1.36398	−	0.486208i
$329$		−	5.86061i		−	0.323106i
$330$		0			0
$331$	−23.8684	−	23.8684i	−1.31193	−	1.31193i	−0.919993	−	0.391934i	$-0.871806\pi$
$331$	−23.8684	−	23.8684i	−1.31193	−	1.31193i	−0.391934	−	0.919993i	$-0.628194\pi$
$332$	−20.2742	+	0.679822i	−1.11269	+	0.0373101i
$333$		0			0
$334$	−10.4895	+	4.55231i	−0.573960	+	0.249091i
$335$	−13.8664	+	22.0397i	−0.757600	+	1.20416i
$336$		0			0
$337$		−	5.23322i		−	0.285072i	−0.989790	−	0.142536i	$-0.954474\pi$
$337$		−	5.23322i		−	0.285072i	0.989790	−	0.142536i	$-0.0455256\pi$
$338$	5.75709	+	13.2656i	0.313144	+	0.721551i
$339$		0			0
$340$	8.25816	−	14.1573i	0.447862	−	0.767786i
$341$	−13.5886	−	13.5886i	−0.735864	−	0.735864i
$342$		0			0
$343$	11.4302			0.617174
$344$	4.17896	+	8.80852i	0.225315	+	0.474924i
$345$		0			0
$346$	20.3298	+	8.02441i	1.09294	+	0.431395i
$347$	−1.44623	+	1.44623i	−0.0776379	+	0.0776379i	−0.744859	−	0.667221i	$-0.767483\pi$
$347$	−1.44623	+	1.44623i	−0.0776379	+	0.0776379i	0.667221	+	0.744859i	$0.267483\pi$
$348$		0			0
$349$	11.6513	−	11.6513i	0.623678	−	0.623678i	−0.322792	−	0.946470i	$-0.604621\pi$
$349$	11.6513	−	11.6513i	0.623678	−	0.623678i	0.946470	+	0.322792i	$0.104621\pi$
$350$	−3.99125	+	4.60891i	−0.213341	+	0.246357i
$351$		0			0
$352$	9.73540	−	30.5073i	0.518899	−	1.62604i
$353$		−	20.0437i		−	1.06682i	−0.845857	−	0.533409i	$-0.820911\pi$
$353$		−	20.0437i		−	1.06682i	0.845857	−	0.533409i	$-0.179089\pi$
$354$		0			0
$355$	−27.2102	+	6.19391i	−1.44417	+	0.328738i
$356$	8.56126	+	8.00575i	0.453746	+	0.424304i
$357$		0			0
$358$	−6.73372	+	17.0598i	−0.355888	+	0.901640i
$359$		−	9.69156i		−	0.511501i	−0.966743	−	0.255750i	$-0.917677\pi$
$359$		−	9.69156i		−	0.511501i	0.966743	−	0.255750i	$-0.0823225\pi$
$360$		0			0
$361$			17.9282i			0.943590i
$362$	−12.7653	−	5.03861i	−0.670928	−	0.264823i
$363$		0			0
$364$	−2.87083	+	0.0962627i	−0.150472	+	0.00504553i
$365$	5.72429	+	25.1472i	0.299623	+	1.31626i
$366$		0			0
$367$		−	14.0169i		−	0.731677i	−0.930678	−	0.365838i	$-0.880782\pi$
$367$		−	14.0169i		−	0.731677i	0.930678	−	0.365838i	$-0.119218\pi$
$368$	1.33325	+	19.8584i	0.0695007	+	1.03519i
$369$		0			0
$370$	−24.2298	−	3.71458i	−1.25965	−	0.193112i
$371$	−2.46682	+	2.46682i	−0.128071	+	0.128071i
$372$		0			0
$373$	7.77707	−	7.77707i	0.402681	−	0.402681i	−0.476495	−	0.879177i	$-0.658093\pi$
$373$	7.77707	−	7.77707i	0.402681	−	0.402681i	0.879177	+	0.476495i	$0.158093\pi$
$374$	−10.7721	+	27.2910i	−0.557012	+	1.41118i
$375$		0			0
$376$	−18.1088	−	6.45512i	−0.933890	−	0.332897i
$377$	−0.597650			−0.0307806
$378$		0			0
$379$	−6.05737	−	6.05737i	−0.311146	−	0.311146i	0.534207	−	0.845354i	$-0.320610\pi$
$379$	−6.05737	−	6.05737i	−0.311146	−	0.311146i	−0.845354	+	0.534207i	$0.820610\pi$
$380$	4.47744	−	1.17834i	0.229688	−	0.0604473i
$381$		0			0
$382$	6.06837	−	2.63360i	0.310485	−	0.134747i
$383$		−	12.9186i		−	0.660110i	−0.943962	−	0.330055i	$-0.892933\pi$
$383$		−	12.9186i		−	0.660110i	0.943962	−	0.330055i	$-0.107067\pi$
$384$		0			0
$385$	5.81213	−	9.23802i	0.296213	−	0.470813i
$386$	4.36469	+	10.0572i	0.222157	+	0.511897i
$387$		0			0
$388$	−23.1353	−	21.6341i	−1.17452	−	1.09830i
$389$	−11.4412	−	11.4412i	−0.580091	−	0.580091i	0.354837	−	0.934928i	$-0.384536\pi$
$389$	−11.4412	−	11.4412i	−0.580091	−	0.580091i	−0.934928	+	0.354837i	$0.884536\pi$
$390$		0			0
$391$		−	18.2356i		−	0.922212i
$392$	5.94183	−	16.6689i	0.300108	−	0.841904i
$393$		0			0
$394$	−9.31691	+	23.6043i	−0.469379	+	1.18917i
$395$	−0.0433565	−	0.190468i	−0.00218150	−	0.00958347i
$396$		0			0
$397$	11.9170	+	11.9170i	0.598098	+	0.598098i	0.939806	−	0.341708i	$-0.111005\pi$
$397$	11.9170	+	11.9170i	0.598098	+	0.598098i	−0.341708	+	0.939806i	$0.611005\pi$
$398$	−1.09437	−	2.52167i	−0.0548559	−	0.126400i
$399$		0			0
$400$	9.84501	+	17.4091i	0.492250	+	0.870454i
$401$	−30.1293			−1.50458			−0.752292	−	0.658830i	$-0.771052\pi$
$401$	−30.1293			−1.50458			−0.752292	+	0.658830i	$0.771052\pi$
$402$		0			0
$403$	3.99839	+	3.99839i	0.199174	+	0.199174i
$404$	24.1333	−	0.809222i	1.20068	−	0.0402603i
$405$		0			0
$406$	−0.160631	+	0.406956i	−0.00797196	+	0.0201969i
$407$	43.8814			2.17512
$408$		0			0
$409$		−	5.49693i		−	0.271806i	−0.990722	−	0.135903i	$-0.956607\pi$
$409$		−	5.49693i		−	0.271806i	0.990722	−	0.135903i	$-0.0433935\pi$
$410$	−23.6352	+	17.3516i	−1.16726	+	0.856937i
$411$		0			0
$412$	−19.3707	+	20.7149i	−0.954328	+	1.02055i
$413$	2.85375	+	2.85375i	0.140424	+	0.140424i
$414$		0			0
$415$	−12.0777	+	19.1967i	−0.592869	+	0.942329i
$416$	−2.86460	+	8.97665i	−0.140449	+	0.440116i
$417$		0			0
$418$	−7.60303	+	3.29962i	−0.371876	+	0.161390i
