LMFDB - Embedded newform 864.2.v.a.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (of order $8$, degree $4$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.3
Character	$\chi$	$=$	864.109
Dual form			864.2.v.a.325.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38295 + 0.295740i) q^{2} +(1.82508 - 0.817983i) q^{4} +(3.70533 - 1.53480i) q^{5} +(1.70420 - 1.70420i) q^{7} +(-2.28207 + 1.67097i) q^{8} +O(q^{10})$	\(q+(-1.38295 + 0.295740i) q^{2} +(1.82508 - 0.817983i) q^{4} +(3.70533 - 1.53480i) q^{5} +(1.70420 - 1.70420i) q^{7} +(-2.28207 + 1.67097i) q^{8} +(-4.67037 + 3.21836i) q^{10} +(-0.539908 - 1.30345i) q^{11} +(4.74278 + 1.96452i) q^{13} +(-1.85282 + 2.86082i) q^{14} +(2.66181 - 2.98576i) q^{16} +5.18418i q^{17} +(6.56852 + 2.72077i) q^{19} +(5.50707 - 5.83202i) q^{20} +(1.13215 + 1.64293i) q^{22} +(-3.07987 - 3.07987i) q^{23} +(7.83834 - 7.83834i) q^{25} +(-7.14000 - 1.31420i) q^{26} +(1.71629 - 4.50431i) q^{28} +(-2.51674 + 6.07595i) q^{29} -7.47332 q^{31} +(-2.79812 + 4.91635i) q^{32} +(-1.53317 - 7.16943i) q^{34} +(3.69903 - 8.93025i) q^{35} +(-4.40696 + 1.82542i) q^{37} +(-9.88854 - 1.82010i) q^{38} +(-5.89122 + 9.69403i) q^{40} +(-1.33547 - 1.33547i) q^{41} +(-2.02307 - 4.88412i) q^{43} +(-2.05157 - 1.93726i) q^{44} +(5.17013 + 3.34845i) q^{46} +0.857860i q^{47} +1.19138i q^{49} +(-8.52189 + 13.1581i) q^{50} +(10.2629 - 0.294109i) q^{52} +(-3.35470 - 8.09895i) q^{53} +(-4.00107 - 4.00107i) q^{55} +(-1.04143 + 6.73679i) q^{56} +(1.68362 - 9.14701i) q^{58} +(2.86121 - 1.18515i) q^{59} +(-2.84041 + 6.85735i) q^{61} +(10.3352 - 2.21016i) q^{62} +(2.41569 - 7.62656i) q^{64} +20.5887 q^{65} +(0.0611610 - 0.147656i) q^{67} +(4.24057 + 9.46152i) q^{68} +(-2.47453 + 13.4440i) q^{70} +(4.00830 - 4.00830i) q^{71} +(0.651872 + 0.651872i) q^{73} +(5.55474 - 3.82778i) q^{74} +(14.2136 - 0.407327i) q^{76} +(-3.14146 - 1.30124i) q^{77} -9.89973i q^{79} +(5.28033 - 15.1486i) q^{80} +(2.24183 + 1.45193i) q^{82} +(-9.41435 - 3.89955i) q^{83} +(7.95666 + 19.2091i) q^{85} +(4.24222 + 6.15617i) q^{86} +(3.41014 + 2.07240i) q^{88} +(4.18011 - 4.18011i) q^{89} +(11.4306 - 4.73472i) q^{91} +(-8.14028 - 3.10171i) q^{92} +(-0.253703 - 1.18637i) q^{94} +28.5144 q^{95} -9.70998 q^{97} +(-0.352338 - 1.64761i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) $ 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	−1.38295	+	0.295740i	−0.977890	+	0.209119i
$2$	−1.38295	+	0.295740i	−0.977890	+	0.209119i
$3$		0			0
$3$		0			0
$4$	1.82508	−	0.817983i	0.912538	−	0.408992i
$5$	3.70533	−	1.53480i	1.65707	−	0.686383i	0.659226	−	0.751945i	$-0.270884\pi$
$5$	3.70533	−	1.53480i	1.65707	−	0.686383i	0.997848	+	0.0655623i	$0.0208841\pi$
$6$		0			0
$7$	1.70420	−	1.70420i	0.644129	−	0.644129i	−0.307439	−	0.951568i	$-0.599472\pi$
$7$	1.70420	−	1.70420i	0.644129	−	0.644129i	0.951568	+	0.307439i	$0.0994721\pi$
$8$	−2.28207	+	1.67097i	−0.806834	+	0.590778i
$9$		0			0
$10$	−4.67037	+	3.21836i	−1.47690	+	1.01773i
$11$	−0.539908	−	1.30345i	−0.162788	−	0.393006i	0.821346	−	0.570430i	$-0.193223\pi$
$11$	−0.539908	−	1.30345i	−0.162788	−	0.393006i	−0.984134	+	0.177424i	$0.943223\pi$
$12$		0			0
$13$	4.74278	+	1.96452i	1.31541	+	0.544861i	0.926459	−	0.376397i	$-0.122837\pi$
$13$	4.74278	+	1.96452i	1.31541	+	0.544861i	0.388953	+	0.921258i	$0.372837\pi$
