LMFDB - Embedded newform 432.2.l.a.107.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(107,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("432.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
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			107.10
Character	$\chi$	$=$	432.107
Dual form			432.2.l.a.323.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.604480 + 1.27852i) q^{2} +(-1.26921 + 1.54568i) q^{4} +(-0.217410 + 0.217410i) q^{5} -3.81401 q^{7} +(-2.74338 - 0.688372i) q^{8} +O(q^{10})$	\(q+(0.604480 + 1.27852i) q^{2} +(-1.26921 + 1.54568i) q^{4} +(-0.217410 + 0.217410i) q^{5} -3.81401 q^{7} +(-2.74338 - 0.688372i) q^{8} +(-0.409383 - 0.146542i) q^{10} +(-3.83163 - 3.83163i) q^{11} +(-2.88926 + 2.88926i) q^{13} +(-2.30549 - 4.87627i) q^{14} +(-0.778226 - 3.92357i) q^{16} +4.71852i q^{17} +(4.77663 + 4.77663i) q^{19} +(-0.0601071 - 0.611985i) q^{20} +(2.58266 - 7.21495i) q^{22} -6.18488i q^{23} +4.90547i q^{25} +(-5.44047 - 1.94747i) q^{26} +(4.84076 - 5.89522i) q^{28} +(-0.322843 - 0.322843i) q^{29} +5.20520i q^{31} +(4.54592 - 3.36669i) q^{32} +(-6.03271 + 2.85225i) q^{34} +(0.829205 - 0.829205i) q^{35} +(-2.92710 - 2.92710i) q^{37} +(-3.21962 + 8.99438i) q^{38} +(0.746099 - 0.446781i) q^{40} -1.31513 q^{41} +(0.505290 - 0.505290i) q^{43} +(10.7856 - 1.05932i) q^{44} +(7.90747 - 3.73864i) q^{46} -5.41806 q^{47} +7.54664 q^{49} +(-6.27172 + 2.96526i) q^{50} +(-0.798789 - 8.13294i) q^{52} +(-1.85772 + 1.85772i) q^{53} +1.66607 q^{55} +(10.4633 + 2.62545i) q^{56} +(0.217608 - 0.607913i) q^{58} +(4.77662 + 4.77662i) q^{59} +(-0.832278 + 0.832278i) q^{61} +(-6.65493 + 3.14644i) q^{62} +(7.05229 + 3.77693i) q^{64} -1.25631i q^{65} +(-6.48244 - 6.48244i) q^{67} +(-7.29331 - 5.98879i) q^{68} +(1.56139 + 0.558914i) q^{70} +2.47601i q^{71} +6.68986i q^{73} +(1.97297 - 5.51171i) q^{74} +(-13.4457 + 1.32059i) q^{76} +(14.6139 + 14.6139i) q^{77} +9.28617i q^{79} +(1.02222 + 0.683830i) q^{80} +(-0.794971 - 1.68142i) q^{82} +(8.24616 - 8.24616i) q^{83} +(-1.02586 - 1.02586i) q^{85} +(0.951459 + 0.340583i) q^{86} +(7.87404 + 13.1492i) q^{88} +12.3741 q^{89} +(11.0197 - 11.0197i) q^{91} +(9.55982 + 7.84989i) q^{92} +(-3.27511 - 6.92708i) q^{94} -2.07698 q^{95} -2.81552 q^{97} +(4.56179 + 9.64850i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 4 q^{10} - 20 q^{16} + 8 q^{19} + 4 q^{22} - 12 q^{28} - 36 q^{34} - 12 q^{40} + 32 q^{43} - 16 q^{46} + 32 q^{49} - 60 q^{52} + 64 q^{55} - 48 q^{58} - 16 q^{61} + 48 q^{64} - 32 q^{67} - 72 q^{70} - 96 q^{76} + 40 q^{82} - 16 q^{85} + 36 q^{88} + 24 q^{91} - 36 q^{94}+O(q^{100}) $ 32 * q - 4 * q^10 - 20 * q^16 + 8 * q^19 + 4 * q^22 - 12 * q^28 - 36 * q^34 - 12 * q^40 + 32 * q^43 - 16 * q^46 + 32 * q^49 - 60 * q^52 + 64 * q^55 - 48 * q^58 - 16 * q^61 + 48 * q^64 - 32 * q^67 - 72 * q^70 - 96 * q^76 + 40 * q^82 - 16 * q^85 + 36 * q^88 + 24 * q^91 - 36 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.604480	+	1.27852i	0.427432	+	0.904047i
$2$	0.604480	+	1.27852i	0.427432	+	0.904047i
$3$		0			0
$3$		0			0
$4$	−1.26921	+	1.54568i	−0.634604	+	0.772838i
$5$	−0.217410	+	0.217410i	−0.0972289	+	0.0972289i	−0.754048	−	0.656819i	$-0.771901\pi$
$5$	−0.217410	+	0.217410i	−0.0972289	+	0.0972289i	0.656819	+	0.754048i	$0.271901\pi$
$6$		0			0
$7$	−3.81401			−1.44156			−0.720779	−	0.693165i	$-0.756216\pi$
$7$	−3.81401			−1.44156			−0.720779	+	0.693165i	$0.756216\pi$
$8$	−2.74338	−	0.688372i	−0.969932	−	0.243376i
$9$		0			0
$10$	−0.409383	−	0.146542i	−0.129458	−	0.0463408i
$11$	−3.83163	−	3.83163i	−1.15528	−	1.15528i	−0.985478	−	0.169803i	$-0.945687\pi$
$11$	−3.83163	−	3.83163i	−1.15528	−	1.15528i	−0.169803	−	0.985478i	$-0.554313\pi$
$12$		0			0
$13$	−2.88926	+	2.88926i	−0.801337	+	0.801337i	−0.983305	−	0.181967i	$-0.941754\pi$
$13$	−2.88926	+	2.88926i	−0.801337	+	0.801337i	0.181967	+	0.983305i	$0.441754\pi$
$14$	−2.30549	−	4.87627i	−0.616168	−	1.30324i
$15$		0			0
$16$	−0.778226	−	3.92357i	−0.194556	−	0.980891i
$17$			4.71852i			1.14441i	0.820111	+	0.572205i	$0.193912\pi$
$17$			4.71852i			1.14441i	−0.820111	+	0.572205i	$0.806088\pi$
$18$		0			0
$19$	4.77663	+	4.77663i	1.09583	+	1.09583i	0.994892	+	0.100943i	$0.0321859\pi$
$19$	4.77663	+	4.77663i	1.09583	+	1.09583i	0.100943	+	0.994892i	$0.467814\pi$
$20$	−0.0601071	−	0.611985i	−0.0134404	−	0.136844i
$21$		0			0
$22$	2.58266	−	7.21495i	0.550625	−	1.53823i
$23$		−	6.18488i		−	1.28964i	−0.764336	−	0.644818i	$-0.776933\pi$
$23$		−	6.18488i		−	1.28964i	0.764336	−	0.644818i	$-0.223067\pi$
$24$		0			0
$25$			4.90547i			0.981093i
$26$	−5.44047	−	1.94747i	−1.06696	−	0.381930i
$27$		0			0
$28$	4.84076	−	5.89522i	0.914818	−	1.11409i
$29$	−0.322843	−	0.322843i	−0.0599505	−	0.0599505i	0.676496	−	0.736446i	$-0.263498\pi$
$29$	−0.322843	−	0.322843i	−0.0599505	−	0.0599505i	−0.736446	+	0.676496i	$0.763498\pi$
$30$		0			0
$31$			5.20520i			0.934881i	0.884024	+	0.467441i	$0.154824\pi$
$31$			5.20520i			0.934881i	−0.884024	+	0.467441i	$0.845176\pi$
$32$	4.54592	−	3.36669i	0.803613	−	0.595153i
$33$		0			0
$34$	−6.03271	+	2.85225i	−1.03460	+	0.489158i
$35$	0.829205	−	0.829205i	0.140161	−	0.140161i
$36$		0			0
$37$	−2.92710	−	2.92710i	−0.481212	−	0.481212i	0.424307	−	0.905519i	$-0.360518\pi$
$37$	−2.92710	−	2.92710i	−0.481212	−	0.481212i	−0.905519	+	0.424307i	$0.860518\pi$
$38$	−3.21962	+	8.99438i	−0.522292	+	1.45908i
$39$		0			0
$40$	0.746099	−	0.446781i	0.117969	−	0.0706422i
$41$	−1.31513			−0.205389			−0.102694	−	0.994713i	$-0.532746\pi$
$41$	−1.31513			−0.205389			−0.102694	+	0.994713i	$0.532746\pi$
$42$		0			0
$43$	0.505290	−	0.505290i	0.0770560	−	0.0770560i	−0.667528	−	0.744584i	$-0.732648\pi$
$43$	0.505290	−	0.505290i	0.0770560	−	0.0770560i	0.744584	+	0.667528i	$0.232648\pi$
$44$	10.7856	−	1.05932i	1.62599	−	0.159699i
$45$		0			0
$46$	7.90747	−	3.73864i	1.16589	−	0.551232i
$47$	−5.41806			−0.790306			−0.395153	−	0.918615i	$-0.629308\pi$
$47$	−5.41806			−0.790306			−0.395153	+	0.918615i	$0.629308\pi$
$48$		0			0
$49$	7.54664			1.07809
$50$	−6.27172	+	2.96526i	−0.886955	+	0.419351i
$51$		0			0
$52$	−0.798789	−	8.13294i	−0.110772	−	1.12784i
$53$	−1.85772	+	1.85772i	−0.255178	+	0.255178i	−0.823090	−	0.567912i	$-0.807752\pi$
$53$	−1.85772	+	1.85772i	−0.255178	+	0.255178i	0.567912	+	0.823090i	$0.307752\pi$
$54$		0			0
$55$	1.66607			0.224653
$56$	10.4633	+	2.62545i	1.39821	+	0.350841i
$57$		0			0
$58$	0.217608	−	0.607913i	0.0285733	−	0.0798229i
$59$	4.77662	+	4.77662i	0.621863	+	0.621863i	0.946007	−	0.324145i	$-0.105077\pi$
$59$	4.77662	+	4.77662i	0.621863	+	0.621863i	−0.324145	+	0.946007i	$0.605077\pi$
$60$		0			0
$61$	−0.832278	+	0.832278i	−0.106562	+	0.106562i	−0.758378	−	0.651815i	$-0.774008\pi$
$61$	−0.832278	+	0.832278i	−0.106562	+	0.106562i	0.651815	+	0.758378i	$0.274008\pi$
$62$	−6.65493	+	3.14644i	−0.845177	+	0.399598i
$63$		0			0
$64$	7.05229	+	3.77693i	0.881536	+	0.472117i
$65$		−	1.25631i		−	0.155826i
$66$		0			0
$67$	−6.48244	−	6.48244i	−0.791956	−	0.791956i	0.189856	−	0.981812i	$-0.439198\pi$
$67$	−6.48244	−	6.48244i	−0.791956	−	0.791956i	−0.981812	+	0.189856i	$0.939198\pi$
$68$	−7.29331	−	5.98879i	−0.884444	−	0.726247i
$69$		0			0
$70$	1.56139	+	0.558914i	0.186622	+	0.0668030i
$71$			2.47601i			0.293849i	0.989148	+	0.146924i	$0.0469374\pi$