$419$	−16.4829	+	16.4829i	−0.805244	+	0.805244i	−0.983910	−	0.178665i	$-0.942822\pi$
$419$	−16.4829	+	16.4829i	−0.805244	+	0.805244i	0.178665	+	0.983910i	$0.442822\pi$
$420$		0			0
$421$	10.4079	+	10.4079i	0.507248	+	0.507248i	0.913681	−	0.406432i	$-0.133227\pi$
$421$	10.4079	+	10.4079i	0.507248	+	0.507248i	−0.406432	+	0.913681i	$0.633227\pi$
$422$	−6.23264	+	15.7903i	−0.303400	+	0.768662i
$423$		0			0
$424$	4.90521	+	10.3393i	0.238218	+	0.502122i
$425$	−7.93143	−	16.5189i	−0.384731	−	0.801285i
$426$		0			0
$427$	2.97344	−	2.97344i	0.143895	−	0.143895i
$428$	0.922682	+	27.5170i	0.0445995	+	1.33009i
$429$		0			0
$430$	10.7745	+	1.65179i	0.519590	+	0.0796564i
$431$	3.91881			0.188763			0.0943813	−	0.995536i	$-0.469913\pi$
$431$	3.91881			0.188763			0.0943813	+	0.995536i	$0.469913\pi$
$432$		0			0
$433$		−	17.0997i		−	0.821757i	−0.911690	−	0.410878i	$-0.865222\pi$
$433$		−	17.0997i		−	0.821757i	0.911690	−	0.410878i	$-0.134778\pi$
$434$	3.79726	−	1.64796i	0.182274	−	0.0791048i
$435$		0			0
$436$	−1.01641	−	30.3124i	−0.0486774	−	1.45170i
$437$	3.64252	−	3.64252i	0.174245	−	0.174245i
$438$		0			0
$439$			21.5155i			1.02688i	0.858126	+	0.513440i	$0.171629\pi$
$439$			21.5155i			1.02688i	−0.858126	+	0.513440i	$0.828371\pi$
$440$	−22.1430	−	28.1341i	−1.05562	−	1.34124i
$441$		0			0
$442$	3.16965	−	8.03027i	0.150765	−	0.381961i
$443$	2.02944	−	2.02944i	0.0964216	−	0.0964216i	−0.657251	−	0.753672i	$-0.728281\pi$
$443$	2.02944	−	2.02944i	0.0964216	−	0.0964216i	0.753672	+	0.657251i	$0.228281\pi$
$444$		0			0
$445$	12.7779	−	2.90864i	0.605729	−	0.137883i
$446$	−4.91168	−	11.3176i	−0.232575	−	0.535902i
$447$		0			0
$448$	5.34252	+	4.36324i	0.252410	+	0.206144i
$449$	−7.75432			−0.365949			−0.182974	−	0.983118i	$-0.558573\pi$
$449$	−7.75432			−0.365949			−0.182974	+	0.983118i	$0.558573\pi$
$450$		0			0
$451$	37.1147	−	37.1147i	1.74766	−	1.74766i
$452$	−20.4551	−	19.1278i	−0.962125	−	0.899696i
$453$		0			0
$454$	5.28436	+	2.08580i	0.248007	+	0.0978916i
$455$	−1.71020	+	2.71825i	−0.0801752	+	0.127434i
$456$		0			0
$457$	−17.0997			−0.799888			−0.399944	−	0.916540i	$-0.630970\pi$
$457$	−17.0997			−0.799888			−0.399944	+	0.916540i	$0.630970\pi$
$458$	29.1165	+	11.4926i	1.36052	+	0.537015i
$459$		0			0
$460$	19.2212	+	11.2121i	0.896195	+	0.522765i
$461$	22.1258	−	22.1258i	1.03050	−	1.03050i	0.0309819	−	0.999520i	$-0.490137\pi$
$461$	22.1258	−	22.1258i	1.03050	−	1.03050i	0.999520	−	0.0309819i	$-0.00986341\pi$
$462$		0			0
$463$			22.2055i			1.03198i	0.856596	+	0.515988i	$0.172575\pi$
$463$			22.2055i			1.03198i	−0.856596	+	0.515988i	$0.827425\pi$
$464$	1.08053	+	0.944573i	0.0501626	+	0.0438507i
$465$		0			0
$466$	10.3863	−	4.50752i	0.481136	−	0.208807i
$467$	−18.3064	−	18.3064i	−0.847118	−	0.847118i	0.142655	−	0.989773i	$-0.454436\pi$
$467$	−18.3064	−	18.3064i	−0.847118	−	0.847118i	−0.989773	+	0.142655i	$0.954436\pi$
$468$		0			0
$469$	7.09981	+	7.09981i	0.327839	+	0.327839i
$470$	−17.3262	+	12.7200i	−0.799200	+	0.586728i
$471$		0			0
$472$	11.9611	−	5.67461i	0.550554	−	0.261195i
$473$	−19.5131			−0.897214
$474$		0			0
$475$	1.71533	−	4.88391i	0.0787049	−	0.224089i
$476$	−4.61612	−	4.31659i	−0.211579	−	0.197851i
$477$		0			0
$478$	16.6724	−	7.23562i	0.762578	−	0.330949i
$479$	26.4619			1.20907			0.604537	−	0.796577i	$-0.293358\pi$
$479$	26.4619			1.20907			0.604537	+	0.796577i	$0.293358\pi$
$480$		0			0
$481$	−12.9119			−0.588734
$482$	32.6048	−	14.1501i	1.48511	−	0.644519i
$483$		0			0
$484$	30.7442	+	28.7493i	1.39747	+	1.30679i
$485$	−34.5299	+	7.86009i	−1.56792	+	0.356908i
$486$		0			0
$487$	−25.9375			−1.17534			−0.587670	−	0.809101i	$-0.699955\pi$
$487$	−25.9375			−1.17534			−0.587670	+	0.809101i	$0.699955\pi$
$488$	−5.91261	−	12.4627i	−0.267651	−	0.564162i
$489$		0			0
$490$	−11.7085	−	15.9485i	−0.528937	−	0.720481i
$491$	−8.15551	−	8.15551i	−0.368053	−	0.368053i	0.498714	−	0.866767i	$-0.333806\pi$
$491$	−8.15551	−	8.15551i	−0.368053	−	0.368053i	−0.866767	+	0.498714i	$0.833806\pi$
$492$		0			0
$493$	−0.929808	−	0.929808i	−0.0418764	−	0.0418764i
$494$	2.23716	−	0.970901i	0.100655	−	0.0436829i
$495$		0			0
$496$	−0.909610	−	13.5483i	−0.0408427	−	0.608339i
$497$			10.7607i			0.482684i
$498$		0			0
$499$	−20.6267	+	20.6267i	−0.923379	+	0.923379i	−0.997267	−	0.0738876i	$-0.976459\pi$
$499$	−20.6267	+	20.6267i	−0.923379	+	0.923379i	0.0738876	+	0.997267i	$0.476459\pi$
$500$	22.2884	+	1.79644i	0.996768	+	0.0803392i
$501$		0			0
$502$	−19.7610	−	7.79991i	−0.881977	−	0.348127i
$503$	8.69417			0.387654			0.193827	−	0.981036i	$-0.437910\pi$
$503$	8.69417			0.387654			0.193827	+	0.981036i	$0.437910\pi$
$504$		0			0