$14$	−1.85282	+	2.86082i	−0.495187	+	0.764587i
$15$		0			0
$16$	2.66181	−	2.98576i	0.665452	−	0.746441i
$17$			5.18418i			1.25735i	0.777669	+	0.628674i	$0.216402\pi$
$17$			5.18418i			1.25735i	−0.777669	+	0.628674i	$0.783598\pi$
$18$		0			0
$19$	6.56852	+	2.72077i	1.50692	+	0.624187i	0.974920	−	0.222556i	$-0.0714401\pi$
$19$	6.56852	+	2.72077i	1.50692	+	0.624187i	0.532001	+	0.846744i	$0.321440\pi$
$20$	5.50707	−	5.83202i	1.23142	−	1.30408i
$21$		0			0
$22$	1.13215	+	1.64293i	0.241374	+	0.350274i
$23$	−3.07987	−	3.07987i	−0.642197	−	0.642197i	0.308898	−	0.951095i	$-0.400040\pi$
$23$	−3.07987	−	3.07987i	−0.642197	−	0.642197i	−0.951095	+	0.308898i	$0.900040\pi$
$24$		0			0
$25$	7.83834	−	7.83834i	1.56767	−	1.56767i
$26$	−7.14000	−	1.31420i	−1.40027	−	0.257736i
$27$		0			0
$28$	1.71629	−	4.50431i	0.324349	−	0.851235i
$29$	−2.51674	+	6.07595i	−0.467347	+	1.12828i	0.497969	+	0.867195i	$0.334079\pi$
$29$	−2.51674	+	6.07595i	−0.467347	+	1.12828i	−0.965317	+	0.261082i	$0.915921\pi$
$30$		0			0
$31$	−7.47332			−1.34225			−0.671124	−	0.741345i	$-0.734188\pi$
$31$	−7.47332			−1.34225			−0.671124	+	0.741345i	$0.734188\pi$
$32$	−2.79812	+	4.91635i	−0.494643	+	0.869096i
$33$		0			0
$34$	−1.53317	−	7.16943i	−0.262936	−	1.22955i
$35$	3.69903	−	8.93025i	0.625250	−	1.50949i
$36$		0			0
$37$	−4.40696	+	1.82542i	−0.724501	+	0.300098i	−0.714290	−	0.699850i	$-0.753250\pi$
$37$	−4.40696	+	1.82542i	−0.724501	+	0.300098i	−0.0102106	+	0.999948i	$0.503250\pi$
$38$	−9.88854	−	1.82010i	−1.60413	−	0.295260i
$39$		0			0
$40$	−5.89122	+	9.69403i	−0.931484	+	1.53276i
$41$	−1.33547	−	1.33547i	−0.208565	−	0.208565i	0.595092	−	0.803657i	$-0.297115\pi$
$41$	−1.33547	−	1.33547i	−0.208565	−	0.208565i	−0.803657	+	0.595092i	$0.797115\pi$
$42$		0			0
$43$	−2.02307	−	4.88412i	−0.308515	−	0.744821i	−0.999754	−	0.0221943i	$-0.992935\pi$
$43$	−2.02307	−	4.88412i	−0.308515	−	0.744821i	0.691239	−	0.722626i	$-0.257065\pi$
$44$	−2.05157	−	1.93726i	−0.309286	−	0.292054i
$45$		0			0
$46$	5.17013	+	3.34845i	0.762294	+	0.493702i
$47$			0.857860i			0.125132i	0.998041	+	0.0625658i	$0.0199283\pi$
$47$			0.857860i			0.125132i	−0.998041	+	0.0625658i	$0.980072\pi$
$48$		0			0
$49$			1.19138i			0.170197i
$50$	−8.52189	+	13.1581i	−1.20518	+	1.86084i
$51$		0			0
$52$	10.2629	−	0.294109i	1.42321	−	0.0407856i
$53$	−3.35470	−	8.09895i	−0.460803	−	1.11248i	−0.968068	−	0.250687i	$-0.919344\pi$
$53$	−3.35470	−	8.09895i	−0.460803	−	1.11248i	0.507265	−	0.861790i	$-0.330656\pi$
$54$		0			0
$55$	−4.00107	−	4.00107i	−0.539504	−	0.539504i
$56$	−1.04143	+	6.73679i	−0.139168	+	0.900242i
$57$		0			0
$58$	1.68362	−	9.14701i	0.221070	−	1.20106i
$59$	2.86121	−	1.18515i	0.372497	−	0.154293i	−0.188578	−	0.982058i	$-0.560388\pi$
$59$	2.86121	−	1.18515i	0.372497	−	0.154293i	0.561075	+	0.827765i	$0.310388\pi$
$60$		0			0
$61$	−2.84041	+	6.85735i	−0.363677	+	0.877994i	0.631079	+	0.775718i	$0.282612\pi$
$61$	−2.84041	+	6.85735i	−0.363677	+	0.877994i	−0.994756	+	0.102275i	$0.967388\pi$
$62$	10.3352	−	2.21016i	1.31257	−	0.280690i
$63$		0			0
$64$	2.41569	−	7.62656i	0.301962	−	0.953320i
$65$	20.5887			2.55372
$66$		0			0
$67$	0.0611610	−	0.147656i	0.00747201	−	0.0180390i	−0.920100	−	0.391685i	$-0.871892\pi$
$67$	0.0611610	−	0.147656i	0.00747201	−	0.0180390i	0.927572	+	0.373646i	$0.121892\pi$