$71$			2.47601i			0.293849i	−0.989148	+	0.146924i	$0.953063\pi$
$72$		0			0
$73$			6.68986i			0.782989i	0.920180	+	0.391494i	$0.128042\pi$
$73$			6.68986i			0.782989i	−0.920180	+	0.391494i	$0.871958\pi$
$74$	1.97297	−	5.51171i	0.229353	−	0.640724i
$75$		0			0
$76$	−13.4457	+	1.32059i	−1.54232	+	0.151482i
$77$	14.6139	+	14.6139i	1.66541	+	1.66541i
$78$		0			0
$79$			9.28617i			1.04478i	0.852708	+	0.522388i	$0.174959\pi$
$79$			9.28617i			1.04478i	−0.852708	+	0.522388i	$0.825041\pi$
$80$	1.02222	+	0.683830i	0.114288	+	0.0764545i
$81$		0			0
$82$	−0.794971	−	1.68142i	−0.0877898	−	0.185681i
$83$	8.24616	−	8.24616i	0.905134	−	0.905134i	−0.0907409	−	0.995875i	$-0.528924\pi$
$83$	8.24616	−	8.24616i	0.905134	−	0.905134i	0.995875	+	0.0907409i	$0.0289235\pi$
$84$		0			0
$85$	−1.02586	−	1.02586i	−0.111270	−	0.111270i
$86$	0.951459	+	0.340583i	0.102598	+	0.0367261i
$87$		0			0
$88$	7.87404	+	13.1492i	0.839376	+	1.40171i
$89$	12.3741			1.31165			0.655825	−	0.754913i	$-0.272321\pi$
$89$	12.3741			1.31165			0.655825	+	0.754913i	$0.272321\pi$
$90$		0			0
$91$	11.0197	−	11.0197i	1.15517	−	1.15517i
$92$	9.55982	+	7.84989i	0.996680	+	0.818408i
$93$		0			0
$94$	−3.27511	−	6.92708i	−0.337802	−	0.714474i
$95$	−2.07698			−0.213094
$96$		0			0
$97$	−2.81552			−0.285873			−0.142937	−	0.989732i	$-0.545654\pi$
$97$	−2.81552			−0.285873			−0.142937	+	0.989732i	$0.545654\pi$
$98$	4.56179	+	9.64850i	0.460811	+	0.974646i
$99$		0			0
$100$	−7.58226	−	6.22605i	−0.758226	−	0.622605i
$101$	−6.38111	+	6.38111i	−0.634944	+	0.634944i	−0.949304	−	0.314360i	$-0.898210\pi$
$101$	−6.38111	+	6.38111i	−0.634944	+	0.634944i	0.314360	+	0.949304i	$0.398210\pi$
$102$		0			0
$103$	−18.5734			−1.83009			−0.915046	−	0.403350i	$-0.867846\pi$
$103$	−18.5734			−1.83009			−0.915046	+	0.403350i	$0.867846\pi$
$104$	9.91524	−	5.93747i	0.972269	−	0.582216i
$105$		0			0
$106$	−3.49809	−	1.25217i	−0.339764	−	0.121622i
$107$	−12.4921	−	12.4921i	−1.20766	−	1.20766i	−0.971783	−	0.235876i	$-0.924204\pi$
$107$	−12.4921	−	12.4921i	−1.20766	−	1.20766i	−0.235876	−	0.971783i	$-0.575796\pi$
$108$		0			0
$109$	4.93373	−	4.93373i	0.472565	−	0.472565i	−0.430179	−	0.902744i	$-0.641549\pi$
$109$	4.93373	−	4.93373i	0.472565	−	0.472565i	0.902744	+	0.430179i	$0.141549\pi$
$110$	1.00711	+	2.13010i	0.0960241	+	0.203097i
$111$		0			0
$112$	2.96816	+	14.9645i	0.280464	+	1.41401i
$113$			11.7427i			1.10466i	0.833626	+	0.552329i	$0.186261\pi$
$113$			11.7427i			1.10466i	−0.833626	+	0.552329i	$0.813739\pi$
$114$		0			0
$115$	1.34466	+	1.34466i	0.125390	+	0.125390i
$116$	0.908766	−	0.0892559i	0.0843768	−	0.00828721i
$117$		0			0
$118$	−3.21961	+	8.99435i	−0.296389	+	0.827997i
$119$		−	17.9965i		−	1.64973i
$120$		0			0
$121$			18.3628i			1.66935i
$122$	−1.56718	−	0.560985i	−0.141885	−	0.0507892i
$123$		0			0
$124$	−8.04555	−	6.60648i	−0.722512	−	0.593279i
$125$	−2.15355	−	2.15355i	−0.192620	−	0.192620i
$126$		0			0
$127$			15.2988i			1.35755i	0.734347	+	0.678774i	$0.237489\pi$
$127$			15.2988i			1.35755i	−0.734347	+	0.678774i	$0.762511\pi$
$128$	−0.565902	+	11.2995i	−0.0500192	+	0.998748i
$129$		0			0
$130$	1.60622	−	0.759416i	0.140874	−	0.0666052i
$131$	−3.55187	+	3.55187i	−0.310329	+	0.310329i	−0.845037	−	0.534708i	$-0.820422\pi$
$131$	−3.55187	+	3.55187i	−0.310329	+	0.310329i	0.534708	+	0.845037i	$0.320422\pi$
$132$		0			0
$133$	−18.2181	−	18.2181i	−1.57971	−	1.57971i
$134$	4.36939	−	12.2064i	0.377458	−	1.05447i
$135$		0			0
$136$	3.24810	−	12.9447i	0.278522	−	1.11000i
$137$	−4.11222			−0.351331			−0.175665	−	0.984450i	$-0.556208\pi$
$137$	−4.11222			−0.351331			−0.175665	+	0.984450i	$0.556208\pi$
$138$		0			0
$139$	6.64500	−	6.64500i	0.563621	−	0.563621i	−0.366713	−	0.930334i	$-0.619517\pi$
$139$	6.64500	−	6.64500i	0.563621	−	0.563621i	0.930334	+	0.366713i	$0.119517\pi$
$140$	0.229249	+	2.33411i	0.0193751	+	0.197269i
$141$		0			0
$142$	−3.16562	+	1.49670i	−0.265653	+	0.125600i
$143$	22.1412			1.85154
$144$		0			0
$145$	0.140379			0.0116578
$146$	−8.55310	+	4.04389i	−0.707859	+	0.334675i
$147$		0			0
$148$	8.23944	−	0.809249i	0.677278	−	0.0665199i
$149$	0.723047	−	0.723047i	0.0592343	−	0.0592343i	−0.676869	−	0.736103i	$-0.736664\pi$
$149$	0.723047	−	0.723047i	0.0592343	−	0.0592343i	0.736103	+	0.676869i	$0.236664\pi$
$150$		0			0
$151$	5.94167			0.483526			0.241763	−	0.970335i	$-0.422274\pi$
$151$	5.94167			0.483526			0.241763	+	0.970335i	$0.422274\pi$
$152$	−9.81603	−	16.3922i	−0.796185	−	1.32959i
$153$		0			0
$154$	−9.85027	+	27.5179i	−0.793758	+	2.21745i
$155$	−1.13166	−	1.13166i	−0.0908975	−	0.0908975i
$156$		0			0
$157$	14.0754	−	14.0754i	1.12334	−	1.12334i	0.132104	−	0.991236i	$-0.457827\pi$
$157$	14.0754	−	14.0754i	1.12334	−	1.12334i	0.991236	−	0.132104i	$-0.0421732\pi$
$158$	−11.8725	+	5.61331i	−0.944527	+	0.446571i
$159$		0			0
$160$	−0.256377	+	1.72028i	−0.0202683	+	0.136000i
$161$			23.5892i			1.85909i
$162$		0			0
$163$	−3.39073	−	3.39073i	−0.265583	−	0.265583i	0.561735	−	0.827317i	$-0.310134\pi$
$163$	−3.39073	−	3.39073i	−0.265583	−	0.265583i	−0.827317	+	0.561735i	$0.810134\pi$
$164$	1.66917	−	2.03277i	0.130341	−	0.158732i
$165$		0			0
$166$	15.5275	+	5.55821i	1.20517	+	0.431401i
$167$			9.15420i			0.708373i	0.935175	+	0.354187i	$0.115242\pi$
$167$			9.15420i			0.708373i	−0.935175	+	0.354187i	$0.884758\pi$
$168$		0			0
$169$		−	3.69568i		−	0.284283i
$170$	0.691464	−	1.93168i	0.0530329	−	0.148153i
$171$		0			0
$172$	0.139697	+	1.42233i	0.0106518	+	0.108452i
$173$	−2.30022	−	2.30022i	−0.174883	−	0.174883i	0.614238	−	0.789121i	$-0.289463\pi$
$173$	−2.30022	−	2.30022i	−0.174883	−	0.174883i	−0.789121	+	0.614238i	$0.789463\pi$
$174$		0			0
$175$		−	18.7095i		−	1.41430i
$176$	−12.0518	+	18.0155i	−0.908438	+	1.35797i
$177$		0			0
$178$	7.47989	+	15.8205i	0.560641	+	1.18579i
$179$	−7.17306	+	7.17306i	−0.536140	+	0.536140i	−0.922393	−	0.386253i	$-0.873769\pi$
$179$	−7.17306	+	7.17306i	−0.536140	+	0.536140i	0.386253	+	0.922393i	$0.373769\pi$
$180$		0			0
$181$	−17.0999	−	17.0999i	−1.27103	−	1.27103i	−0.945550	−	0.325476i	$-0.894476\pi$
$181$	−17.0999	−	17.0999i	−1.27103	−	1.27103i	−0.325476	−	0.945550i	$-0.605524\pi$
$182$	20.7500	+	7.42765i	1.53809	+	0.550574i
$183$		0			0
$184$	−4.25750	+	16.9675i	−0.313867	+	1.25086i
$185$	1.27276			0.0935754
$186$		0			0
$187$	18.0797	−	18.0797i	1.32212	−	1.32212i
$188$	6.87664	−	8.37457i	0.501531	−	0.610778i
$189$		0			0
$190$	−1.25549	−	2.65545i	−0.0910831	−	0.192647i
$191$	−23.6865			−1.71390			−0.856949	−	0.515401i	$-0.827643\pi$
$191$	−23.6865			−1.71390			−0.856949	+	0.515401i	$0.827643\pi$
$192$		0			0
$193$	26.5740			1.91284			0.956420	−	0.291995i	$-0.0943191\pi$
$193$	26.5740			1.91284			0.956420	+	0.291995i	$0.0943191\pi$
$194$	−1.70193	−	3.59969i	−0.122191	−	0.258443i
$195$		0			0
$196$	−9.57825	+	11.6647i	−0.684161	+	0.833190i
$197$	14.5507	−	14.5507i	1.03670	−	1.03670i	0.0373962	−	0.999301i	$-0.488094\pi$
$197$	14.5507	−	14.5507i	1.03670	−	1.03670i	0.999301	−	0.0373962i	$-0.0119064\pi$
$198$		0			0
$199$	−0.329215			−0.0233375			−0.0116687	−	0.999932i	$-0.503714\pi$
$199$	−0.329215			−0.0233375			−0.0116687	+	0.999932i	$0.503714\pi$
$200$	3.37678	−	13.4576i	0.238775	−	0.951594i
$201$		0			0