$505$	14.3766	−	22.8507i	0.639749	−	1.01684i
$506$	−37.0528	−	14.6252i	−1.64720	−	0.650170i
$507$		0			0
$508$	32.1992	+	30.1099i	1.42861	+	1.33591i
$509$	17.2537	−	17.2537i	0.764757	−	0.764757i	−0.212421	−	0.977178i	$-0.568135\pi$
$509$	17.2537	−	17.2537i	0.764757	−	0.764757i	0.977178	+	0.212421i	$0.0681349\pi$
$510$		0			0
$511$	9.94484			0.439934
$512$	19.3665	−	11.7021i	0.855887	−	0.517163i
$513$		0			0
$514$	−14.2120	−	32.7475i	−0.626864	−	1.44443i
$515$	7.03777	+	30.9174i	0.310121	+	1.36238i
$516$		0			0
$517$	27.2076	−	27.2076i	1.19659	−	1.19659i
$518$	−3.47034	+	8.79208i	−0.152478	+	0.386302i
$519$		0			0
$520$	6.51548	+	8.27835i	0.285723	+	0.363030i
$521$			15.8755i			0.695520i	0.937584	+	0.347760i	$0.113058\pi$
$521$			15.8755i			0.695520i	−0.937584	+	0.347760i	$0.886942\pi$
$522$		0			0
$523$	−19.2784	+	19.2784i	−0.842987	+	0.842987i	−0.989246	−	0.146259i	$-0.953277\pi$
$523$	−19.2784	+	19.2784i	−0.842987	+	0.842987i	0.146259	+	0.989246i	$0.453277\pi$
$524$	−0.0577335	−	1.72178i	−0.00252210	−	0.0752162i
$525$		0			0
$526$	37.8369	−	16.4207i	1.64977	−	0.715978i
$527$			12.4412i			0.541946i
$528$		0			0
$529$	1.75830			0.0764479
$530$	12.6469	+	1.93885i	0.549347	+	0.0842183i
$531$		0			0
$532$	−0.0598297	−	1.78429i	−0.00259394	−	0.0773589i
$533$	−10.9208	+	10.9208i	−0.473034	+	0.473034i
$534$		0			0
$535$	26.0546	+	16.3923i	1.12644	+	0.708701i
$536$	29.7578	−	14.1178i	1.28534	−	0.609796i
$537$		0			0
$538$	6.62208	−	16.7770i	0.285498	−	0.723307i
$539$	25.0442	+	25.0442i	1.07873	+	1.07873i
$540$		0			0
$541$	−9.89164	+	9.89164i	−0.425275	+	0.425275i	−0.887015	−	0.461740i	$-0.847225\pi$
$541$	−9.89164	+	9.89164i	−0.425275	+	0.425275i	0.461740	+	0.887015i	$0.347225\pi$
$542$	−27.5056	+	11.9371i	−1.18147	+	0.512742i
$543$		0			0
$544$	−18.4223	+	9.50894i	−0.789849	+	0.407693i
$545$	−28.7013	−	18.0575i	−1.22943	−	0.773500i
$546$		0			0
$547$	18.9058	+	18.9058i	0.808355	+	0.808355i	0.984385	−	0.176029i	$-0.0563254\pi$
$547$	18.9058	+	18.9058i	0.808355	+	0.808355i	−0.176029	+	0.984385i	$0.556325\pi$
$548$	12.4476	−	13.3113i	0.531736	−	0.568632i
$549$		0			0
$550$	−39.9259	+	2.86744i	−1.70245	+	0.122268i
$551$		−	0.371455i		−	0.0158245i
$552$		0			0
$553$	−0.0753234			−0.00320308
$554$	0.401389	−	1.01692i	0.0170534	−	0.0432046i
$555$		0			0
$556$	−34.6219	+	1.16092i	−1.46830	+	0.0492339i
$557$	−14.2215	−	14.2215i	−0.602582	−	0.602582i	0.338415	−	0.940997i	$-0.390109\pi$
$557$	−14.2215	−	14.2215i	−0.602582	−	0.602582i	−0.940997	+	0.338415i	$0.890109\pi$
$558$		0			0
$559$	5.74166			0.242846
$560$	7.38812	−	2.21159i	0.312205	−	0.0934569i
$561$		0			0
$562$	11.7430	+	27.0583i	0.495348	+	1.14139i
$563$	−13.6907	−	13.6907i	−0.576993	−	0.576993i	0.357080	−	0.934074i	$-0.383772\pi$
$563$	−13.6907	−	13.6907i	−0.576993	−	0.576993i	−0.934074	+	0.357080i	$0.883772\pi$
$564$		0			0
$565$	−30.5296	+	6.94950i	−1.28439	+	0.292368i
$566$	−17.0920	+	43.3025i	−0.718431	+	1.82014i
$567$		0			0
$568$	33.2497	+	11.8523i	1.39513	+	0.497311i
$569$			0.878871i			0.0368442i	0.999830	+	0.0184221i	$0.00586427\pi$
$569$			0.878871i			0.0368442i	−0.999830	+	0.0184221i	$0.994136\pi$
$570$		0			0
$571$	−3.72964	−	3.72964i	−0.156081	−	0.156081i	0.624747	−	0.780827i	$-0.285202\pi$
$571$	−3.72964	−	3.72964i	−0.156081	−	0.156081i	−0.780827	+	0.624747i	$0.785202\pi$
$572$	−13.7746	−	12.8808i	−0.575945	−	0.538574i
$573$		0			0
$574$	4.50110	+	10.3715i	0.187872	+	0.432898i
$575$	22.4276	−	10.7684i	0.935296	−	0.449075i
$576$		0			0
$577$			33.4588i			1.39291i	0.717601	+	0.696454i	$0.245240\pi$
$577$			33.4588i			1.39291i	−0.717601	+	0.696454i	$0.754760\pi$
$578$	−4.62974	+	2.00925i	−0.192572	+	0.0835738i
$579$		0			0
$580$	1.55175	−	0.408378i	0.0644331	−	0.0169570i
$581$	6.18397	+	6.18397i	0.256554	+	0.256554i
$582$		0			0
$583$	−22.9042			−0.948597
$584$	10.9537	−	30.7287i	0.453266	−	1.27156i
$585$		0			0
$586$	5.06338	−	12.8280i	0.209166	−	0.529921i
$587$	−8.81152	+	8.81152i	−0.363690	+	0.363690i	−0.865170	−	0.501479i	$-0.832789\pi$
$587$	−8.81152	+	8.81152i	−0.363690	+	0.363690i	0.501479	+	0.865170i	$0.332789\pi$
$588$		0			0
$589$	−2.48510	+	2.48510i	−0.102397	+	0.102397i
$590$	2.24297	−	14.6306i	0.0923415	−	0.602333i
$591$		0			0
$592$	23.3444	+	20.4070i	0.959449	+	0.838723i
$593$		−	3.15239i		−	0.129453i	−0.997903	−	0.0647267i	$-0.979382\pi$
$593$		−	3.15239i		−	0.129453i	0.997903	−	0.0647267i	$-0.0206175\pi$
$594$		0			0
$595$	−6.88966	+	1.56830i	−0.282448	+	0.0642942i
$596$	25.4933	−	0.854823i	1.04425	−	0.0350149i
$597$		0			0
$598$	10.9027	+	4.30341i	0.445843	+	0.175980i
$599$			39.8254i			1.62722i	0.581410	+	0.813611i	$0.302501\pi$