$68$	4.24057	+	9.46152i	0.514245	+	1.14738i
$69$		0			0
$70$	−2.47453	+	13.4440i	−0.295763	+	1.60686i
$71$	4.00830	−	4.00830i	0.475697	−	0.475697i	−0.428055	−	0.903753i	$-0.640801\pi$
$71$	4.00830	−	4.00830i	0.475697	−	0.475697i	0.903753	+	0.428055i	$0.140801\pi$
$72$		0			0
$73$	0.651872	+	0.651872i	0.0762959	+	0.0762959i	0.744225	−	0.667929i	$-0.232819\pi$
$73$	0.651872	+	0.651872i	0.0762959	+	0.0762959i	−0.667929	+	0.744225i	$0.732819\pi$
$74$	5.55474	−	3.82778i	0.645726	−	0.444970i
$75$		0			0
$76$	14.2136	−	0.407327i	1.63041	−	0.0467236i
$77$	−3.14146	−	1.30124i	−0.358003	−	0.148290i
$78$		0			0
$79$		−	9.89973i		−	1.11381i	−0.830577	−	0.556903i	$-0.811989\pi$
$79$		−	9.89973i		−	1.11381i	0.830577	−	0.556903i	$-0.188011\pi$
$80$	5.28033	−	15.1486i	0.590359	−	1.69366i
$81$		0			0
$82$	2.24183	+	1.45193i	0.247568	+	0.160339i
$83$	−9.41435	−	3.89955i	−1.03336	−	0.428031i	−0.199436	−	0.979911i	$-0.563911\pi$
$83$	−9.41435	−	3.89955i	−1.03336	−	0.428031i	−0.833924	+	0.551879i	$0.813911\pi$
$84$		0			0
$85$	7.95666	+	19.2091i	0.863021	+	2.08352i
$86$	4.24222	+	6.15617i	0.457450	+	0.663836i
$87$		0			0
$88$	3.41014	+	2.07240i	0.363522	+	0.220918i
$89$	4.18011	−	4.18011i	0.443091	−	0.443091i	−0.449959	−	0.893049i	$-0.648561\pi$
$89$	4.18011	−	4.18011i	0.443091	−	0.443091i	0.893049	+	0.449959i	$0.148561\pi$
$90$		0			0
$91$	11.4306	−	4.73472i	1.19825	−	0.496333i
$92$	−8.14028	−	3.10171i	−0.848683	−	0.323376i
$93$		0			0
$94$	−0.253703	−	1.18637i	−0.0261675	−	0.122365i
$95$	28.5144			2.92551
$96$		0			0
$97$	−9.70998			−0.985899			−0.492949	−	0.870058i	$-0.664081\pi$
$97$	−9.70998			−0.985899			−0.492949	+	0.870058i	$0.664081\pi$
$98$	−0.352338	−	1.64761i	−0.0355915	−	0.166434i
$99$		0			0
$100$	7.89393	−	20.7172i	0.789393	−	2.07172i
$101$	10.8762	−	4.50507i	1.08222	−	0.448271i	0.230934	−	0.972969i	$-0.425822\pi$
$101$	10.8762	−	4.50507i	1.08222	−	0.448271i	0.851288	+	0.524699i	$0.175822\pi$
$102$		0			0
$103$	−11.2705	+	11.2705i	−1.11052	+	1.11052i	−0.117437	+	0.993080i	$0.537468\pi$
$103$	−11.2705	+	11.2705i	−1.11052	+	1.11052i	−0.993080	+	0.117437i	$0.962532\pi$
$104$	−14.1060	+	3.44188i	−1.38321	+	0.337504i
$105$		0			0
$106$	7.03454	+	10.2083i	0.683255	+	0.991517i
$107$	6.21139	+	14.9956i	0.600478	+	1.44968i	0.873091	+	0.487558i	$0.162112\pi$
$107$	6.21139	+	14.9956i	0.600478	+	1.44968i	−0.272613	+	0.962124i	$0.587888\pi$
$108$		0			0
$109$	−1.92557	−	0.797598i	−0.184436	−	0.0763961i	0.288554	−	0.957464i	$-0.406826\pi$
$109$	−1.92557	−	0.797598i	−0.184436	−	0.0763961i	−0.472990	+	0.881068i	$0.656826\pi$
$110$	6.71654	+	4.34999i	0.640397	+	0.414755i
$111$		0			0
$112$	−0.552089	−	9.62461i	−0.0521675	−	0.909440i
$113$			17.8783i			1.68185i	0.541152	+	0.840925i	$0.317988\pi$
$113$			17.8783i			1.68185i	−0.541152	+	0.840925i	$0.682012\pi$
$114$		0			0
$115$	−16.1389	−	6.68496i	−1.50496	−	0.623375i
$116$	0.376782	+	13.1477i	0.0349833	+	1.22074i
$117$		0			0
$118$	−3.60640	+	2.48517i	−0.331996	+	0.228778i
$119$	8.83489	+	8.83489i	0.809893	+	0.809893i
$120$		0			0
$121$	6.37069	−	6.37069i	0.579153	−	0.579153i
$122$	1.90014	−	10.3234i	0.172030	−	0.934633i
$123$		0			0
$124$	−13.6394	+	6.11305i	−1.22485	+	0.548968i
$125$	9.33937	−	22.5472i	0.835339	−	2.01669i
$126$		0			0