$202$	−12.0156	−	4.30110i	−0.845415	−	0.302624i
$203$	1.23133	+	1.23133i	0.0864222	+	0.0864222i
$204$		0			0
$205$	0.285923	−	0.285923i	0.0199697	−	0.0199697i
$206$	−11.2273	−	23.7464i	−0.782240	−	1.65449i
$207$		0			0
$208$	13.5847	+	9.08771i	0.941930	+	0.630120i
$209$		−	36.6046i		−	2.53199i
$210$		0			0
$211$	−5.20144	−	5.20144i	−0.358082	−	0.358082i	0.505024	−	0.863105i	$-0.331484\pi$
$211$	−5.20144	−	5.20144i	−0.358082	−	0.358082i	−0.863105	+	0.505024i	$0.831484\pi$
$212$	−0.513601	−	5.22927i	−0.0352743	−	0.359148i
$213$		0			0
$214$	8.42014	−	23.5226i	0.575589	−	1.60797i
$215$			0.219711i			0.0149841i
$216$		0			0
$217$		−	19.8527i		−	1.34769i
$218$	9.29019	+	3.32551i	0.629211	+	0.225232i
$219$		0			0
$220$	−2.11459	+	2.57521i	−0.142566	+	0.173621i
$221$	−13.6331	−	13.6331i	−0.917059	−	0.917059i
$222$		0			0
$223$		−	0.790802i		−	0.0529560i	−0.999649	−	0.0264780i	$-0.991571\pi$
$223$		−	0.790802i		−	0.0529560i	0.999649	−	0.0264780i	$-0.00842919\pi$
$224$	−17.3382	+	12.8406i	−1.15845	+	0.857947i
$225$		0			0
$226$	−15.0132	+	7.09822i	−0.998664	+	0.472167i
$227$	−4.35838	+	4.35838i	−0.289276	+	0.289276i	−0.836794	−	0.547518i	$-0.815573\pi$
$227$	−4.35838	+	4.35838i	−0.289276	+	0.289276i	0.547518	+	0.836794i	$0.315573\pi$
$228$		0			0
$229$	11.9442	+	11.9442i	0.789298	+	0.789298i	0.981379	−	0.192081i	$-0.0615237\pi$
$229$	11.9442	+	11.9442i	0.789298	+	0.789298i	−0.192081	+	0.981379i	$0.561524\pi$
$230$	−0.906348	+	2.53199i	−0.0597628	+	0.166954i
$231$		0			0
$232$	0.663446	+	1.10792i	0.0435574	+	0.0727385i
$233$	−26.4938			−1.73567			−0.867833	−	0.496855i	$-0.834488\pi$
$233$	−26.4938			−1.73567			−0.867833	+	0.496855i	$0.834488\pi$
$234$		0			0
$235$	1.17794	−	1.17794i	0.0768406	−	0.0768406i
$236$	−13.4456	+	1.32058i	−0.875235	+	0.0859626i
$237$		0			0
$238$	23.0088	−	10.8785i	1.49144	−	0.705149i
$239$	1.09196			0.0706333			0.0353167	−	0.999376i	$-0.488756\pi$
$239$	1.09196			0.0706333			0.0353167	+	0.999376i	$0.488756\pi$
$240$		0			0
$241$	14.3414			0.923814			0.461907	−	0.886928i	$-0.347165\pi$
$241$	14.3414			0.923814			0.461907	+	0.886928i	$0.347165\pi$
$242$	−23.4772	+	11.1000i	−1.50917	+	0.713533i
$243$		0			0
$244$	−0.230098	−	2.34276i	−0.0147305	−	0.149980i
$245$	−1.64072	+	1.64072i	−0.104822	+	0.104822i
$246$		0			0
$247$	−27.6019			−1.75627
$248$	3.58311	−	14.2798i	0.227528	−	0.906771i
$249$		0			0
$250$	1.45157	−	4.05513i	0.0918054	−	0.256469i
$251$	5.97677	+	5.97677i	0.377250	+	0.377250i	0.870109	−	0.492859i	$-0.164048\pi$
$251$	5.97677	+	5.97677i	0.377250	+	0.377250i	−0.492859	+	0.870109i	$0.664048\pi$
$252$		0			0
$253$	−23.6982	+	23.6982i	−1.48989	+	1.48989i
$254$	−19.5598	+	9.24782i	−1.22729	+	0.580260i
$255$		0			0
$256$	−14.7887	+	6.10684i	−0.924296	+	0.381677i
$257$		−	23.4079i		−	1.46015i	−0.683369	−	0.730073i	$-0.739486\pi$
$257$		−	23.4079i		−	1.46015i	0.683369	−	0.730073i	$-0.260514\pi$
$258$		0			0
$259$	11.1640	+	11.1640i	0.693695	+	0.693695i
$260$	1.94185	+	1.59452i	0.120428	+	0.0988880i
$261$		0			0
$262$	−6.68816	−	2.39409i	−0.413196	−	0.147907i
$263$			13.3165i			0.821128i	0.911832	+	0.410564i	$0.134668\pi$
$263$			13.3165i			0.821128i	−0.911832	+	0.410564i	$0.865332\pi$
$264$		0			0
$265$		−	0.807777i		−	0.0496213i
$266$	12.2797	−	34.3046i	0.752914	−	2.10335i
$267$		0			0
$268$	18.2473	−	1.79219i	1.11463	−	0.109475i
$269$	−8.78530	−	8.78530i	−0.535649	−	0.535649i	0.386599	−	0.922248i	$-0.373650\pi$
$269$	−8.78530	−	8.78530i	−0.535649	−	0.535649i	−0.922248	+	0.386599i	$0.873650\pi$
$270$		0			0
$271$		−	1.46274i		−	0.0888554i	−0.999013	−	0.0444277i	$-0.985854\pi$
$271$		−	1.46274i		−	0.0888554i	0.999013	−	0.0444277i	$-0.0141464\pi$
$272$	18.5134	−	3.67208i	1.12254	−	0.222652i
$273$		0			0
$274$	−2.48575	−	5.25754i	−0.150170	−	0.317619i
$275$	18.7959	−	18.7959i	1.13344	−	1.13344i
$276$		0			0
$277$	2.83891	+	2.83891i	0.170573	+	0.170573i	0.787231	−	0.616658i	$-0.211514\pi$
$277$	2.83891	+	2.83891i	0.170573	+	0.170573i	−0.616658	+	0.787231i	$0.711514\pi$
$278$	12.5125	+	4.47897i	0.750450	+	0.268631i
$279$		0			0
$280$	−2.84563	+	1.70402i	−0.170059	+	0.101835i
$281$	6.53163			0.389644			0.194822	−	0.980839i	$-0.437587\pi$
$281$	6.53163			0.389644			0.194822	+	0.980839i	$0.437587\pi$
$282$		0			0
$283$	−1.82128	+	1.82128i	−0.108264	+	0.108264i	−0.759164	−	0.650900i	$-0.774392\pi$
$283$	−1.82128	+	1.82128i	−0.108264	+	0.108264i	0.650900	+	0.759164i	$0.274392\pi$
$284$	−3.82711	−	3.14257i	−0.227097	−	0.186477i
$285$		0			0
$286$	13.3839	+	28.3079i	0.791407	+	1.67388i
$287$	5.01592			0.296080
$288$		0			0
$289$	−5.26448			−0.309675
$290$	0.0848564	+	0.179477i	0.00498294	+	0.0105392i
$291$		0			0
$292$	−10.3404	−	8.49082i	−0.605123	−	0.496888i
$293$	−22.9270	+	22.9270i	−1.33941	+	1.33941i	−0.442778	+	0.896631i	$0.646007\pi$
$293$	−22.9270	+	22.9270i	−1.33941	+	1.33941i	−0.896631	+	0.442778i	$0.853993\pi$
$294$		0			0
$295$	−2.07697			−0.120926
$296$	6.01522	+	10.0451i	0.349627	+	0.583858i
$297$		0			0
$298$	1.36149	+	0.487360i	0.0788693	+	0.0282320i
$299$	17.8697	+	17.8697i	1.03343	+	1.03343i
$300$		0			0
$301$	−1.92718	+	1.92718i	−0.111081	+	0.111081i
$302$	3.59162	+	7.59652i	0.206674	+	0.437130i
$303$		0			0
$304$	15.0241	−	22.4587i	0.861693	−	1.28810i
$305$		−	0.361892i		−	0.0207219i
$306$		0			0
$307$	10.8441	+	10.8441i	0.618904	+	0.618904i	0.945250	−	0.326346i	$-0.105817\pi$
$307$	10.8441	+	10.8441i	0.618904	+	0.618904i	−0.326346	+	0.945250i	$0.605817\pi$
$308$	−41.1363	+	4.04027i	−2.34396	+	0.230216i
$309$		0			0
$310$	0.762783	−	2.13092i	0.0433231	−	0.121028i
$311$			16.4393i			0.932189i	0.884735	+	0.466095i	$0.154339\pi$
$311$			16.4393i			0.932189i	−0.884735	+	0.466095i	$0.845661\pi$
$312$		0			0
$313$		−	0.171508i		−	0.00969419i	−0.999988	−	0.00484710i	$-0.998457\pi$
$313$		−	0.171508i		−	0.00969419i	0.999988	−	0.00484710i	$-0.00154288\pi$
$314$	26.5039	+	9.48733i	1.49570	+	0.535401i
$315$		0			0
$316$	−14.3534	−	11.7861i	−0.807442	−	0.663019i
$317$	11.9635	+	11.9635i	0.671937	+	0.671937i	0.958162	−	0.286226i	$-0.0924007\pi$
$317$	11.9635	+	11.9635i	0.671937	+	0.671937i	−0.286226	+	0.958162i	$0.592401\pi$
$318$		0			0
$319$			2.47403i			0.138519i
$320$	−2.35439	+	0.712096i	−0.131614	+	0.0398074i
$321$		0			0
$322$	−30.1591	+	14.2592i	−1.68070	+	0.794633i
$323$	−22.5387	+	22.5387i	−1.25408	+	1.25408i
$324$		0			0
$325$	−14.1732	−	14.1732i	−0.786187	−	0.786187i
$326$	2.28547	−	6.38473i	0.126581	−	0.353618i
$327$		0			0
$328$	3.60791	+	0.905299i	0.199213	+	0.0499868i
$329$	20.6645			1.13927
$330$		0			0
$331$	−2.32460	+	2.32460i	−0.127772	+	0.127772i	−0.768101	−	0.640329i	$-0.778798\pi$
$331$	−2.32460	+	2.32460i	−0.127772	+	0.127772i	0.640329	+	0.768101i	$0.278798\pi$
$332$	2.27980	+	23.2120i	0.125120	+	1.27392i
$333$		0			0
$334$	−11.7038	+	5.53353i	−0.640403	+	0.302781i
$335$	2.81870			0.154002
$336$		0			0
$337$	−10.9566			−0.596842			−0.298421	−	0.954434i	$-0.596460\pi$
$337$	−10.9566			−0.596842			−0.298421	+	0.954434i	$0.596460\pi$
$338$	4.72499	−	2.23397i	0.257006	−	0.121512i
$339$		0			0
$340$	2.88767	−	0.283617i	0.156606	−	0.0153813i
$341$	19.9444	−	19.9444i	1.08005	−	1.08005i
$342$		0			0
$343$	−2.08489			−0.112573
$344$	−1.73403	+	1.03838i	−0.0934926	+	0.0559854i
$345$		0			0