$599$			39.8254i			1.62722i	−0.581410	+	0.813611i	$0.697499\pi$
$600$		0			0
$601$			23.2146i			0.946942i	0.880810	+	0.473471i	$0.156999\pi$
$601$			23.2146i			0.946942i	−0.880810	+	0.473471i	$0.843001\pi$
$602$	1.54319	−	3.90965i	0.0628956	−	0.159345i
$603$		0			0
$604$	−2.61753	−	2.44769i	−0.106506	−	0.0995950i
$605$	45.8864	−	10.4452i	1.86555	−	0.424658i
$606$		0			0
$607$		−	11.0584i		−	0.448845i	−0.974492	−	0.224423i	$-0.927950\pi$
$607$		−	11.0584i		−	0.448845i	0.974492	−	0.224423i	$-0.0720496\pi$
$608$	−5.57921	−	1.78042i	−0.226267	−	0.0722057i
$609$		0			0
$610$	−15.2442	−	2.33704i	−0.617221	−	0.0946239i
$611$	−8.00575	+	8.00575i	−0.323878	+	0.323878i
$612$		0			0
$613$	−20.3006	+	20.3006i	−0.819932	+	0.819932i	−0.986098	−	0.166166i	$-0.946861\pi$
$613$	−20.3006	+	20.3006i	−0.819932	+	0.819932i	0.166166	+	0.986098i	$0.446861\pi$
$614$	−19.2196	−	7.58619i	−0.775638	−	0.306154i
$615$		0			0
$616$	−12.4731	+	5.91752i	−0.502555	+	0.238423i
$617$	−9.58356			−0.385819			−0.192910	−	0.981217i	$-0.561792\pi$
$617$	−9.58356			−0.385819			−0.192910	+	0.981217i	$0.561792\pi$
$618$		0			0
$619$	29.0190	+	29.0190i	1.16637	+	1.16637i	0.983053	+	0.183320i	$0.0586844\pi$
$619$	29.0190	+	29.0190i	1.16637	+	1.16637i	0.183320	+	0.983053i	$0.441316\pi$
$620$	−13.1137	−	7.64941i	−0.526657	−	0.307208i
$621$		0			0
$622$	−9.44197	−	21.7563i	−0.378589	−	0.872349i
$623$		−	5.05320i		−	0.202452i
$624$		0			0
$625$	15.6327	−	19.5095i	0.625307	−	0.780379i
$626$	−3.94514	+	1.71214i	−0.157679	+	0.0684309i
$627$		0			0
$628$	29.2748	−	0.981622i	1.16819	−	0.0391710i
$629$	−20.0880	−	20.0880i	−0.800962	−	0.800962i
$630$		0			0
$631$		−	33.6303i		−	1.33880i	−0.742902	−	0.669400i	$-0.766551\pi$
$631$		−	33.6303i		−	1.33880i	0.742902	−	0.669400i	$-0.233449\pi$
$632$	−0.0829643	+	0.232743i	−0.00330014	+	0.00925802i
$633$		0			0
$634$	25.9458	+	10.2411i	1.03044	+	0.406727i
$635$	48.0581	−	10.9395i	1.90713	−	0.434122i
$636$		0			0
$637$	−7.36916	−	7.36916i	−0.291977	−	0.291977i
$638$	−2.63500	+	1.14356i	−0.104321	+	0.0452738i
$639$		0			0
$640$	1.30394	−	25.2646i	0.0515428	−	0.998671i
$641$	48.7259			1.92456			0.962280	−	0.272062i	$-0.0877057\pi$
$641$	48.7259			1.92456			0.962280	+	0.272062i	$0.0877057\pi$
$642$		0			0
$643$	−25.7142	−	25.7142i	−1.01407	−	1.01407i	−0.999900	−	0.0141702i	$-0.995489\pi$
$643$	−25.7142	−	25.7142i	−1.01407	−	1.01407i	−0.0141702	−	0.999900i	$-0.504511\pi$
$644$	5.86061	−	6.26728i	0.230940	−	0.246965i
$645$		0			0
$646$	4.99102	+	1.97002i	0.196369	+	0.0775092i
$647$	38.6931			1.52118			0.760591	−	0.649231i	$-0.224909\pi$
$647$	38.6931			1.52118			0.760591	+	0.649231i	$0.224909\pi$
$648$		0			0
$649$			26.4968i			1.04009i
$650$	11.7480	−	0.843733i	0.460796	−	0.0330939i
$651$		0			0
$652$	7.94336	−	0.266351i	0.311086	−	0.0104311i
$653$	−4.04183	−	4.04183i	−0.158169	−	0.158169i	0.623586	−	0.781755i	$-0.285675\pi$
$653$	−4.04183	−	4.04183i	−0.158169	−	0.158169i	−0.781755	+	0.623586i	$0.785675\pi$
$654$		0			0
$655$	−1.63027	−	1.02569i	−0.0636999	−	0.0400770i
$656$	37.0047	−	2.48443i	1.44479	−	0.0970006i
$657$		0			0
$658$	3.29962	+	7.60303i	0.128633	+	0.296397i
$659$	−5.08341	+	5.08341i	−0.198021	+	0.198021i	−0.799151	−	0.601130i	$-0.794717\pi$
$659$	−5.08341	+	5.08341i	−0.198021	+	0.198021i	0.601130	+	0.799151i	$0.294717\pi$
$660$		0			0
$661$	−9.82288	−	9.82288i	−0.382066	−	0.382066i	0.489780	−	0.871846i	$-0.337077\pi$
$661$	−9.82288	−	9.82288i	−0.382066	−	0.382066i	−0.871846	+	0.489780i	$0.837077\pi$
$662$	44.4030	+	17.5264i	1.72577	+	0.681184i
$663$		0			0
$664$	25.9192	−	12.2967i	1.00586	−	0.477203i
$665$	−1.68946	−	1.06293i	−0.0655145	−	0.0412187i
$666$		0			0
$667$	1.26239	−	1.26239i	0.0488801	−	0.0488801i
$668$	11.0451	−	11.8115i	0.427348	−	0.457001i
$669$		0			0
$670$	5.58024	−	36.3993i	0.215584	−	1.40623i
$671$	27.6081			1.06580
$672$		0			0
$673$		−	10.6794i		−	0.411659i	−0.978588	−	0.205830i	$-0.934011\pi$
$673$		−	10.6794i		−	0.411659i	0.978588	−	0.205830i	$-0.0659893\pi$
$674$	2.94639	+	6.78910i	0.113491	+	0.261507i
$675$		0			0
$676$	−14.9374	−	13.9682i	−0.574517	−	0.537239i
$677$	27.5019	−	27.5019i	1.05698	−	1.05698i	0.0587084	−	0.998275i	$-0.481302\pi$
$677$	27.5019	−	27.5019i	1.05698	−	1.05698i	0.998275	−	0.0587084i	$-0.0186982\pi$
$678$		0			0
$679$			13.6554i			0.524045i
$680$	−2.74262	+	23.0158i	−0.105175	+	0.882617i
$681$		0			0
$682$	25.2792	+	9.97802i	0.967992	+	0.382078i
$683$	30.3888	−	30.3888i	1.16279	−	1.16279i	0.178932	−	0.983861i	$-0.442736\pi$
$683$	30.3888	−	30.3888i	1.16279	−	1.16279i	0.983861	−	0.178932i	$-0.0572642\pi$
$684$		0			0
$685$	−4.52246	−	19.8675i	−0.172794	−	0.759097i