$127$	−0.629017			−0.0558162			−0.0279081	−	0.999610i	$-0.508885\pi$
$127$	−0.629017			−0.0558162			−0.0279081	+	0.999610i	$0.508885\pi$
$128$	−1.08530	+	11.2615i	−0.0959278	+	0.995388i
$129$		0			0
$130$	−28.4731	+	6.08890i	−2.49725	+	0.534032i
$131$	−0.471715	+	1.13882i	−0.0412140	+	0.0994993i	−0.943146	−	0.332379i	$-0.892149\pi$
$131$	−0.471715	+	1.13882i	−0.0412140	+	0.0994993i	0.901932	+	0.431878i	$0.142149\pi$
$132$		0			0
$133$	15.8308	−	6.55735i	1.37271	−	0.568594i
$134$	−0.0409147	+	0.222288i	−0.00353449	+	0.0192027i
$135$		0			0
$136$	−8.66262	−	11.8307i	−0.742814	−	1.01447i
$137$	−5.42168	−	5.42168i	−0.463205	−	0.463205i	0.436499	−	0.899705i	$-0.356218\pi$
$137$	−5.42168	−	5.42168i	−0.463205	−	0.463205i	−0.899705	+	0.436499i	$0.856218\pi$
$138$		0			0
$139$	−4.34905	−	10.4995i	−0.368881	−	0.890559i	−0.993934	−	0.109976i	$-0.964923\pi$
$139$	−4.34905	−	10.4995i	−0.368881	−	0.890559i	0.625053	−	0.780582i	$-0.285077\pi$
$140$	−0.553783	−	19.3241i	−0.0468032	−	1.63319i
$141$		0			0
$142$	−4.35785	+	6.72867i	−0.365702	+	0.564657i
$143$		−	7.24265i		−	0.605661i
$144$		0			0
$145$			26.3761i			2.19042i
$146$	−1.09429	−	0.708719i	−0.0905639	−	0.0586540i
$147$		0			0
$148$	−6.54988	+	6.93636i	−0.538397	+	0.570165i
$149$	−6.97967	−	16.8504i	−0.571797	−	1.38044i	−0.900024	−	0.435841i	$-0.856451\pi$
$149$	−6.97967	−	16.8504i	−0.571797	−	1.38044i	0.328227	−	0.944599i	$-0.393549\pi$
$150$		0			0
$151$	−9.76625	−	9.76625i	−0.794766	−	0.794766i	0.187499	−	0.982265i	$-0.439962\pi$
$151$	−9.76625	−	9.76625i	−0.794766	−	0.794766i	−0.982265	+	0.187499i	$0.939962\pi$
$152$	−19.5362	+	4.76683i	−1.58459	+	0.386641i
$153$		0			0
$154$	4.72930	+	0.870484i	0.381097	+	0.0701456i
$155$	−27.6911	+	11.4700i	−2.22420	+	0.921295i
$156$		0			0
$157$	1.80726	−	4.36311i	0.144235	−	0.348214i	−0.835208	−	0.549934i	$-0.814653\pi$
$157$	1.80726	−	4.36311i	0.144235	−	0.348214i	0.979443	+	0.201720i	$0.0646530\pi$
$158$	2.92774	+	13.6908i	0.232919	+	1.08918i
$159$		0			0
$160$	−2.82237	+	22.5113i	−0.223128	+	1.77967i
$161$	−10.4975			−0.827315
$162$		0			0
$163$	−5.31301	+	12.8267i	−0.416147	+	1.00467i	0.567307	+	0.823506i	$0.307985\pi$
$163$	−5.31301	+	12.8267i	−0.416147	+	1.00467i	−0.983454	+	0.181160i	$0.942015\pi$
$164$	−3.52972	−	1.34494i	−0.275625	−	0.105022i
$165$		0			0
$166$	14.1728	+	2.60867i	1.10002	+	0.202472i
$167$	−4.34359	+	4.34359i	−0.336117	+	0.336117i	−0.854904	−	0.518787i	$-0.826384\pi$
$167$	−4.34359	+	4.34359i	−0.336117	+	0.336117i	0.518787	+	0.854904i	$0.326384\pi$
$168$		0			0
$169$	9.44224	+	9.44224i	0.726326	+	0.726326i
$170$	−16.6845	−	24.2120i	−1.27964	−	1.85698i
$171$		0			0
$172$	−7.68738	−	7.25905i	−0.586157	−	0.553497i
$173$	−13.5919	−	5.62995i	−1.03337	−	0.428037i	−0.199444	−	0.979909i	$-0.563914\pi$
$173$	−13.5919	−	5.62995i	−1.03337	−	0.428037i	−0.833929	+	0.551872i	$0.813914\pi$
$174$		0			0
$175$		−	26.7162i		−	2.01956i
$176$	−5.32893	−	1.85750i	−0.401683	−	0.140014i
$177$		0			0
$178$	−4.54464	+	7.01709i	−0.340635	+	0.525953i
$179$	−3.07103	−	1.27206i	−0.229539	−	0.0950783i	0.264949	−	0.964262i	$-0.414645\pi$
$179$	−3.07103	−	1.27206i	−0.229539	−	0.0950783i	−0.494489	+	0.869184i	$0.664645\pi$
$180$		0			0
$181$	2.28224	+	5.50981i	0.169637	+	0.409541i	0.985720	−	0.168395i	$-0.0538584\pi$