$346$	1.55043	−	4.33131i	0.0833517	−	0.232853i
$347$	−1.35986	−	1.35986i	−0.0730012	−	0.0730012i	0.669663	−	0.742665i	$-0.266438\pi$
$347$	−1.35986	−	1.35986i	−0.0730012	−	0.0730012i	−0.742665	+	0.669663i	$0.766438\pi$
$348$		0			0
$349$	2.55298	−	2.55298i	0.136658	−	0.136658i	−0.635469	−	0.772127i	$-0.719193\pi$
$349$	2.55298	−	2.55298i	0.136658	−	0.136658i	0.772127	+	0.635469i	$0.219193\pi$
$350$	23.9204	−	11.3095i	1.27860	−	0.604519i
$351$		0			0
$352$	−30.3182	−	4.51837i	−1.61597	−	0.240830i
$353$			12.5253i			0.666656i	0.942811	+	0.333328i	$0.108172\pi$
$353$			12.5253i			0.666656i	−0.942811	+	0.333328i	$0.891828\pi$
$354$		0			0
$355$	−0.538311	−	0.538311i	−0.0285706	−	0.0285706i
$356$	−15.7053	+	19.1263i	−0.832378	+	1.01369i
$357$		0			0
$358$	−13.5068	−	4.83490i	−0.713859	−	0.255532i
$359$		−	11.1836i		−	0.590248i	−0.955459	−	0.295124i	$-0.904639\pi$
$359$		−	11.1836i		−	0.590248i	0.955459	−	0.295124i	$-0.0953610\pi$
$360$		0			0
$361$			26.6325i			1.40171i
$362$	11.5260	−	32.1991i	0.605791	−	1.69235i
$363$		0			0
$364$	3.04659	+	31.0191i	0.159685	+	1.62584i
$365$	−1.45445	−	1.45445i	−0.0761292	−	0.0761292i
$366$		0			0
$367$			13.0743i			0.682473i	0.939977	+	0.341237i	$0.110846\pi$
$367$			13.0743i			0.682473i	−0.939977	+	0.341237i	$0.889154\pi$
$368$	−24.2668	+	4.81323i	−1.26499	+	0.250907i
$369$		0			0
$370$	0.769360	+	1.62725i	0.0399971	+	0.0845966i
$371$	7.08537	−	7.08537i	0.367854	−	0.367854i
$372$		0			0
$373$	−5.64329	−	5.64329i	−0.292198	−	0.292198i	0.545750	−	0.837948i	$-0.316245\pi$
$373$	−5.64329	−	5.64329i	−0.292198	−	0.292198i	−0.837948	+	0.545750i	$0.816245\pi$
$374$	34.0439	+	12.1863i	1.76037	+	0.630141i
$375$		0			0
$376$	14.8638	+	3.72964i	0.766543	+	0.192342i
$377$	1.86556			0.0960812
$378$		0			0
$379$	−9.86282	+	9.86282i	−0.506619	+	0.506619i	−0.913487	−	0.406868i	$-0.866621\pi$
$379$	−9.86282	+	9.86282i	−0.506619	+	0.506619i	0.406868	+	0.913487i	$0.366621\pi$
$380$	2.63612	−	3.21034i	0.135230	−	0.164687i
$381$		0			0
$382$	−14.3180	−	30.2836i	−0.732575	−	1.54945i
$383$	−14.8365			−0.758111			−0.379055	−	0.925374i	$-0.623751\pi$
$383$	−14.8365			−0.758111			−0.379055	+	0.925374i	$0.623751\pi$
$384$		0			0
$385$	−6.35442			−0.323851
$386$	16.0635	+	33.9753i	0.817609	+	1.72930i
$387$		0			0
$388$	3.57348	−	4.35189i	0.181416	−	0.220934i
$389$	−3.64954	+	3.64954i	−0.185039	+	0.185039i	−0.793548	−	0.608508i	$-0.791768\pi$
$389$	−3.64954	+	3.64954i	−0.185039	+	0.185039i	0.608508	+	0.793548i	$0.291768\pi$
$390$		0			0
$391$	29.1835			1.47587
$392$	−20.7033	−	5.19489i	−1.04568	−	0.262382i
$393$		0			0
$394$	27.3990	+	9.80772i	1.38034	+	0.494106i
$395$	−2.01891	−	2.01891i	−0.101582	−	0.101582i
$396$		0			0
$397$	13.3913	−	13.3913i	0.672088	−	0.672088i	−0.286109	−	0.958197i	$-0.592362\pi$
$397$	13.3913	−	13.3913i	0.672088	−	0.672088i	0.958197	+	0.286109i	$0.0923619\pi$
$398$	−0.199004	−	0.420907i	−0.00997518	−	0.0210982i
$399$		0			0
$400$	19.2469	−	3.81756i	0.962346	−	0.190878i
$401$		−	27.5346i		−	1.37501i	−0.726179	−	0.687505i	$-0.758706\pi$
$401$		−	27.5346i		−	1.37501i	0.726179	−	0.687505i	$-0.241294\pi$
$402$		0			0
$403$	−15.0392	−	15.0392i	−0.749155	−	0.749155i
$404$	−1.76417	−	17.9621i	−0.0877709	−	0.893646i
$405$		0			0
$406$	−0.829958	+	2.31858i	−0.0411901	+	0.115069i
$407$			22.4311i			1.11187i
$408$		0			0
$409$			16.2349i			0.802762i	0.915911	+	0.401381i	$0.131470\pi$
$409$			16.2349i			0.802762i	−0.915911	+	0.401381i	$0.868530\pi$
$410$	0.538392	+	0.192723i	0.0265893	+	0.00951789i
$411$		0			0
$412$	23.5735	−	28.7084i	1.16138	−	1.41436i
$413$	−18.2180	−	18.2180i	−0.896451	−	0.896451i
$414$		0			0
$415$			3.58560i			0.176010i
$416$	−3.40710	+	22.8616i	−0.167047	+	1.12088i
$417$		0			0
$418$	46.7996	−	22.1268i	2.28904	−	1.08226i
$419$	2.15752	−	2.15752i	0.105402	−	0.105402i	−0.652439	−	0.757841i	$-0.726254\pi$
$419$	2.15752	−	2.15752i	0.105402	−	0.105402i	0.757841	+	0.652439i	$0.226254\pi$
$420$		0			0
$421$	17.2411	+	17.2411i	0.840281	+	0.840281i	0.988895	−	0.148615i	$-0.0474814\pi$
$421$	17.2411	+	17.2411i	0.840281	+	0.840281i	−0.148615	+	0.988895i	$0.547481\pi$
$422$	3.50596	−	9.79429i	0.170667	−	0.476778i
$423$		0			0
$424$	6.37525	−	3.81764i	0.309609	−	0.185401i
$425$	−23.1466			−1.12277
$426$		0			0
$427$	3.17431	−	3.17431i	0.153616	−	0.153616i
$428$	35.1639	−	3.45367i	1.69971	−	0.166940i
$429$		0			0
$430$	−0.280903	+	0.132811i	−0.0135464	+	0.00640470i
$431$	33.3451			1.60618			0.803089	−	0.595860i	$-0.203189\pi$
$431$	33.3451			1.60618			0.803089	+	0.595860i	$0.203189\pi$
$432$		0			0
$433$	−22.2248			−1.06805			−0.534027	−	0.845467i	$-0.679322\pi$
$433$	−22.2248			−1.06805			−0.534027	+	0.845467i	$0.679322\pi$
$434$	25.3819	−	12.0005i	1.21837	−	0.576044i
$435$		0			0
$436$	1.36402	+	13.8879i	0.0653246	+	0.665108i
$437$	29.5429	−	29.5429i	1.41323	−	1.41323i
$438$		0			0
$439$	−0.240504			−0.0114786			−0.00573932	−	0.999984i	$-0.501827\pi$
$439$	−0.240504			−0.0114786			−0.00573932	+	0.999984i	$0.501827\pi$
$440$	−4.57068	−	1.14688i	−0.217899	−	0.0546753i
$441$		0			0
$442$	9.18917	−	25.6710i	0.437084	−	1.22105i
$443$	26.5432	+	26.5432i	1.26110	+	1.26110i	0.950559	+	0.310546i	$0.100512\pi$
$443$	26.5432	+	26.5432i	1.26110	+	1.26110i	0.310546	+	0.950559i	$0.399488\pi$
$444$		0			0
$445$	−2.69025	+	2.69025i	−0.127530	+	0.127530i
$446$	1.01105	−	0.478024i	0.0478747	−	0.0226351i
$447$		0			0
$448$	−26.8975	−	14.4052i	−1.27079	−	0.680584i
$449$			31.9534i			1.50797i	0.656890	+	0.753987i	$0.271872\pi$
$449$			31.9534i			1.50797i	−0.656890	+	0.753987i	$0.728128\pi$
$450$		0			0
$451$	5.03910	+	5.03910i	0.237282	+	0.237282i
$452$	−18.1504	−	14.9039i	−0.853722	−	0.701020i
$453$		0			0
$454$	−8.20681	−	2.93770i	−0.385165	−	0.137873i
$455$			4.79158i			0.224633i
$456$		0			0
$457$			13.0060i			0.608395i	0.952609	+	0.304198i	$0.0983883\pi$
$457$			13.0060i			0.608395i	−0.952609	+	0.304198i	$0.901612\pi$
$458$	−8.05085	+	22.4910i	−0.376191	+	1.05093i
$459$		0			0
$460$	−3.78505	+	0.371755i	−0.176479	+	0.0173332i
$461$	14.0979	+	14.0979i	0.656603	+	0.656603i	0.954575	−	0.297972i	$-0.0963101\pi$
$461$	14.0979	+	14.0979i	0.656603	+	0.656603i	−0.297972	+	0.954575i	$0.596310\pi$
$462$		0			0
$463$			35.7903i			1.66331i	0.555289	+	0.831657i	$0.312607\pi$
$463$			35.7903i			1.66331i	−0.555289	+	0.831657i	$0.687393\pi$
$464$	−1.01545	+	1.51794i	−0.0471412	+	0.0704687i
$465$		0			0
$466$	−16.0150	−	33.8728i	−0.741880	−	1.56912i
$467$	−15.2548	+	15.2548i	−0.705909	+	0.705909i	−0.965672	−	0.259763i	$-0.916355\pi$
$467$	−15.2548	+	15.2548i	−0.705909	+	0.705909i	0.259763	+	0.965672i	$0.416355\pi$
$468$		0			0
$469$	24.7240	+	24.7240i	1.14165	+	1.14165i
$470$	2.21806	+	0.793976i	0.102312	+	0.0366234i
$471$		0			0
$472$	−9.81600	−	16.3922i	−0.451818	−	0.754511i
$473$	−3.87217			−0.178043
$474$		0			0
$475$	−23.4316	+	23.4316i	−1.07512	+	1.07512i
$476$	27.8167	+	22.8413i	1.27498	+	1.04693i
$477$		0			0
$478$	0.660071	+	1.39609i	0.0301909	+	0.0638559i
$479$	23.2925			1.06426			0.532131	−	0.846662i	$-0.321391\pi$
$479$	23.2925			1.06426			0.532131	+	0.846662i	$0.321391\pi$
$480$		0			0
$481$	16.9143			0.771226
$482$	8.66912	+	18.3358i	0.394868	+	0.835172i
$483$		0			0
$484$	−28.3830	−	23.3062i	−1.29013	−	1.05937i