$686$	−14.8285	+	6.43540i	−0.566156	+	0.245705i
$687$		0			0
$688$	−10.3808	−	9.07456i	−0.395762	−	0.345964i
$689$	6.73948			0.256754
$690$		0			0
$691$	−4.06344	+	4.06344i	−0.154580	+	0.154580i	−0.780160	−	0.625580i	$-0.784862\pi$
$691$	−4.06344	+	4.06344i	−0.154580	+	0.154580i	0.625580	+	0.780160i	$0.284862\pi$
$692$	−30.8919	+	1.03585i	−1.17433	+	0.0393769i
$693$		0			0
$694$	1.06196	−	2.69047i	0.0403115	−	0.102129i
$695$	−20.6248	+	32.7818i	−0.782343	+	1.24349i
$696$		0			0
$697$	−33.9807			−1.28711
$698$	−8.55545	+	21.6752i	−0.323829	+	0.820417i
$699$		0			0
$700$	2.58300	−	8.22632i	0.0976283	−	0.310926i
$701$	−31.9270	+	31.9270i	−1.20587	+	1.20587i	−0.233513	+	0.972354i	$0.575022\pi$
$701$	−31.9270	+	31.9270i	−1.20587	+	1.20587i	−0.972354	+	0.233513i	$0.924978\pi$
$702$		0			0
$703$		−	8.02509i		−	0.302672i
$704$	4.54625	+	45.0586i	0.171343	+	1.69821i
$705$		0			0
$706$	11.2849	+	26.0029i	0.424714	+	0.978632i
$707$	−7.36105	−	7.36105i	−0.276841	−	0.276841i
$708$		0			0
$709$	29.5514	+	29.5514i	1.10983	+	1.10983i	0.993173	+	0.116653i	$0.0372164\pi$
$709$	29.5514	+	29.5514i	1.10983	+	1.10983i	0.116653	+	0.993173i	$0.462784\pi$
$710$	31.8128	−	23.3552i	1.19391	−	0.876506i
$711$		0			0
$712$	−15.6140	−	5.56580i	−0.585158	−	0.208587i
$713$	−16.8913			−0.632585
$714$		0			0
$715$	−20.5589	+	4.67985i	−0.768859	+	0.175017i
$716$	−0.869235	−	25.9231i	−0.0324848	−	0.968791i
$717$		0			0
$718$	5.45651	+	12.5730i	0.203635	+	0.469218i
$719$	10.6102			0.395694			0.197847	−	0.980233i	$-0.436605\pi$
$719$	10.6102			0.395694			0.197847	+	0.980233i	$0.436605\pi$
$720$		0			0
$721$	12.2268			0.455348
$722$	−10.0939	−	23.2584i	−0.375655	−	0.865589i
$723$		0			0
$724$	19.3973	−	0.650418i	0.720896	−	0.0241726i
$725$	0.594486	−	1.69263i	0.0220787	−	0.0628625i
$726$		0			0
$727$	−20.3175			−0.753536			−0.376768	−	0.926308i	$-0.622965\pi$
$727$	−20.3175			−0.753536			−0.376768	+	0.926308i	$0.622965\pi$
$728$	3.67016	−	1.74121i	0.136025	−	0.0645334i
$729$		0			0
$730$	−21.5845	−	29.4008i	−0.798876	−	1.08817i
$731$	8.93271	+	8.93271i	0.330388	+	0.330388i
$732$		0			0
$733$	−32.3903	−	32.3903i	−1.19636	−	1.19636i	−0.975248	−	0.221114i	$-0.929031\pi$
$733$	−32.3903	−	32.3903i	−1.19636	−	1.19636i	−0.221114	−	0.975248i	$-0.570969\pi$
$734$	7.89175	+	18.1843i	0.291290	+	0.671194i
$735$		0			0
$736$	−12.9102	−	25.0118i	−0.475878	−	0.921948i
$737$			65.9211i			2.42824i
$738$		0			0
$739$	−23.8193	+	23.8193i	−0.876208	+	0.876208i	−0.993140	−	0.116932i	$-0.962694\pi$
$739$	−23.8193	+	23.8193i	−0.876208	+	0.876208i	0.116932	+	0.993140i	$0.462694\pi$
$740$	33.5249	−	8.82280i	1.23240	−	0.324333i
$741$		0			0
$742$	1.81137	−	4.58909i	0.0664975	−	0.168471i
$743$	−29.0300			−1.06501			−0.532503	−	0.846428i	$-0.678749\pi$
$743$	−29.0300			−1.06501			−0.532503	+	0.846428i	$0.678749\pi$
$744$		0			0
$745$	15.1867	−	24.1384i	0.556399	−	0.884361i
$746$	−5.71065	+	14.4679i	−0.209082	+	0.529707i
$747$		0			0
$748$	−1.39053	−	41.4697i	−0.0508430	−	1.51628i
$749$	8.39314	−	8.39314i	0.306679	−	0.306679i
$750$		0			0
$751$	−13.7034			−0.500044			−0.250022	−	0.968240i	$-0.580438\pi$
$751$	−13.7034			−0.500044			−0.250022	+	0.968240i	$0.580438\pi$
$752$	27.1271	−	1.82126i	0.989222	−	0.0664145i
$753$		0			0
$754$	0.775338	−	0.336487i	0.0282361	−	0.0122541i
$755$	−3.90672	+	0.889293i	−0.142180	+	0.0323647i
$756$		0			0
$757$	−2.90229	+	2.90229i	−0.105486	+	0.105486i	−0.757880	−	0.652394i	$-0.773765\pi$
$757$	−2.90229	+	2.90229i	−0.105486	+	0.105486i	0.652394	+	0.757880i	$0.273765\pi$
$758$	11.2687	+	4.44789i	0.409297	+	0.161555i
$759$		0			0
$760$	−5.14520	+	4.04954i	−0.186636	+	0.146892i
$761$		−	15.0364i		−	0.545070i	−0.962146	−	0.272535i	$-0.912138\pi$
$761$		−	15.0364i		−	0.545070i	0.962146	−	0.272535i	$-0.0878621\pi$
$762$		0			0
$763$	−9.24576	+	9.24576i	−0.334719	+	0.334719i
$764$	−6.38980	+	6.83318i	−0.231175	+	0.247216i
$765$		0			0
$766$	7.27339	+	16.7594i	0.262798	+	0.605543i
$767$		−	7.79660i		−	0.281519i
$768$		0			0
$769$	−2.85110			−0.102813			−0.0514066	−	0.998678i	$-0.516370\pi$
$769$	−2.85110			−0.102813			−0.0514066	+	0.998678i	$0.516370\pi$
$770$	−2.33898	+	15.2569i	−0.0842909	+	0.549820i
$771$		0			0
$772$	−11.3247	−	10.5899i	−0.407585	−	0.381138i
$773$	−6.38311	+	6.38311i	−0.229584	+	0.229584i	−0.812519	−	0.582935i	$-0.801904\pi$
$773$	−6.38311	+	6.38311i	−0.229584	+	0.229584i	0.582935	+	0.812519i	$0.301904\pi$
$774$		0			0
$775$	−15.3012	+	7.34676i	−0.549636	+	0.263903i
$776$	42.1940	+	15.0406i	1.51467	+	0.539926i
$777$		0			0
$778$	21.2843	+	8.40119i	0.763081	+	0.301197i
$779$	−6.78758	−	6.78758i	−0.243190	−	0.243190i