$181$	2.28224	+	5.50981i	0.169637	+	0.409541i	−0.816082	+	0.577936i	$0.803858\pi$
$182$	−14.4077	+	9.92834i	−1.06797	+	0.735938i
$183$		0			0
$184$	12.1749	+	1.88210i	0.897543	+	0.138750i
$185$	−13.5276	+	13.5276i	−0.994569	+	0.994569i
$186$		0			0
$187$	6.75732	−	2.79898i	0.494144	−	0.204681i
$188$	0.701715	+	1.56566i	0.0511778	+	0.114187i
$189$		0			0
$190$	−39.4338	+	8.43282i	−2.86083	+	0.611781i
$191$	20.9256			1.51412			0.757062	−	0.653343i	$-0.226634\pi$
$191$	20.9256			1.51412			0.757062	+	0.653343i	$0.226634\pi$
$192$		0			0
$193$	24.8819			1.79104			0.895521	−	0.445020i	$-0.146803\pi$
$193$	24.8819			1.79104			0.895521	+	0.445020i	$0.146803\pi$
$194$	13.4284	−	2.87162i	0.964101	−	0.206171i
$195$		0			0
$196$	0.974528	+	2.17436i	0.0696091	+	0.155311i
$197$	15.8626	−	6.57052i	1.13017	−	0.468130i	0.262329	−	0.964978i	$-0.415509\pi$
$197$	15.8626	−	6.57052i	1.13017	−	0.468130i	0.867838	+	0.496848i	$0.165509\pi$
$198$		0			0
$199$	−8.06115	+	8.06115i	−0.571440	+	0.571440i	−0.932531	−	0.361091i	$-0.882404\pi$
$199$	−8.06115	+	8.06115i	−0.571440	+	0.571440i	0.361091	+	0.932531i	$0.382404\pi$
$200$	−4.78999	+	30.9853i	−0.338703	+	2.19099i
$201$		0			0
$202$	−13.7089	+	9.44678i	−0.964552	+	0.664673i
$203$	6.06562	+	14.6437i	0.425723	+	1.02779i
$204$		0			0
$205$	−6.99802	−	2.89867i	−0.488763	−	0.202452i
$206$	12.2534	−	18.9197i	0.853733	−	1.31819i
$207$		0			0
$208$	18.4900	−	8.93164i	1.28205	−	0.619298i
$209$		−	10.0307i		−	0.693839i
$210$		0			0
$211$	−12.1195	−	5.02006i	−0.834340	−	0.345595i	−0.0757209	−	0.997129i	$-0.524126\pi$
$211$	−12.1195	−	5.02006i	−0.834340	−	0.345595i	−0.758619	+	0.651534i	$0.774126\pi$
$212$	−12.7474	−	12.0371i	−0.875494	−	0.826713i
$213$		0			0
$214$	−13.0248	−	18.9012i	−0.890358	−	1.29206i
$215$	−14.9923	−	14.9923i	−1.02246	−	1.02246i
$216$		0			0
$217$	−12.7361	+	12.7361i	−0.864580	+	0.864580i
$218$	2.89884	+	0.533567i	0.196334	+	0.0361377i
$219$		0			0
$220$	−10.5751	−	4.02945i	−0.712971	−	0.271666i
$221$	−10.1844	+	24.5874i	−0.685080	+	1.65393i
$222$		0			0
$223$	1.39968			0.0937293			0.0468647	−	0.998901i	$-0.485077\pi$
$223$	1.39968			0.0937293			0.0468647	+	0.998901i	$0.485077\pi$
$224$	3.60989	+	13.1470i	0.241196	+	0.878423i
$225$		0			0
$226$	−5.28732	−	24.7247i	−0.351708	−	1.64466i
$227$	2.51348	−	6.06808i	0.166826	−	0.402753i	−0.818253	−	0.574858i	$-0.805057\pi$
$227$	2.51348	−	6.06808i	0.166826	−	0.402753i	0.985078	+	0.172106i	$0.0550571\pi$
$228$		0			0
$229$	−12.4901	+	5.17357i	−0.825369	+	0.341879i	−0.755068	−	0.655647i	$-0.772396\pi$
$229$	−12.4901	+	5.17357i	−0.825369	+	0.341879i	−0.0703012	+	0.997526i	$0.522396\pi$
$230$	24.2962	+	4.47202i	1.60205	+	0.294876i
$231$		0			0
$232$	−4.40937	−	18.0712i	−0.289490	−	1.18643i
$233$	4.34742	+	4.34742i	0.284809	+	0.284809i	0.835023	−	0.550214i	$-0.185454\pi$
$233$	4.34742	+	4.34742i	0.284809	+	0.284809i	−0.550214	+	0.835023i	$0.685454\pi$
$234$		0			0
$235$	1.31664	+	3.17865i	0.0858882	+	0.207352i
$236$	4.25249	−	4.50341i	0.276813	−	0.293147i
$237$		0			0
$238$	−14.8310	−	9.60535i	−0.961351	−	0.622622i
$239$		−	2.83874i		−	0.183623i	−0.995776	−	0.0918114i	$-0.970734\pi$
$239$		−	2.83874i		−	0.183623i	0.995776	−	0.0918114i	$-0.0292657\pi$
$240$		0			0
$241$			1.28049i			0.0824837i	0.999149	+	0.0412419i	$0.0131314\pi$