$485$	0.612124	−	0.612124i	0.0277951	−	0.0277951i
$486$		0			0
$487$	6.49302			0.294227			0.147113	−	0.989120i	$-0.453002\pi$
$487$	6.49302			0.294227			0.147113	+	0.989120i	$0.453002\pi$
$488$	2.85617	−	1.71034i	0.129293	−	0.0774234i
$489$		0			0
$490$	−3.08947	−	1.10590i	−0.139568	−	0.0499596i
$491$	9.99765	+	9.99765i	0.451188	+	0.451188i	0.895749	−	0.444561i	$-0.146640\pi$
$491$	9.99765	+	9.99765i	0.451188	+	0.451188i	−0.444561	+	0.895749i	$0.646640\pi$
$492$		0			0
$493$	1.52334	−	1.52334i	0.0686080	−	0.0686080i
$494$	−16.6848	−	35.2895i	−0.750685	−	1.58775i
$495$		0			0
$496$	20.4229	−	4.05082i	0.917017	−	0.181887i
$497$		−	9.44353i		−	0.423600i
$498$		0			0
$499$	−16.6215	−	16.6215i	−0.744080	−	0.744080i	0.229281	−	0.973360i	$-0.426363\pi$
$499$	−16.6215	−	16.6215i	−0.744080	−	0.744080i	−0.973360	+	0.229281i	$0.926363\pi$
$500$	6.06200	−	0.595389i	0.271101	−	0.0266266i
$501$		0			0
$502$	−4.02856	+	11.2542i	−0.179803	+	0.502301i
$503$			22.3009i			0.994348i	0.867651	+	0.497174i	$0.165629\pi$
$503$			22.3009i			0.994348i	−0.867651	+	0.497174i	$0.834371\pi$
$504$		0			0
$505$		−	2.77464i		−	0.123470i
$506$	−44.6236	−	15.9734i	−1.98376	−	0.710106i
$507$		0			0
$508$	−23.6470	−	19.4173i	−1.04916	−	0.861505i
$509$	−19.1255	−	19.1255i	−0.847721	−	0.847721i	0.142128	−	0.989848i	$-0.454606\pi$
$509$	−19.1255	−	19.1255i	−0.847721	−	0.847721i	−0.989848	+	0.142128i	$0.954606\pi$
$510$		0			0
$511$		−	25.5152i		−	1.12872i
$512$	−16.7472	−	15.2162i	−0.740128	−	0.672466i
$513$		0			0
$514$	29.9274	−	14.1496i	1.32004	−	0.624114i
$515$	4.03805	−	4.03805i	0.177938	−	0.177938i
$516$		0			0
$517$	20.7600	+	20.7600i	0.913025	+	0.913025i
$518$	−7.52492	+	21.0217i	−0.330626	+	0.923641i
$519$		0			0
$520$	−0.864810	+	3.44654i	−0.0379244	+	0.151141i
$521$	5.15019			0.225634			0.112817	−	0.993616i	$-0.464013\pi$
$521$	5.15019			0.225634			0.112817	+	0.993616i	$0.464013\pi$
$522$		0			0
$523$	−0.348495	+	0.348495i	−0.0152386	+	0.0152386i	−0.714685	−	0.699446i	$-0.753430\pi$
$523$	−0.348495	+	0.348495i	−0.0152386	+	0.0152386i	0.699446	+	0.714685i	$0.253430\pi$
$524$	−0.981980	−	9.99810i	−0.0428980	−	0.436769i
$525$		0			0
$526$	−17.0253	+	8.04953i	−0.742338	+	0.350976i
$527$	−24.5609			−1.06989
$528$		0			0
$529$	−15.2527			−0.663163
$530$	1.03276	−	0.488285i	0.0448600	−	0.0212098i
$531$		0			0
$532$	51.2818	−	5.03673i	2.22335	−	0.218370i
$533$	3.79976	−	3.79976i	0.164586	−	0.164586i
$534$		0			0
$535$	5.43184			0.234839
$536$	13.3215	+	22.2461i	0.575400	+	0.960886i
$537$		0			0
$538$	5.92161	−	16.5427i	0.255299	−	0.713206i
$539$	−28.9160	−	28.9160i	−1.24550	−	1.24550i
$540$		0			0
$541$	13.2936	−	13.2936i	0.571536	−	0.571536i	−0.361021	−	0.932558i	$-0.617572\pi$
$541$	13.2936	−	13.2936i	0.571536	−	0.571536i	0.932558	+	0.361021i	$0.117572\pi$
$542$	1.87014	−	0.884200i	0.0803295	−	0.0379797i
$543$		0			0
$544$	15.8858	+	21.4500i	0.681099	+	0.919663i
$545$			2.14529i			0.0918940i
$546$		0			0
$547$	17.0584	+	17.0584i	0.729366	+	0.729366i	0.970494	−	0.241127i	$-0.0775171\pi$
$547$	17.0584	+	17.0584i	0.729366	+	0.729366i	−0.241127	+	0.970494i	$0.577517\pi$
$548$	5.21926	−	6.35615i	0.222956	−	0.271521i
$549$		0			0
$550$	35.3927	+	12.6691i	1.50915	+	0.540214i
$551$		−	3.08421i		−	0.131392i
$552$		0			0
$553$		−	35.4175i		−	1.50611i
$554$	−1.91352	+	5.34565i	−0.0812979	+	0.227115i
$555$		0			0
$556$	1.83713	+	18.7049i	0.0779117	+	0.793264i
$557$	−14.5673	−	14.5673i	−0.617236	−	0.617236i	0.327586	−	0.944822i	$-0.393765\pi$
$557$	−14.5673	−	14.5673i	−0.617236	−	0.617236i	−0.944822	+	0.327586i	$0.893765\pi$
$558$		0			0
$559$			2.91983i			0.123496i
$560$	−3.89875	−	2.60813i	−0.164752	−	0.110214i
$561$		0			0
$562$	3.94824	+	8.35079i	0.166546	+	0.352257i
$563$	−21.3310	+	21.3310i	−0.898994	+	0.898994i	−0.995347	−	0.0963535i	$-0.969282\pi$
$563$	−21.3310	+	21.3310i	−0.898994	+	0.898994i	0.0963535	+	0.995347i	$0.469282\pi$
$564$		0			0
$565$	−2.55298	−	2.55298i	−0.107405	−	0.107405i
$566$	−3.42946	−	1.22761i	−0.144151	−	0.0516001i
$567$		0			0
$568$	1.70442	−	6.79265i	0.0715158	−	0.285013i
$569$	21.5582			0.903765			0.451882	−	0.892077i	$-0.350753\pi$
$569$	21.5582			0.903765			0.451882	+	0.892077i	$0.350753\pi$
$570$		0			0
$571$	−31.5802	+	31.5802i	−1.32159	+	1.32159i	−0.409100	+	0.912490i	$0.634157\pi$
$571$	−31.5802	+	31.5802i	−1.32159	+	1.32159i	−0.912490	+	0.409100i	$0.865843\pi$
$572$	−28.1018	+	34.2231i	−1.17499	+	1.43094i
$573$		0			0
$574$	3.03202	+	6.41293i	0.126554	+	0.267671i
$575$	30.3397			1.26525
$576$		0			0
$577$	−26.0498			−1.08447			−0.542235	−	0.840227i	$-0.682422\pi$
$577$	−26.0498			−1.08447			−0.542235	+	0.840227i	$0.682422\pi$
$578$	−3.18227	−	6.73072i	−0.132365	−	0.279961i
$579$		0			0
$580$	−0.178170	+	0.216981i	−0.00739811	+	0.00900963i
$581$	−31.4509	+	31.4509i	−1.30480	+	1.30480i
$582$		0			0
$583$	14.2362			0.589604
$584$	4.60511	−	18.3528i	0.190561	−	0.759446i
$585$		0			0
$586$	−43.1714	−	15.4536i	−1.78340	−	0.638383i
$587$	0.757628	+	0.757628i	0.0312707	+	0.0312707i	0.722569	−	0.691299i	$-0.242961\pi$
$587$	0.757628	+	0.757628i	0.0312707	+	0.0312707i	−0.691299	+	0.722569i	$0.742961\pi$
$588$		0			0
$589$	−24.8633	+	24.8633i	−1.02448	+	1.02448i
$590$	−1.25549	−	2.65544i	−0.0516877	−	0.109323i
$591$		0			0
$592$	−9.20672	+	13.7626i	−0.378394	+	0.565639i
$593$		−	32.5463i		−	1.33652i	−0.743929	−	0.668259i	$-0.767040\pi$
$593$		−	32.5463i		−	1.33652i	0.743929	−	0.668259i	$-0.232960\pi$
$594$		0			0
$595$	3.91262	+	3.91262i	0.160402	+	0.160402i
$596$	0.199899	+	2.03529i	0.00818820	+	0.0833688i
$597$		0			0
$598$	−12.0449	+	33.6487i	−0.492551	+	1.37600i
$599$		−	30.0578i		−	1.22813i	−0.789256	−	0.614065i	$-0.789533\pi$
$599$		−	30.0578i		−	1.22813i	0.789256	−	0.614065i	$-0.210467\pi$
$600$		0			0
$601$		−	23.7148i		−	0.967348i	−0.875248	−	0.483674i	$-0.839302\pi$
$601$		−	23.7148i		−	0.967348i	0.875248	−	0.483674i	$-0.160698\pi$
$602$	−3.62887	−	1.29899i	−0.147902	−	0.0529428i
$603$		0			0
$604$	−7.54121	+	9.18389i	−0.306847	+	0.373687i
$605$	−3.99227	−	3.99227i	−0.162309	−	0.162309i
$606$		0			0
$607$		−	36.9838i		−	1.50113i	−0.660799	−	0.750563i	$-0.729782\pi$
$607$		−	36.9838i		−	1.50113i	0.660799	−	0.750563i	$-0.270218\pi$
$608$	37.7956	+	5.63274i	1.53282	+	0.228438i
$609$		0			0
$610$	0.462685	−	0.218756i	0.0187336	−	0.00885719i
$611$	15.6542	−	15.6542i	0.633302	−	0.633302i
$612$		0			0
$613$	9.51791	+	9.51791i	0.384425	+	0.384425i	0.872693	−	0.488269i	$-0.162371\pi$
$613$	9.51791	+	9.51791i	0.384425	+	0.384425i	−0.488269	+	0.872693i	$0.662371\pi$
$614$	−7.30930	+	20.4194i	−0.294979	+	0.824058i
$615$		0			0
$616$	−30.0316	−	50.1512i	−1.21001	−	2.02065i
$617$	−37.4296			−1.50686			−0.753430	−	0.657528i	$-0.771602\pi$
$617$	−37.4296			−1.50686			−0.753430	+	0.657528i	$0.771602\pi$
$618$		0			0
$619$	−0.0391337	+	0.0391337i	−0.00157291	+	0.00157291i	−0.707893	−	0.706320i	$-0.750354\pi$
$619$	−0.0391337	+	0.0391337i	−0.00157291	+	0.00157291i	0.706320	+	0.707893i	$0.250354\pi$
$620$	3.18550	−	0.312869i	0.127933	−	0.0125651i
$621$		0			0
$622$	−21.0180	+	9.93725i	−0.842743	+	0.398448i
$623$	−47.1948			−1.89082
$624$		0			0
$625$	−23.5909			−0.943637
$626$	0.219275	−	0.103673i	0.00876401	−	0.00414361i