$780$		0			0
$781$	−49.9561	+	49.9561i	−1.78757	+	1.78757i
$782$	10.2669	+	23.6572i	0.367144	+	0.845979i
$783$		0			0
$784$	1.67644	+	24.9700i	0.0598728	+	0.891786i
$785$	17.4394	−	27.7189i	0.622440	−	0.989330i
$786$		0			0
$787$	−15.8450	−	15.8450i	−0.564813	−	0.564813i	0.365857	−	0.930671i	$-0.380776\pi$
$787$	−15.8450	−	15.8450i	−0.564813	−	0.564813i	−0.930671	+	0.365857i	$0.880776\pi$
$788$	−1.20269	−	35.8677i	−0.0428440	−	1.27773i
$789$		0			0
$790$	0.163483	+	0.222685i	0.00581647	+	0.00792278i
$791$			12.0734i			0.429281i
$792$		0			0
$793$	−8.12359			−0.288477
$794$	−22.1695	−	8.75059i	−0.786768	−	0.310547i
$795$		0			0
$796$	2.83948	+	2.65523i	0.100643	+	0.0941122i
$797$	−14.7638	−	14.7638i	−0.522961	−	0.522961i	0.395503	−	0.918465i	$-0.370570\pi$
$797$	−14.7638	−	14.7638i	−0.522961	−	0.522961i	−0.918465	+	0.395503i	$0.870570\pi$
$798$		0			0
$799$	−24.9102			−0.881261
$800$	−22.5736	−	17.0421i	−0.798098	−	0.602528i
$801$		0			0
$802$	39.0870	−	16.9633i	1.38021	−	0.598994i
$803$	46.1685	+	46.1685i	1.62925	+	1.62925i
$804$		0			0
$805$	−2.12928	−	9.35404i	−0.0750471	−	0.329687i
$806$	−7.43832	−	2.93599i	−0.262004	−	0.103416i
$807$		0			0
$808$	−30.8528	+	14.6373i	−1.08540	+	0.514937i
$809$		−	17.9052i		−	0.629513i	−0.949172	−	0.314757i	$-0.898077\pi$
$809$		−	17.9052i		−	0.629513i	0.949172	−	0.314757i	$-0.101923\pi$
$810$		0			0
$811$	10.1471	+	10.1471i	0.356311	+	0.356311i	0.862451	−	0.506140i	$-0.168928\pi$
$811$	10.1471	+	10.1471i	0.356311	+	0.356311i	−0.506140	+	0.862451i	$0.668928\pi$
$812$	−0.0207353	−	0.618386i	−0.000727666	−	0.0217011i
$813$		0			0
$814$	−56.9278	+	24.7059i	−1.99532	+	0.865943i
$815$	4.73198	−	7.52119i	0.165754	−	0.263456i
$816$		0			0
$817$			3.56858i			0.124849i
$818$	3.09486	+	7.13122i	0.108209	+	0.249337i
$819$		0			0
$820$	20.8929	−	35.8174i	0.729611	−	1.25080i
$821$	−17.6996	−	17.6996i	−0.617720	−	0.617720i	0.327226	−	0.944946i	$-0.393886\pi$
$821$	−17.6996	−	17.6996i	−0.617720	−	0.617720i	−0.944946	+	0.327226i	$0.893886\pi$
$822$		0			0
$823$	20.1979			0.704054			0.352027	−	0.935990i	$-0.385493\pi$
$823$	20.1979			0.704054			0.352027	+	0.935990i	$0.385493\pi$
$824$	13.4671	−	37.7796i	0.469147	−	1.31612i
$825$		0			0
$826$	−5.30891	−	2.09549i	−0.184721	−	0.0729115i
$827$	−14.2753	+	14.2753i	−0.496401	+	0.496401i	−0.910316	−	0.413915i	$-0.864161\pi$
$827$	−14.2753	+	14.2753i	−0.496401	+	0.496401i	0.413915	+	0.910316i	$0.364161\pi$
$828$		0			0
$829$	3.72004	−	3.72004i	0.129202	−	0.129202i	−0.639549	−	0.768751i	$-0.720879\pi$
$829$	3.72004	−	3.72004i	0.129202	−	0.129202i	0.768751	+	0.639549i	$0.220879\pi$
$830$	4.86042	−	31.7040i	0.168708	−	1.10046i
$831$		0			0
$832$	−1.33772	−	13.2583i	−0.0463770	−	0.459649i
$833$		−	22.9295i		−	0.794459i
$834$		0			0
$835$	−4.01290	−	17.6289i	−0.138872	−	0.610075i
$836$	8.00575	−	8.56126i	0.276885	−	0.296097i
$837$		0			0
$838$	12.1033	−	30.6636i	0.418102	−	1.05926i
$839$		−	3.88360i		−	0.134077i	−0.997750	−	0.0670384i	$-0.978645\pi$
$839$		−	3.88360i		−	0.134077i	0.997750	−	0.0670384i	$-0.0213550\pi$
$840$		0			0
$841$			28.8713i			0.995561i
$842$	−19.3620	−	7.64243i	−0.667259	−	0.263376i
$843$		0			0
$844$	−0.804552	−	23.9940i	−0.0276938	−	0.825909i
$845$	−22.2945	+	5.07492i	−0.766952	+	0.174583i
$846$		0			0
$847$		−	18.1465i		−	0.623521i
$848$	−12.1848	−	10.6516i	−0.418427	−	0.365777i
$849$		0			0
$850$	19.5899	+	16.9646i	0.671929	+	0.581882i
$851$	27.2734	−	27.2734i	0.934920	−	0.934920i
$852$		0			0
$853$	−10.0574	+	10.0574i	−0.344359	+	0.344359i	−0.858003	−	0.513644i	$-0.828295\pi$
$853$	−10.0574	+	10.0574i	−0.344359	+	0.344359i	0.513644	+	0.858003i	$0.328295\pi$
$854$	−2.18338	+	5.53157i	−0.0747136	+	0.189286i
$855$		0			0
$856$	−16.6895	−	35.1786i	−0.570437	−	1.20238i
$857$	−20.4938			−0.700056			−0.350028	−	0.936739i	$-0.613828\pi$
$857$	−20.4938			−0.700056			−0.350028	+	0.936739i	$0.613828\pi$
$858$		0			0
$859$	28.4317	+	28.4317i	0.970077	+	0.970077i	0.999565	−	0.0294877i	$-0.00938760\pi$
$859$	28.4317	+	28.4317i	0.970077	+	0.970077i	−0.0294877	+	0.999565i	$0.509388\pi$
$860$	−14.9078	+	3.92331i	−0.508351	+	0.133784i
$861$		0			0
$862$	−5.08391	+	2.20635i	−0.173159	+	0.0751487i
$863$			9.49626i			0.323257i	0.986852	+	0.161628i	$0.0516746\pi$
$863$			9.49626i			0.323257i	−0.986852	+	0.161628i	$0.948325\pi$
$864$		0			0
$865$	−18.4028	+	29.2501i	−0.625713	+	0.994532i
$866$	9.62738	+	22.1835i	0.327152	+	0.753828i
$867$		0			0
$868$	−3.99839	+	4.27584i	−0.135714	+	0.145131i
$869$	−0.349686	−	0.349686i	−0.0118623	−	0.0118623i
$870$		0			0
$871$		−	19.3970i		−	0.657244i
$872$	18.3850	+	38.7523i	0.622593	+	1.31232i