$241$			1.28049i			0.0824837i	−0.999149	+	0.0412419i	$0.986869\pi$
$242$	−6.92625	+	10.6944i	−0.445236	+	0.687461i
$243$		0			0
$244$	0.425238	+	14.8386i	0.0272231	+	0.949943i
$245$	1.82853	+	4.41445i	0.116820	+	0.282029i
$246$		0			0
$247$	25.8080	+	25.8080i	1.64213	+	1.64213i
$248$	17.0546	−	12.4877i	1.08297	−	0.792971i
$249$		0			0
$250$	−6.24773	+	33.9436i	−0.395141	+	2.14678i
$251$	−12.6690	+	5.24768i	−0.799661	+	0.331231i	−0.744821	−	0.667265i	$-0.767465\pi$
$251$	−12.6690	+	5.24768i	−0.799661	+	0.331231i	−0.0548406	+	0.998495i	$0.517465\pi$
$252$		0			0
$253$	−2.35162	+	5.67731i	−0.147845	+	0.356929i
$254$	0.869896	−	0.186025i	0.0545821	−	0.0116723i
$255$		0			0
$256$	−1.82957	−	15.8951i	−0.114348	−	0.993441i
$257$	−7.94989			−0.495901			−0.247950	−	0.968773i	$-0.579757\pi$
$257$	−7.94989			−0.495901			−0.247950	+	0.968773i	$0.579757\pi$
$258$		0			0
$259$	−4.39947	+	10.6213i	−0.273370	+	0.659973i
$260$	37.5760	−	16.8412i	2.33036	−	1.04445i
$261$		0			0
$262$	0.315562	−	1.71443i	0.0194955	−	0.105918i
$263$	−5.27091	+	5.27091i	−0.325018	+	0.325018i	−0.850688	−	0.525670i	$-0.823815\pi$
$263$	−5.27091	+	5.27091i	−0.325018	+	0.325018i	0.525670	+	0.850688i	$0.323815\pi$
$264$		0			0
$265$	−24.8605	−	24.8605i	−1.52717	−	1.52717i
$266$	−19.9539	+	13.7503i	−1.22345	+	0.843082i
$267$		0			0
$268$	−0.00915643	−	0.319512i	−0.000559318	−	0.0195173i
$269$	−3.58405	−	1.48456i	−0.218523	−	0.0905152i	0.270736	−	0.962654i	$-0.412733\pi$
$269$	−3.58405	−	1.48456i	−0.218523	−	0.0905152i	−0.489259	+	0.872138i	$0.662733\pi$
$270$		0			0
$271$			0.896143i			0.0544368i	0.999630	+	0.0272184i	$0.00866496\pi$
$271$			0.896143i			0.0544368i	−0.999630	+	0.0272184i	$0.991335\pi$
$272$	15.4787	+	13.7993i	0.938535	+	0.836704i
$273$		0			0
$274$	9.10129	+	5.89448i	0.549829	+	0.356099i
$275$	−14.4489	−	5.98492i	−0.871300	−	0.360904i
$276$		0			0
$277$	−12.0572	−	29.1086i	−0.724445	−	1.74897i	−0.660272	−	0.751026i	$-0.729559\pi$
$277$	−12.0572	−	29.1086i	−0.724445	−	1.74897i	−0.0641727	−	0.997939i	$-0.520441\pi$
$278$	9.11962	+	13.2341i	0.546959	+	0.793728i
$279$		0			0
$280$	6.48076	+	26.5604i	0.387299	+	1.58729i
$281$	4.83576	−	4.83576i	0.288477	−	0.288477i	−0.548001	−	0.836478i	$-0.684611\pi$
$281$	4.83576	−	4.83576i	0.288477	−	0.288477i	0.836478	+	0.548001i	$0.184611\pi$
$282$		0			0
$283$	−24.3529	+	10.0873i	−1.44763	+	0.599627i	−0.961634	−	0.274335i	$-0.911542\pi$
$283$	−24.3529	+	10.0873i	−1.44763	+	0.599627i	−0.485994	+	0.873962i	$0.661542\pi$
$284$	4.03673	−	10.5942i	0.239536	−	0.628648i
$285$		0			0
$286$	2.14194	+	10.0162i	0.126655	+	0.592270i
$287$	−4.55181			−0.268685
$288$		0			0
$289$	−9.87567			−0.580922
$290$	−7.80046	−	36.4767i	−0.458059	−	2.14199i
$291$		0			0
$292$	1.72294	+	0.656496i	0.100827	+	0.0384185i
$293$	−14.8252	+	6.14082i	−0.866100	+	0.358751i	−0.771090	−	0.636726i	$-0.780288\pi$
$293$	−14.8252	+	6.14082i	−0.866100	+	0.358751i	−0.0950100	+	0.995476i	$0.530288\pi$
$294$		0			0
$295$	8.78275	−	8.78275i	0.511351	−	0.511351i
$296$	7.00677	−	11.5297i	0.407260	−	0.670148i
$297$		0			0
$298$	14.6358	+	21.2390i	0.847831	+	1.23034i
$299$	−8.55667	−	20.6576i	−0.494845	−	1.19466i
$300$		0			0
$301$	−11.7712	−	4.87581i	−0.678483	−	0.281037i
$302$	16.3944	+	10.6179i	0.943395	+	0.610993i
$303$		0			0