$627$		0			0
$628$	3.89140	+	39.6206i	0.155284	+	1.58103i
$629$	13.8116	−	13.8116i	0.550704	−	0.550704i
$630$		0			0
$631$	36.6535			1.45915			0.729576	−	0.683900i	$-0.239717\pi$
$631$	36.6535			1.45915			0.729576	+	0.683900i	$0.239717\pi$
$632$	6.39234	−	25.4755i	0.254274	−	1.01336i
$633$		0			0
$634$	−8.06382	+	22.5272i	−0.320255	+	0.894670i
$635$	−3.32612	−	3.32612i	−0.131993	−	0.131993i
$636$		0			0
$637$	−21.8042	+	21.8042i	−0.863915	+	0.863915i
$638$	−3.16309	+	1.49551i	−0.125228	+	0.0592076i
$639$		0			0
$640$	−2.33361	−	2.57967i	−0.0922439	−	0.101971i
$641$		−	12.4650i		−	0.492339i	−0.969227	−	0.246169i	$-0.920828\pi$
$641$		−	12.4650i		−	0.492339i	0.969227	−	0.246169i	$-0.0791719\pi$
$642$		0			0
$643$	−5.95415	−	5.95415i	−0.234809	−	0.234809i	0.579888	−	0.814696i	$-0.303096\pi$
$643$	−5.95415	−	5.95415i	−0.234809	−	0.234809i	−0.814696	+	0.579888i	$0.803096\pi$
$644$	−36.4612	−	29.9395i	−1.43677	−	1.17978i
$645$		0			0
$646$	−42.4402	−	15.1919i	−1.66979	−	0.597716i
$647$			8.17712i			0.321476i	0.986997	+	0.160738i	$0.0513874\pi$
$647$			8.17712i			0.321476i	−0.986997	+	0.160738i	$0.948613\pi$
$648$		0			0
$649$		−	36.6045i		−	1.43685i
$650$	9.55323	−	26.6880i	0.374709	−	1.04679i
$651$		0			0
$652$	9.54451	−	0.937429i	0.373792	−	0.0367126i
$653$	26.9263	+	26.9263i	1.05371	+	1.05371i	0.998473	+	0.0552346i	$0.0175907\pi$
$653$	26.9263	+	26.9263i	1.05371	+	1.05371i	0.0552346	+	0.998473i	$0.482409\pi$
$654$		0			0
$655$		−	1.54443i		−	0.0603458i
$656$	1.02347	+	5.16000i	0.0399597	+	0.201464i
$657$		0			0
$658$	12.4913	+	26.4199i	0.486961	+	1.02996i
$659$	1.76198	−	1.76198i	0.0686372	−	0.0686372i	−0.671955	−	0.740592i	$-0.734545\pi$
$659$	1.76198	−	1.76198i	0.0686372	−	0.0686372i	0.740592	+	0.671955i	$0.234545\pi$
$660$		0			0
$661$	−0.153923	−	0.153923i	−0.00598692	−	0.00598692i	0.704107	−	0.710094i	$-0.251348\pi$
$661$	−0.153923	−	0.153923i	−0.00598692	−	0.00598692i	−0.710094	+	0.704107i	$0.751348\pi$
$662$	−4.37721	−	1.56686i	−0.170125	−	0.0608979i
$663$		0			0
$664$	−28.2988	+	16.9459i	−1.09821	+	0.657630i
$665$	7.92162			0.307187
$666$		0			0
$667$	−1.99675	+	1.99675i	−0.0773144	+	0.0773144i
$668$	−14.1494	−	11.6186i	−0.547458	−	0.449536i
$669$		0			0
$670$	1.70385	+	3.60375i	0.0658254	+	0.139225i
$671$	6.37797			0.246219
$672$		0			0
$673$	−23.0014			−0.886639			−0.443320	−	0.896364i	$-0.646199\pi$
$673$	−23.0014			−0.886639			−0.443320	+	0.896364i	$0.646199\pi$
$674$	−6.62302	−	14.0081i	−0.255109	−	0.539573i
$675$		0			0
$676$	5.71233	+	4.69059i	0.219705	+	0.180407i
$677$	−25.8728	+	25.8728i	−0.994374	+	0.994374i	−0.999984	−	0.00561069i	$-0.998214\pi$
$677$	−25.8728	+	25.8728i	−0.994374	+	0.994374i	0.00561069	+	0.999984i	$0.498214\pi$
$678$		0			0
$679$	10.7384			0.412103
$680$	2.10815	+	3.52049i	0.0808437	+	0.135005i
$681$		0			0
$682$	37.5553	+	13.4432i	1.43806	+	0.514769i
$683$	−16.4249	−	16.4249i	−0.628480	−	0.628480i	0.319205	−	0.947686i	$-0.396584\pi$
$683$	−16.4249	−	16.4249i	−0.628480	−	0.628480i	−0.947686	+	0.319205i	$0.896584\pi$
$684$		0			0
$685$	0.894039	−	0.894039i	0.0341595	−	0.0341595i
$686$	−1.26027	−	2.66556i	−0.0481175	−	0.101772i
$687$		0			0
$688$	−2.37577	−	1.58931i	−0.0905752	−	0.0605918i
$689$		−	10.7349i		−	0.408967i
$690$		0			0
$691$	0.0989768	+	0.0989768i	0.00376526	+	0.00376526i	0.708987	−	0.705222i	$-0.249153\pi$
$691$	0.0989768	+	0.0989768i	0.00376526	+	0.00376526i	−0.705222	+	0.708987i	$0.749153\pi$
$692$	6.47485	−	0.635938i	0.246137	−	0.0241747i
$693$		0			0
$694$	0.916595	−	2.56061i	0.0347935	−	0.0971996i
$695$			2.88938i			0.109601i
$696$		0			0
$697$		−	6.20548i		−	0.235049i
$698$	4.80726	+	1.72080i	0.181957	+	0.0651333i
$699$		0			0
$700$	28.9188	+	23.7462i	1.09303	+	0.897522i
$701$	−9.89571	−	9.89571i	−0.373756	−	0.373756i	0.495087	−	0.868843i	$-0.335136\pi$
$701$	−9.89571	−	9.89571i	−0.373756	−	0.373756i	−0.868843	+	0.495087i	$0.835136\pi$
$702$		0			0
$703$		−	27.9633i		−	1.05466i
$704$	−12.5500	−	41.4936i	−0.472994	−	1.56385i
$705$		0			0
$706$	−16.0138	+	7.57131i	−0.602688	+	0.284950i
$707$	24.3376	−	24.3376i	0.915309	−	0.915309i
$708$		0			0
$709$	−8.60454	−	8.60454i	−0.323150	−	0.323150i	0.526824	−	0.849974i	$-0.323383\pi$
$709$	−8.60454	−	8.60454i	−0.323150	−	0.323150i	−0.849974	+	0.526824i	$0.823383\pi$
$710$	0.362841	−	1.01364i	0.0136172	−	0.0380412i
$711$		0			0
$712$	−33.9468	−	8.51797i	−1.27221	−	0.319224i
$713$	32.1935			1.20566
$714$		0			0
$715$	−4.81373	+	4.81373i	−0.180023	+	0.180023i
$716$	−1.98312	−	20.1913i	−0.0741128	−	0.754585i
$717$		0			0
$718$	14.2984	−	6.76027i	0.533612	−	0.252291i
$719$	−39.6092			−1.47717			−0.738586	−	0.674159i	$-0.764506\pi$
$719$	−39.6092			−1.47717			−0.738586	+	0.674159i	$0.764506\pi$
$720$		0			0
$721$	70.8390			2.63818
$722$	−34.0500	+	16.0988i	−1.26721	+	0.599135i
$723$		0			0
$724$	48.1342	−	4.72758i	1.78889	−	0.175699i
$725$	1.58370	−	1.58370i	0.0588170	−	0.0588170i
$726$		0			0
$727$	−17.9378			−0.665278			−0.332639	−	0.943054i	$-0.607939\pi$
$727$	−17.9378			−0.665278			−0.332639	+	0.943054i	$0.607939\pi$
$728$	−37.8168	+	22.6455i	−1.40158	+	0.839299i
$729$		0			0
$730$	0.980349	−	2.73872i	0.0362843	−	0.101364i
$731$	2.38422	+	2.38422i	0.0881836	+	0.0881836i
$732$		0			0
$733$	17.8729	−	17.8729i	0.660152	−	0.660152i	−0.295264	−	0.955416i	$-0.595408\pi$
$733$	17.8729	−	17.8729i	0.660152	−	0.660152i	0.955416	+	0.295264i	$0.0954075\pi$
$734$	−16.7157	+	7.90316i	−0.616988	+	0.291711i
$735$		0			0
$736$	−20.8226	−	28.1160i	−0.767531	−	1.03637i
$737$			49.6766i			1.82986i
$738$		0			0
$739$	−17.9555	−	17.9555i	−0.660504	−	0.660504i	0.294995	−	0.955499i	$-0.404682\pi$
$739$	−17.9555	−	17.9555i	−0.660504	−	0.660504i	−0.955499	+	0.294995i	$0.904682\pi$
$740$	−1.61540	+	1.96728i	−0.0593833	+	0.0723186i
$741$		0			0
$742$	13.3417	+	4.77579i	0.489790	+	0.175325i
$743$		−	48.9933i		−	1.79739i	−0.438576	−	0.898694i	$-0.644517\pi$
$743$		−	48.9933i		−	1.79739i	0.438576	−	0.898694i	$-0.355483\pi$
$744$		0			0
$745$			0.314396i			0.0115186i
$746$	3.80378	−	10.6263i	0.139266	−	0.389056i
$747$		0			0
$748$	4.99845	+	50.8921i	0.182761	+	1.86080i
$749$	47.6450	+	47.6450i	1.74091	+	1.74091i
$750$		0			0
$751$		−	28.5197i		−	1.04070i	−0.853954	−	0.520349i	$-0.825802\pi$
$751$		−	28.5197i		−	1.04070i	0.853954	−	0.520349i	$-0.174198\pi$
$752$	4.21647	+	21.2581i	0.153759	+	0.775204i
$753$		0			0
$754$	1.12769	+	2.38515i	0.0410682	+	0.0868620i
$755$	−1.29178	+	1.29178i	−0.0470127	+	0.0470127i
$756$		0			0
$757$	34.5077	+	34.5077i	1.25420	+	1.25420i	0.953817	+	0.300388i	$0.0971161\pi$
$757$	34.5077	+	34.5077i	1.25420	+	1.25420i	0.300388	+	0.953817i	$0.402884\pi$
$758$	−18.5717	−	6.64790i	−0.674553	−	0.241462i
$759$		0			0
$760$	5.69795	+	1.42973i	0.206686	+	0.0518619i
$761$	−25.2483			−0.915248			−0.457624	−	0.889146i	$-0.651299\pi$
$761$	−25.2483			−0.915248			−0.457624	+	0.889146i	$0.651299\pi$
$762$		0			0
$763$	−18.8173	+	18.8173i	−0.681230	+	0.681230i
$764$	30.0631	−	36.6117i	1.08765	−	1.32456i
$765$		0			0
$766$	−8.96838	−	18.9687i	−0.324041	−	0.685368i
$767$	−27.6018			−0.996644
$768$		0			0
$769$	−19.4742			−0.702259			−0.351129	−	0.936327i	$-0.614202\pi$
$769$	−19.4742			−0.702259			−0.351129	+	0.936327i	$0.614202\pi$