$873$		0			0
$874$	−2.67468	+	6.77627i	−0.0904723	+	0.229211i
$875$	−5.99731	−	7.54736i	−0.202746	−	0.255147i
$876$		0			0
$877$	−19.8385	−	19.8385i	−0.669898	−	0.669898i	0.287794	−	0.957692i	$-0.407078\pi$
$877$	−19.8385	−	19.8385i	−0.669898	−	0.669898i	−0.957692	+	0.287794i	$0.907078\pi$
$878$	−12.1136	−	27.9123i	−0.408814	−	0.941994i
$879$		0			0
$880$	44.5663	+	24.0318i	1.50233	+	0.810112i
$881$	−26.6217			−0.896908			−0.448454	−	0.893806i	$-0.648025\pi$
$881$	−26.6217			−0.896908			−0.448454	+	0.893806i	$0.648025\pi$
$882$		0			0
$883$	8.94715	+	8.94715i	0.301096	+	0.301096i	0.841442	−	0.540347i	$-0.181707\pi$
$883$	8.94715	+	8.94715i	0.301096	+	0.301096i	−0.540347	+	0.841442i	$0.681707\pi$
$884$	0.409160	+	12.2023i	0.0137615	+	0.410408i
$885$		0			0
$886$	−1.49020	+	3.77542i	−0.0500644	+	0.126838i
$887$	30.8407			1.03553			0.517764	−	0.855523i	$-0.326765\pi$
$887$	30.8407			1.03553			0.517764	+	0.855523i	$0.326765\pi$
$888$		0			0
$889$		−	19.0053i		−	0.637418i
$890$	−14.9392	+	10.9676i	−0.500764	+	0.367633i
$891$		0			0
$892$	12.7439	+	11.9170i	0.426699	+	0.399011i
$893$	−4.97577	−	4.97577i	−0.166508	−	0.166508i
$894$		0			0
$895$	−24.5453	−	15.4428i	−0.820459	−	0.516195i
$896$	−9.38747	−	2.65255i	−0.313614	−	0.0886155i
$897$		0			0
$898$	10.0598	−	4.36581i	0.335698	−	0.145689i
$899$	−0.861267	+	0.861267i	−0.0287248	+	0.0287248i
$900$		0			0
$901$	10.4851	+	10.4851i	0.349309	+	0.349309i
$902$	−27.2531	+	69.0454i	−0.907428	+	2.29896i
$903$		0			0
$904$	37.3058	+	13.2981i	1.24077	+	0.442290i
$905$	11.5553	−	18.3664i	0.384110	−	0.610520i
$906$		0			0
$907$	−35.6729	+	35.6729i	−1.18450	+	1.18450i	−0.205933	+	0.978566i	$0.566023\pi$
$907$	−35.6729	+	35.6729i	−1.18450	+	1.18450i	−0.978566	+	0.205933i	$0.933977\pi$
$908$	−8.02980	+	0.269250i	−0.266478	+	0.00893536i
$909$		0			0
$910$	0.688235	−	4.48928i	0.0228148	−	0.148818i
$911$	−58.4656			−1.93705			−0.968526	−	0.248913i	$-0.919927\pi$
$911$	−58.4656			−1.93705			−0.968526	+	0.248913i	$0.919927\pi$
$912$		0			0
$913$			57.4176i			1.90025i
$914$	22.1835	−	9.62738i	0.733766	−	0.318445i
$915$		0			0
$916$	−44.2436	+	1.48355i	−1.46185	+	0.0490177i
$917$	−0.525170	+	0.525170i	−0.0173426	+	0.0173426i
$918$		0			0
$919$			28.9617i			0.955357i	0.878535	+	0.477678i	$0.158522\pi$
$919$			28.9617i			0.955357i	−0.878535	+	0.477678i	$0.841478\pi$
$920$	−31.2485	−	3.72364i	−1.03023	−	0.122765i
$921$		0			0
$922$	−16.2468	+	41.1612i	−0.535061	+	1.35557i
$923$	14.6994	−	14.6994i	0.483837	−	0.483837i
$924$		0			0
$925$	12.8436	−	36.5683i	0.422294	−	1.20236i
$926$	−12.5020	−	28.8074i	−0.410842	−	0.946669i
$927$		0			0
$928$	−1.93360	−	0.617045i	−0.0634735	−	0.0202555i
$929$	−23.8093			−0.781159			−0.390580	−	0.920569i	$-0.627725\pi$
$929$	−23.8093			−0.781159			−0.390580	+	0.920569i	$0.627725\pi$
$930$		0			0
$931$	4.58012	−	4.58012i	0.150107	−	0.150107i
$932$	−10.9364	+	11.6953i	−0.358235	+	0.383093i
$933$		0			0
$934$	34.0558	+	13.4422i	1.11434	+	0.439844i
$935$	−39.2657	−	24.7042i	−1.28413	−	0.807912i
$936$		0			0
$937$	36.3858			1.18867			0.594337	−	0.804216i	$-0.297415\pi$
$937$	36.3858			1.18867			0.594337	+	0.804216i	$0.297415\pi$
$938$	−13.2080	−	5.21334i	−0.431255	−	0.170222i
$939$		0			0
$940$	15.3160	−	26.2567i	0.499551	−	0.856399i
$941$	19.5670	−	19.5670i	0.637865	−	0.637865i	−0.312164	−	0.950028i	$-0.601054\pi$
$941$	19.5670	−	19.5670i	0.637865	−	0.637865i	0.950028	+	0.312164i	$0.101054\pi$
$942$		0			0
$943$		−	46.1354i		−	1.50237i
$944$	−12.3223	+	14.0960i	−0.401058	+	0.458786i
$945$		0			0
$946$	25.3146	−	10.9862i	0.823047	−	0.357192i
$947$	−15.2620	−	15.2620i	−0.495949	−	0.495949i	0.414226	−	0.910174i	$-0.364052\pi$
$947$	−15.2620	−	15.2620i	−0.495949	−	0.495949i	−0.910174	+	0.414226i	$0.864052\pi$
$948$		0			0
$949$	−13.5849	−	13.5849i	−0.440985	−	0.440985i
$950$	0.524401	+	7.30170i	0.0170138	+	0.236898i
$951$		0			0
$952$	8.41885	+	3.00101i	0.272856	+	0.0972633i
$953$	34.8080			1.12754			0.563772	−	0.825931i	$-0.309350\pi$
$953$	34.8080			1.12754			0.563772	+	0.825931i	$0.309350\pi$
$954$		0			0
$955$	2.32154	+	10.1987i	0.0751232	+	0.330021i
$956$	−17.5555	+	18.7737i	−0.567786	+	0.607184i
$957$		0			0
$958$	−34.3293	+	14.8985i	−1.10913	+	0.481348i
$959$	−7.85690			−0.253712
$960$		0			0
$961$	−19.4759			−0.628256
$962$	16.7508	−	7.26963i	0.540067	−	0.234382i
$963$		0			0
$964$	−34.3318	+	36.7141i	−1.10575	+	1.18248i
$965$	−16.9024	+	3.84751i	−0.544107	+	0.123856i
$966$		0			0
$967$	46.6707			1.50083			0.750414	−	0.660968i	$-0.229854\pi$
$967$	46.6707			1.50083			0.750414	+	0.660968i	$0.229854\pi$
$968$	−56.0712	−	19.9873i	−1.80220	−	0.642416i