$304$	25.6077	−	12.3699i	1.46870	−	0.709461i
$305$			29.7682i			1.70452i
$306$		0			0
$307$	−27.9081	−	11.5599i	−1.59280	−	0.659760i	−0.602426	−	0.798175i	$-0.705799\pi$
$307$	−27.9081	−	11.5599i	−1.59280	−	0.659760i	−0.990374	+	0.138415i	$0.955799\pi$
$308$	−6.79779	+	0.194808i	−0.387340	+	0.0111002i
$309$		0			0
$310$	34.9032	−	24.0518i	1.98237	−	1.36605i
$311$	8.85165	+	8.85165i	0.501931	+	0.501931i	0.912038	−	0.410107i	$-0.134509\pi$
$311$	8.85165	+	8.85165i	0.501931	+	0.501931i	−0.410107	+	0.912038i	$0.634509\pi$
$312$		0			0
$313$	3.78382	−	3.78382i	0.213874	−	0.213874i	−0.592037	−	0.805911i	$-0.701676\pi$
$313$	3.78382	−	3.78382i	0.213874	−	0.213874i	0.805911	+	0.592037i	$0.201676\pi$
$314$	−1.20900	+	6.56842i	−0.0682276	+	0.370677i
$315$		0			0
$316$	−8.09781	−	18.0678i	−0.455537	−	1.01639i
$317$	3.09599	−	7.47438i	0.173888	−	0.419803i	−0.812775	−	0.582577i	$-0.802044\pi$
$317$	3.09599	−	7.47438i	0.173888	−	0.419803i	0.986663	+	0.162774i	$0.0520443\pi$
$318$		0			0
$319$	9.27852			0.519498
$320$	−2.75428	−	31.9665i	−0.153969	−	1.78698i
$321$		0			0
$322$	14.5174	−	3.10451i	0.809023	−	0.173008i
$323$	−14.1049	+	34.0523i	−0.784820	+	1.89472i
$324$		0			0
$325$	52.5741	−	21.7769i	2.91629	−	1.20797i
$326$	3.55423	−	19.3099i	0.196850	−	1.06948i
$327$		0			0
$328$	5.27916	+	0.816100i	0.291493	+	0.0450616i
$329$	1.46197	+	1.46197i	0.0806009	+	0.0806009i
$330$		0			0
$331$	−3.33156	−	8.04310i	−0.183119	−	0.442089i	0.805487	−	0.592613i	$-0.201904\pi$
$331$	−3.33156	−	8.04310i	−0.183119	−	0.442089i	−0.988606	+	0.150525i	$0.951904\pi$
$332$	−20.3717	+	0.583803i	−1.11804	+	0.0320403i
$333$		0			0
$334$	4.72238	−	7.29152i	0.258397	−	0.398974i
$335$		−	0.640983i		−	0.0350207i
$336$		0			0
$337$			32.4938i			1.77005i	0.465541	+	0.885026i	$0.345860\pi$
$337$			32.4938i			1.77005i	−0.465541	+	0.885026i	$0.654140\pi$
$338$	−15.8505	−	10.2657i	−0.862156	−	0.558378i
$339$		0			0
$340$	30.2342	+	28.5496i	1.63968	+	1.54832i
$341$	4.03490	+	9.74111i	0.218502	+	0.527511i
$342$		0			0
$343$	13.9598	+	13.9598i	0.753757	+	0.753757i
$344$	12.7780	+	7.76541i	0.688944	+	0.418683i
$345$		0			0
$346$	20.4618	+	3.76625i	1.10004	+	0.202475i
$347$	9.23528	−	3.82538i	0.495776	−	0.205357i	−0.120763	−	0.992681i	$-0.538534\pi$
$347$	9.23528	−	3.82538i	0.495776	−	0.205357i	0.616539	+	0.787324i	$0.288534\pi$
$348$		0			0
$349$	−1.54309	+	3.72534i	−0.0825996	+	0.199413i	−0.959783	−	0.280742i	$-0.909420\pi$
$349$	−1.54309	+	3.72534i	−0.0825996	+	0.199413i	0.877184	+	0.480155i	$0.159420\pi$
$350$	7.90105	+	36.9471i	0.422329	+	1.97491i
$351$		0			0
$352$	7.91896	+	0.992847i	0.422082	+	0.0529189i
$353$	2.47481			0.131721			0.0658604	−	0.997829i	$-0.479021\pi$
$353$	2.47481			0.131721			0.0658604	+	0.997829i	$0.479021\pi$
$354$		0			0
$355$	8.70014	−	21.0040i	0.461756	−	1.11478i
$356$	4.20976	−	11.0483i	0.223117	−	0.585558i
$357$		0			0
$358$	4.62326	+	0.850967i	0.244347	+	0.0449750i
$359$	18.1326	−	18.1326i	0.957000	−	0.957000i	−0.0421125	−	0.999113i	$-0.513409\pi$
$359$	18.1326	−	18.1326i	0.957000	−	0.957000i	0.999113	+	0.0421125i	$0.0134088\pi$
$360$		0			0
$361$	22.3078	+	22.3078i	1.17409	+	1.17409i
$362$	−4.78568	−	6.94482i	−0.251530	−	0.365012i
$363$		0			0
$364$	16.9888	−	17.9913i	0.890457	−	0.942999i
$365$	3.41589	+	1.41491i	0.178796	+	0.0740598i