$770$	−3.84112	−	8.12422i	−0.138424	−	0.292777i
$771$		0			0
$772$	−33.7279	+	41.0748i	−1.21389	+	1.47831i
$773$	−10.2401	+	10.2401i	−0.368309	+	0.368309i	−0.866860	−	0.498551i	$-0.833866\pi$
$773$	−10.2401	+	10.2401i	−0.368309	+	0.368309i	0.498551	+	0.866860i	$0.333866\pi$
$774$		0			0
$775$	−25.5339			−0.917206
$776$	7.72406	+	1.93813i	0.277278	+	0.0695747i
$777$		0			0
$778$	−6.87208	−	2.45992i	−0.246376	−	0.0881925i
$779$	−6.28190	−	6.28190i	−0.225072	−	0.225072i
$780$		0			0
$781$	9.48717	−	9.48717i	0.339478	−	0.339478i
$782$	17.6409	+	37.3116i	0.630836	+	1.33426i
$783$		0			0
$784$	−5.87299	−	29.6097i	−0.209750	−	1.05749i
$785$			6.12028i			0.218442i
$786$		0			0
$787$	32.7690	+	32.7690i	1.16809	+	1.16809i	0.982657	+	0.185432i	$0.0593683\pi$
$787$	32.7690	+	32.7690i	1.16809	+	1.16809i	0.185432	+	0.982657i	$0.440632\pi$
$788$	4.02281	+	40.9586i	0.143307	+	1.45909i
$789$		0			0
$790$	1.36082	−	3.80160i	0.0484158	−	0.135255i
$791$		−	44.7867i		−	1.59243i
$792$		0			0
$793$		−	4.80934i		−	0.170785i
$794$	25.2157	+	9.02619i	0.894872	+	0.320328i
$795$		0			0
$796$	0.417842	−	0.508860i	0.0148100	−	0.0180361i
$797$	18.9380	+	18.9380i	0.670817	+	0.670817i	0.957904	−	0.287087i	$-0.0926870\pi$
$797$	18.9380	+	18.9380i	0.670817	+	0.670817i	−0.287087	+	0.957904i	$0.592687\pi$
$798$		0			0
$799$		−	25.5653i		−	0.904434i
$800$	16.5152	+	22.2999i	0.583900	+	0.788419i
$801$		0			0
$802$	35.2034	−	16.6441i	1.24307	−	0.587723i
$803$	25.6331	−	25.6331i	0.904572	−	0.904572i
$804$		0			0
$805$	−5.12853	−	5.12853i	−0.180757	−	0.180757i
$806$	10.1370	−	28.3187i	0.357059	−	0.997485i
$807$		0			0
$808$	21.8984	−	13.1132i	0.770383	−	0.461322i
$809$	−29.2888			−1.02974			−0.514870	−	0.857268i	$-0.672160\pi$
$809$	−29.2888			−1.02974			−0.514870	+	0.857268i	$0.672160\pi$
$810$		0			0
$811$	−12.8548	+	12.8548i	−0.451393	+	0.451393i	−0.895817	−	0.444424i	$-0.853408\pi$
$811$	−12.8548	+	12.8548i	−0.451393	+	0.451393i	0.444424	+	0.895817i	$0.353408\pi$
$812$	−3.46604	+	0.340423i	−0.121634	+	0.0119465i
$813$		0			0
$814$	−28.6786	+	13.5592i	−1.00518	+	0.475249i
$815$	1.47436			0.0516446
$816$		0			0
$817$	4.82717			0.168881
$818$	−20.7565	+	9.81365i	−0.725735	+	0.343126i
$819$		0			0
$820$	0.0790487	+	0.804840i	0.00276050	+	0.0281062i
$821$	−18.6497	+	18.6497i	−0.650880	+	0.650880i	−0.953205	−	0.302325i	$-0.902237\pi$
$821$	−18.6497	+	18.6497i	−0.650880	+	0.650880i	0.302325	+	0.953205i	$0.402237\pi$
$822$		0			0
$823$	−2.21917			−0.0773554			−0.0386777	−	0.999252i	$-0.512315\pi$
$823$	−2.21917			−0.0773554			−0.0386777	+	0.999252i	$0.512315\pi$
$824$	50.9539	+	12.7854i	1.77506	+	0.445401i
$825$		0			0
$826$	12.2796	−	34.3045i	0.427263	−	1.19361i
$827$	−21.7284	−	21.7284i	−0.755570	−	0.755570i	0.219943	−	0.975513i	$-0.429413\pi$
$827$	−21.7284	−	21.7284i	−0.755570	−	0.755570i	−0.975513	+	0.219943i	$0.929413\pi$
$828$		0			0
$829$	1.37469	−	1.37469i	0.0477451	−	0.0477451i	−0.682831	−	0.730576i	$-0.739252\pi$
$829$	1.37469	−	1.37469i	0.0477451	−	0.0477451i	0.730576	+	0.682831i	$0.239252\pi$
$830$	−4.58425	+	2.16743i	−0.159122	+	0.0752325i
$831$		0			0
$832$	−31.2885	+	9.46336i	−1.08473	+	0.328083i
$833$			35.6090i			1.23378i
$834$		0			0
$835$	−1.99022	−	1.99022i	−0.0688744	−	0.0688744i
$836$	56.5789	+	46.4588i	1.95682	+	1.60681i
$837$		0			0
$838$	4.06261	+	1.45425i	0.140340	+	0.0502362i
$839$		−	2.77829i		−	0.0959171i	−0.998849	−	0.0479585i	$-0.984728\pi$
$839$		−	2.77829i		−	0.0959171i	0.998849	−	0.0479585i	$-0.0152715\pi$
$840$		0			0
$841$		−	28.7915i		−	0.992812i
$842$	−11.6211	+	32.4650i	−0.400491	+	1.11882i
$843$		0			0
$844$	14.6414	−	1.43803i	0.503979	−	0.0494991i
$845$	0.803481	+	0.803481i	0.0276406	+	0.0276406i
$846$		0			0
$847$		−	70.0359i		−	2.40646i
$848$	8.73463	+	5.84317i	0.299948	+	0.200655i
$849$		0			0
$850$	−13.9916	−	29.5933i	−0.479909	−	1.01504i
$851$	−18.1037	+	18.1037i	−0.620588	+	0.620588i
$852$		0			0
$853$	17.0961	+	17.0961i	0.585360	+	0.585360i	0.936371	−	0.351011i	$-0.114162\pi$
$853$	17.0961	+	17.0961i	0.585360	+	0.585360i	−0.351011	+	0.936371i	$0.614162\pi$
$854$	5.97722	+	2.13960i	0.204536	+	0.0732156i
$855$		0			0
$856$	25.6714	+	42.8699i	0.877432	+	1.46526i
$857$	49.4967			1.69078			0.845388	−	0.534153i	$-0.179369\pi$
$857$	49.4967			1.69078			0.845388	+	0.534153i	$0.179369\pi$
$858$		0			0
$859$	25.5374	−	25.5374i	0.871324	−	0.871324i	−0.121293	−	0.992617i	$-0.538704\pi$
$859$	25.5374	−	25.5374i	0.871324	−	0.871324i	0.992617	+	0.121293i	$0.0387040\pi$
$860$	−0.339601	−	0.278858i	−0.0115803	−	0.00950899i
$861$		0			0
$862$	20.1565	+	42.6323i	0.686532	+	1.45206i
$863$	45.8222			1.55981			0.779904	−	0.625900i	$-0.215268\pi$
$863$	45.8222			1.55981			0.779904	+	0.625900i	$0.215268\pi$
$864$		0			0
$865$	1.00018			0.0340073
$866$	−13.4344	−	28.4147i	−0.456520	−	0.965571i
$867$		0			0
$868$	30.6858	+	25.1971i	1.04154	+	0.855247i
$869$	35.5812	−	35.5812i	1.20701	−	1.20701i
$870$		0			0
$871$	37.4589			1.26925
$872$	−16.9313	+	10.1389i	−0.573367	+	0.343345i
$873$		0			0
$874$	55.6292	+	19.9130i	1.88169	+	0.673567i
$875$	8.21366	+	8.21366i	0.277672	+	0.277672i
$876$		0			0
$877$	9.65581	−	9.65581i	0.326054	−	0.326054i	−0.525030	−	0.851084i	$-0.675946\pi$
$877$	9.65581	−	9.65581i	0.326054	−	0.326054i	0.851084	+	0.525030i	$0.175946\pi$
$878$	−0.145380	−	0.307489i	−0.00490634	−	0.0103772i
$879$		0			0
$880$	−1.29658	−	6.53695i	−0.0437078	−	0.220361i
$881$			54.5487i			1.83779i	0.394499	+	0.918896i	$0.370918\pi$
$881$			54.5487i			1.83779i	−0.394499	+	0.918896i	$0.629082\pi$
$882$		0			0
$883$	−12.7878	−	12.7878i	−0.430344	−	0.430344i	0.458401	−	0.888745i	$-0.348422\pi$
$883$	−12.7878	−	12.7878i	−0.430344	−	0.430344i	−0.888745	+	0.458401i	$0.848422\pi$
$884$	38.3755	−	3.76911i	1.29071	−	0.126769i
$885$		0			0
$886$	−17.8911	+	49.9807i	−0.601062	+	1.67913i
$887$			29.3515i			0.985527i	0.870163	+	0.492763i	$0.164013\pi$
$887$			29.3515i			0.985527i	−0.870163	+	0.492763i	$0.835987\pi$
$888$		0			0
$889$		−	58.3497i		−	1.95699i
$890$	−5.06574	−	1.81333i	−0.169804	−	0.0607829i
$891$		0			0
$892$	1.22232	+	1.00369i	0.0409264	+	0.0336061i
$893$	−25.8801	−	25.8801i	−0.866045	−	0.866045i
$894$		0			0
$895$		−	3.11900i		−	0.104257i
$896$	2.15835	−	43.0965i	0.0721055	−	1.43975i
$897$		0			0
$898$	−40.8529	+	19.3152i	−1.36328	+	0.644556i
$899$	1.68046	−	1.68046i	0.0560466	−	0.0560466i
$900$		0			0
$901$	−8.76571	−	8.76571i	−0.292028	−	0.292028i
$902$	−3.39653	+	9.48861i	−0.113092	+	0.315936i
$903$		0			0
$904$	8.08333	−	32.2147i	0.268848	−	1.07144i
$905$	7.43540			0.247161
$906$		0			0
$907$	22.0905	−	22.0905i	0.733505	−	0.733505i	−0.237808	−	0.971312i	$-0.576429\pi$
$907$	22.0905	−	22.0905i	0.733505	−	0.733505i	0.971312	+	0.237808i	$0.0764288\pi$
$908$	−1.20495	−	12.2683i	−0.0399878	−	0.407139i
$909$		0			0
$910$	−6.12612	+	2.89642i	−0.203079	+	0.0960153i
$911$	48.9197			1.62078			0.810391	−	0.585889i	$-0.199255\pi$
$911$	48.9197			1.62078			0.810391	+	0.585889i	$0.199255\pi$
$912$		0			0
$913$	−63.1925			−2.09137
$914$	−16.6284	+	7.86187i	−0.550018	+	0.260048i
$915$		0			0
$916$	−33.6216	+	3.30220i	−1.11089	+	0.109108i
$917$	13.5469	−	13.5469i	0.447357	−	0.447357i
$918$		0			0
$919$	21.4269			0.706810			0.353405	−	0.935470i	$-0.385024\pi$