$969$		0			0
$970$	40.3706	−	29.6379i	1.29622	−	0.951614i
$971$	−7.25903	−	7.25903i	−0.232953	−	0.232953i	0.580971	−	0.813924i	$-0.302673\pi$
$971$	−7.25903	−	7.25903i	−0.232953	−	0.232953i	−0.813924	+	0.580971i	$0.802673\pi$
$972$		0			0
$973$	10.5602	+	10.5602i	0.338546	+	0.338546i
$974$	33.6490	−	14.6032i	1.07818	−	0.467918i
$975$		0			0
$976$	14.6872	+	12.8391i	0.470126	+	0.410971i
$977$			58.1421i			1.86013i	0.367394	+	0.930065i	$0.380250\pi$
$977$			58.1421i			1.86013i	−0.367394	+	0.930065i	$0.619750\pi$
$978$		0			0
$979$	23.4593	−	23.4593i	0.749762	−	0.749762i
$980$	24.1689	+	14.0981i	0.772046	+	0.450347i
$981$		0			0
$982$	15.1719	+	5.98854i	0.484155	+	0.191102i
$983$	23.9250			0.763089			0.381544	−	0.924350i	$-0.375392\pi$
$983$	23.9250			0.763089			0.381544	+	0.924350i	$0.375392\pi$
$984$		0			0
$985$	−33.9614	−	21.3669i	−1.08210	−	0.680806i
$986$	1.72975	+	0.682752i	0.0550863	+	0.0217433i
$987$		0			0
$988$	−2.35566	+	2.51912i	−0.0749435	+	0.0801438i
$989$	−12.1279	+	12.1279i	−0.385644	+	0.385644i
$990$		0			0
$991$	29.5680			0.939259			0.469630	−	0.882864i	$-0.344387\pi$
$991$	29.5680			0.939259			0.469630	+	0.882864i	$0.344387\pi$
$992$	8.80799	+	17.0643i	0.279654	+	0.541791i
$993$		0			0
$994$	−6.05845	−	13.9600i	−0.192162	−	0.442783i
$995$	4.23798	−	0.964698i	0.134353	−	0.0305830i
$996$		0			0
$997$	−27.7001	+	27.7001i	−0.877272	+	0.877272i	−0.993252	−	0.115980i	$-0.962999\pi$
$997$	−27.7001	+	27.7001i	−0.877272	+	0.877272i	0.115980	+	0.993252i	$0.462999\pi$
$998$	15.1461	−	38.3724i	0.479440	−	1.21466i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bm.g.469.3	yes	32
3.2	odd	2	inner	720.2.bm.g.469.14	yes	32
5.4	even	2	inner	720.2.bm.g.469.13	yes	32
15.14	odd	2	inner	720.2.bm.g.469.4	yes	32
16.13	even	4	inner	720.2.bm.g.109.15	yes	32
48.29	odd	4	inner	720.2.bm.g.109.2	yes	32
80.29	even	4	inner	720.2.bm.g.109.1	✓	32
240.29	odd	4	inner	720.2.bm.g.109.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.bm.g.109.1	✓	32	80.29	even	4	inner
720.2.bm.g.109.2	yes	32	48.29	odd	4	inner
720.2.bm.g.109.15	yes	32	16.13	even	4	inner
720.2.bm.g.109.16	yes	32	240.29	odd	4	inner
720.2.bm.g.469.3	yes	32	1.1	even	1	trivial
720.2.bm.g.469.4	yes	32	15.14	odd	2	inner
720.2.bm.g.469.13	yes	32	5.4	even	2	inner
720.2.bm.g.469.14	yes	32	3.2	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q+(-1.29731 + 0.563016i) q^{2} +(1.36603 - 1.46081i) q^{4} +(-0.496304 - 2.18029i) q^{5} -0.862231 q^{7} +(-0.949697 + 2.66422i) q^{8} +(1.87140 + 2.54909i) q^{10} +(-4.00287 - 4.00287i) q^{11} +(1.17783 + 1.17783i) q^{13} +(1.11858 - 0.485450i) q^{14} +(-0.267949 - 3.99102i) q^{16} +3.66487i q^{17} +(-0.732051 + 0.732051i) q^{19} +(-3.86297 - 2.25333i) q^{20} +(7.44665 + 2.93928i) q^{22} -4.97577 q^{23} +(-4.50736 + 2.16418i) q^{25} +(-2.19115 - 0.864873i) q^{26} +(-1.17783 + 1.25956i) q^{28} +(-0.253708 + 0.253708i) q^{29} +3.39471 q^{31} +(2.59462 + 5.02672i) q^{32} +(-2.06338 - 4.75447i) q^{34} +(0.427929 + 1.87992i) q^{35} +(-5.48124 + 5.48124i) q^{37} +(0.537540 - 1.36185i) q^{38} +(6.28012 + 0.748355i) q^{40} +9.27201i q^{41} +(2.43739 - 2.43739i) q^{43} +(-11.3155 + 0.379423i) q^{44} +(6.45512 - 2.80144i) q^{46} +6.79703i q^{47} -6.25656 q^{49} +(4.62898 - 5.34533i) q^{50} +(3.32953 - 0.111644i) q^{52} +(2.86097 - 2.86097i) q^{53} +(-6.74080 + 10.7141i) q^{55} +(0.818858 - 2.29718i) q^{56} +(0.186296 - 0.471980i) q^{58} +(-3.30973 - 3.30973i) q^{59} +(-3.44854 + 3.44854i) q^{61} +(-4.40399 + 1.91128i) q^{62} +(-6.19615 - 5.06040i) q^{64} +(1.98345 - 3.15258i) q^{65} +(-8.23423 - 8.23423i) q^{67} +(5.35369 + 5.00631i) q^{68} +(-1.61358 - 2.19791i) q^{70} -12.4801i q^{71} -11.5338 q^{73} +(4.02484 - 10.1969i) q^{74} +(0.0693893 + 2.06939i) q^{76} +(3.45140 + 3.45140i) q^{77} +0.0873587 q^{79} +(-8.56860 + 2.56496i) q^{80} +(-5.22029 - 12.0287i) q^{82} +(-7.17205 - 7.17205i) q^{83} +(7.99050 - 1.81889i) q^{85} +(-1.78976 + 4.53434i) q^{86} +(14.4661 - 6.86302i) q^{88} +5.86061i q^{89} +(-1.01556 - 1.01556i) q^{91} +(-6.79703 + 7.26867i) q^{92} +(-3.82684 - 8.81785i) q^{94} +(1.95941 + 1.23277i) q^{95} -15.8373i q^{97} +(8.11669 - 3.52254i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 24 q^{10} - 64 q^{16} + 32 q^{19} + 32 q^{31} - 72 q^{40} - 32 q^{46} + 128 q^{49} - 32 q^{64} - 104 q^{70} - 32 q^{76} + 224 q^{79} - 48 q^{85} - 32 q^{91} - 48 q^{94}+O(q^{100}) \) 32 * q + 16 * q^4 - 24 * q^10 - 64 * q^16 + 32 * q^19 + 32 * q^31 - 72 * q^40 - 32 * q^46 + 128 * q^49 - 32 * q^64 - 104 * q^70 - 32 * q^76 + 224 * q^79 - 48 * q^85 - 32 * q^91 - 48 * q^94

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