$919$	21.4269			0.706810			0.353405	+	0.935470i	$0.385024\pi$
$920$	−2.76328	−	4.61453i	−0.0911028	−	0.152137i
$921$		0			0
$922$	−9.50247	+	26.5462i	−0.312947	+	0.874254i
$923$	−7.15385	−	7.15385i	−0.235472	−	0.235472i
$924$		0			0
$925$	14.3588	−	14.3588i	0.472114	−	0.472114i
$926$	−45.7584	+	21.6345i	−1.50372	+	0.710954i
$927$		0			0
$928$	−2.55453	−	0.380706i	−0.0838567	−	0.0124973i
$929$			15.5610i			0.510539i	0.966870	+	0.255269i	$0.0821642\pi$
$929$			15.5610i			0.510539i	−0.966870	+	0.255269i	$0.917836\pi$
$930$		0			0
$931$	36.0475	+	36.0475i	1.18141	+	1.18141i
$932$	33.6261	−	40.9508i	1.10146	−	1.34139i
$933$		0			0
$934$	−28.7248	−	10.2823i	−0.939903	−	0.336447i
$935$			7.86141i			0.257096i
$936$		0			0
$937$		−	19.4793i		−	0.636360i	−0.948030	−	0.318180i	$-0.896928\pi$
$937$		−	19.4793i		−	0.636360i	0.948030	−	0.318180i	$-0.103072\pi$
$938$	−16.6649	+	46.5553i	−0.544128	+	1.52008i
$939$		0			0
$940$	0.325664	+	3.31577i	0.0106220	+	0.108149i
$941$	5.26841	+	5.26841i	0.171745	+	0.171745i	0.787746	−	0.616001i	$-0.211248\pi$
$941$	5.26841	+	5.26841i	0.171745	+	0.171745i	−0.616001	+	0.787746i	$0.711248\pi$
$942$		0			0
$943$			8.13393i			0.264877i
$944$	15.0241	−	22.4587i	0.488992	−	0.730967i
$945$		0			0
$946$	−2.34065	−	4.95063i	−0.0761011	−	0.160959i
$947$	−23.4075	+	23.4075i	−0.760641	+	0.760641i	−0.976438	−	0.215797i	$-0.930765\pi$
$947$	−23.4075	+	23.4075i	−0.760641	+	0.760641i	0.215797	+	0.976438i	$0.430765\pi$
$948$		0			0
$949$	−19.3288	−	19.3288i	−0.627438	−	0.627438i
$950$	−44.1216	−	15.7937i	−1.43150	−	0.512417i
$951$		0			0
$952$	−12.3883	+	49.3712i	−0.401506	+	1.60013i
$953$	61.1868			1.98204			0.991018	−	0.133731i	$-0.0426958\pi$
$953$	61.1868			1.98204			0.991018	+	0.133731i	$0.0426958\pi$
$954$		0			0
$955$	5.14970	−	5.14970i	0.166640	−	0.166640i
$956$	−1.38593	+	1.68782i	−0.0448242	+	0.0545881i
$957$		0			0
$958$	14.0799	+	29.7799i	0.454900	+	0.962144i
$959$	15.6840			0.506464
$960$		0			0
$961$	3.90591			0.125997
$962$	10.2244	+	21.6252i	0.329647	+	0.697225i
$963$		0			0
$964$	−18.2023	+	22.1672i	−0.586256	+	0.713958i
$965$	−5.77747	+	5.77747i	−0.185983	+	0.185983i
$966$		0			0
$967$	34.4866			1.10902			0.554508	−	0.832178i	$-0.312907\pi$
$967$	34.4866			1.10902			0.554508	+	0.832178i	$0.312907\pi$
$968$	12.6404	−	50.3762i	0.406279	−	1.61915i
$969$		0			0
$970$	1.15263	+	0.412594i	0.0370087	+	0.0132476i
$971$	17.8898	+	17.8898i	0.574110	+	0.574110i	0.933274	−	0.359165i	$-0.116938\pi$
$971$	17.8898	+	17.8898i	0.574110	+	0.574110i	−0.359165	+	0.933274i	$0.616938\pi$
$972$		0			0
$973$	−25.3441	+	25.3441i	−0.812493	+	0.812493i
$974$	3.92490	+	8.30143i	0.125762	+	0.265995i
$975$		0			0
$976$	3.91320	+	2.61780i	0.125258	+	0.0837936i
$977$		−	33.3136i		−	1.06580i	−0.846180	−	0.532898i	$-0.821103\pi$
$977$		−	33.3136i		−	1.06580i	0.846180	−	0.532898i	$-0.178897\pi$
$978$		0			0
$979$	−47.4129	−	47.4129i	−1.51532	−	1.51532i
$980$	−0.453606	−	4.61843i	−0.0144899	−	0.147530i
$981$		0			0
$982$	−6.73878	+	18.8255i	−0.215043	+	0.600747i
$983$		−	2.60454i		−	0.0830720i	−0.999137	−	0.0415360i	$-0.986775\pi$
$983$		−	2.60454i		−	0.0830720i	0.999137	−	0.0415360i	$-0.0132251\pi$
$984$		0			0
$985$			6.32696i			0.201594i
$986$	2.86845	+	1.02679i	0.0913501	+	0.0326996i
$987$		0			0
$988$	35.0325	−	42.6636i	1.11453	−	1.35731i
$989$	−3.12516	−	3.12516i	−0.0993742	−	0.0993742i
$990$		0			0
$991$			53.4871i			1.69907i	0.527530	+	0.849537i	$0.323118\pi$
$991$			53.4871i			1.69907i	−0.527530	+	0.849537i	$0.676882\pi$
$992$	17.5243	+	23.6624i	0.556397	+	0.751282i
$993$		0			0
$994$	12.0737	−	5.70843i	0.382955	−	0.181060i
$995$	0.0715749	−	0.0715749i	0.00226908	−	0.00226908i
$996$		0			0
$997$	33.9323	+	33.9323i	1.07465	+	1.07465i	0.996979	+	0.0776671i	$0.0247471\pi$
$997$	33.9323	+	33.9323i	1.07465	+	1.07465i	0.0776671	+	0.996979i	$0.475253\pi$
$998$	11.2035	−	31.2982i	0.354640	−	0.990727i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.l.a.107.10	yes	32
3.2	odd	2	inner	432.2.l.a.107.7	✓	32
4.3	odd	2		1728.2.l.a.1295.8		32
12.11	even	2		1728.2.l.a.1295.9		32
16.3	odd	4	inner	432.2.l.a.323.7	yes	32
16.13	even	4		1728.2.l.a.431.9		32
48.29	odd	4		1728.2.l.a.431.8		32
48.35	even	4	inner	432.2.l.a.323.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.l.a.107.7	✓	32	3.2	odd	2	inner
432.2.l.a.107.10	yes	32	1.1	even	1	trivial
432.2.l.a.323.7	yes	32	16.3	odd	4	inner
432.2.l.a.323.10	yes	32	48.35	even	4	inner
1728.2.l.a.431.8		32	48.29	odd	4
1728.2.l.a.431.9		32	16.13	even	4
1728.2.l.a.1295.8		32	4.3	odd	2
1728.2.l.a.1295.9		32	12.11	even	2

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.604480 + 1.27852i) q^{2} +(-1.26921 + 1.54568i) q^{4} +(-0.217410 + 0.217410i) q^{5} -3.81401 q^{7} +(-2.74338 - 0.688372i) q^{8} +O(q^{10})\)	\(q+(0.604480 + 1.27852i) q^{2} +(-1.26921 + 1.54568i) q^{4} +(-0.217410 + 0.217410i) q^{5} -3.81401 q^{7} +(-2.74338 - 0.688372i) q^{8} +(-0.409383 - 0.146542i) q^{10} +(-3.83163 - 3.83163i) q^{11} +(-2.88926 + 2.88926i) q^{13} +(-2.30549 - 4.87627i) q^{14} +(-0.778226 - 3.92357i) q^{16} +4.71852i q^{17} +(4.77663 + 4.77663i) q^{19} +(-0.0601071 - 0.611985i) q^{20} +(2.58266 - 7.21495i) q^{22} -6.18488i q^{23} +4.90547i q^{25} +(-5.44047 - 1.94747i) q^{26} +(4.84076 - 5.89522i) q^{28} +(-0.322843 - 0.322843i) q^{29} +5.20520i q^{31} +(4.54592 - 3.36669i) q^{32} +(-6.03271 + 2.85225i) q^{34} +(0.829205 - 0.829205i) q^{35} +(-2.92710 - 2.92710i) q^{37} +(-3.21962 + 8.99438i) q^{38} +(0.746099 - 0.446781i) q^{40} -1.31513 q^{41} +(0.505290 - 0.505290i) q^{43} +(10.7856 - 1.05932i) q^{44} +(7.90747 - 3.73864i) q^{46} -5.41806 q^{47} +7.54664 q^{49} +(-6.27172 + 2.96526i) q^{50} +(-0.798789 - 8.13294i) q^{52} +(-1.85772 + 1.85772i) q^{53} +1.66607 q^{55} +(10.4633 + 2.62545i) q^{56} +(0.217608 - 0.607913i) q^{58} +(4.77662 + 4.77662i) q^{59} +(-0.832278 + 0.832278i) q^{61} +(-6.65493 + 3.14644i) q^{62} +(7.05229 + 3.77693i) q^{64} -1.25631i q^{65} +(-6.48244 - 6.48244i) q^{67} +(-7.29331 - 5.98879i) q^{68} +(1.56139 + 0.558914i) q^{70} +2.47601i q^{71} +6.68986i q^{73} +(1.97297 - 5.51171i) q^{74} +(-13.4457 + 1.32059i) q^{76} +(14.6139 + 14.6139i) q^{77} +9.28617i q^{79} +(1.02222 + 0.683830i) q^{80} +(-0.794971 - 1.68142i) q^{82} +(8.24616 - 8.24616i) q^{83} +(-1.02586 - 1.02586i) q^{85} +(0.951459 + 0.340583i) q^{86} +(7.87404 + 13.1492i) q^{88} +12.3741 q^{89} +(11.0197 - 11.0197i) q^{91} +(9.55982 + 7.84989i) q^{92} +(-3.27511 - 6.92708i) q^{94} -2.07698 q^{95} -2.81552 q^{97} +(4.56179 + 9.64850i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 4 q^{10} - 20 q^{16} + 8 q^{19} + 4 q^{22} - 12 q^{28} - 36 q^{34} - 12 q^{40} + 32 q^{43} - 16 q^{46} + 32 q^{49} - 60 q^{52} + 64 q^{55} - 48 q^{58} - 16 q^{61} + 48 q^{64} - 32 q^{67} - 72 q^{70} - 96 q^{76} + 40 q^{82} - 16 q^{85} + 36 q^{88} + 24 q^{91} - 36 q^{94}+O(q^{100}) \) 32 * q - 4 * q^10 - 20 * q^16 + 8 * q^19 + 4 * q^22 - 12 * q^28 - 36 * q^34 - 12 * q^40 + 32 * q^43 - 16 * q^46 + 32 * q^49 - 60 * q^52 + 64 * q^55 - 48 * q^58 - 16 * q^61 + 48 * q^64 - 32 * q^67 - 72 * q^70 - 96 * q^76 + 40 * q^82 - 16 * q^85 + 36 * q^88 + 24 * q^91 - 36 * q^94

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