$366$		0			0
$367$			11.6232i			0.606726i	0.952875	+	0.303363i	$0.0981095\pi$
$367$			11.6232i			0.606726i	−0.952875	+	0.303363i	$0.901890\pi$
$368$	−17.3938	+	0.997746i	−0.906713	+	0.0520111i
$369$		0			0
$370$	14.7073	−	22.7086i	0.764596	−	1.18056i
$371$	−19.5193	−	8.08518i	−1.01339	−	0.419762i
$372$		0			0
$373$	12.9695	+	31.3110i	0.671533	+	1.62122i	0.779007	+	0.627016i	$0.215724\pi$
$373$	12.9695	+	31.3110i	0.671533	+	1.62122i	−0.107474	+	0.994208i	$0.534276\pi$
$374$	−8.51724	+	5.86924i	−0.440416	+	0.303491i
$375$		0			0
$376$	−1.43346	−	1.95770i	−0.0739251	−	0.100960i
$377$	−23.8727	+	23.8727i	−1.22951	+	1.22951i
$378$		0			0
$379$	11.3117	−	4.68548i	0.581045	−	0.240677i	−0.0727476	−	0.997350i	$-0.523177\pi$
$379$	11.3117	−	4.68548i	0.581045	−	0.240677i	0.653793	+	0.756674i	$0.273177\pi$
$380$	52.0409	−	23.3243i	2.66964	−	1.19651i
$381$		0			0
$382$	−28.9390	+	6.18853i	−1.48065	+	0.316633i
$383$	−14.4899			−0.740402			−0.370201	−	0.928952i	$-0.620711\pi$
$383$	−14.4899			−0.740402			−0.370201	+	0.928952i	$0.620711\pi$
$384$		0			0
$385$	−13.6373			−0.695020
$386$	−34.4104	+	7.35857i	−1.75144	+	0.374542i
$387$		0			0
$388$	−17.7214	+	7.94260i	−0.899670	+	0.403224i
$389$	0.878959	−	0.364077i	0.0445650	−	0.0184594i	−0.360290	−	0.932840i	$-0.617322\pi$
$389$	0.878959	−	0.364077i	0.0445650	−	0.0184594i	0.404855	+	0.914381i	$0.367322\pi$
$390$		0			0
$391$	15.9666	−	15.9666i	0.807465	−	0.807465i
$392$	−1.99076	−	2.71881i	−0.100549	−	0.137321i
$393$		0			0
$394$	−19.9940	+	13.7779i	−1.00728	+	0.694120i
$395$	−15.1941	−	36.6818i	−0.764497	−	1.84566i
$396$		0			0
$397$	−7.20806	−	2.98567i	−0.361762	−	0.149847i	0.194396	−	0.980923i	$-0.437725\pi$
$397$	−7.20806	−	2.98567i	−0.361762	−	0.149847i	−0.556158	+	0.831076i	$0.687725\pi$
$398$	8.76413	−	13.5321i	0.439306	−	0.678305i
$399$		0			0
$400$	−2.53929	−	44.2676i	−0.126964	−	2.21338i
$401$			15.5146i			0.774764i	0.921919	+	0.387382i	$0.126621\pi$
$401$			15.5146i			0.774764i	−0.921919	+	0.387382i	$0.873379\pi$
$402$		0			0
$403$	−35.4443	−	14.6815i	−1.76561	−	0.731338i
$404$	16.1648	−	17.1186i	0.804230	−	0.851684i
$405$		0			0
$406$	−12.7191	−	18.4576i	−0.631241	−	0.916035i
$407$	4.75871	+	4.75871i	0.235880	+	0.235880i
$408$		0			0
$409$	5.48893	−	5.48893i	0.271410	−	0.271410i	−0.558258	−	0.829668i	$-0.688530\pi$
$409$	5.48893	−	5.48893i	0.271410	−	0.271410i	0.829668	+	0.558258i	$0.188530\pi$
$410$	10.5351	+	1.93912i	0.520293	+	0.0957662i
$411$		0			0
$412$	−11.3505	+	29.7887i	−0.559197	+	1.46758i
$413$	2.85634	−	6.89582i	0.140551	−	0.339321i
$414$		0			0
$415$	−40.8683			−2.00615
$416$	−22.9292	+	17.8202i	−1.12420	+	0.873707i
$417$		0			0
$418$	2.96648	+	13.8719i	0.145095	+	0.678498i
$419$	4.73118	−	11.4221i	0.231133	−	0.558005i	−0.765178	−	0.643819i	$-0.777349\pi$
$419$	4.73118	−	11.4221i	0.231133	−	0.558005i	0.996311	+	0.0858140i	$0.0273491\pi$
$420$		0			0
$421$	8.57014	−	3.54987i	0.417683	−	0.173010i	−0.163937	−	0.986471i	$-0.552419\pi$
$421$	8.57014	−	3.54987i	0.417683	−	0.173010i	0.581620	+	0.813461i	$0.302419\pi$
$422$	18.2452	+	3.35825i	0.888164	+	0.163477i
$423$		0			0
$424$	21.1888	+	12.8768i	1.02902	+	0.625351i
$425$	40.6353	+	40.6353i	1.97110	+	1.97110i
$426$		0			0
$427$	6.84569	+	16.5270i	0.331286	+	0.799795i
$428$	23.6024	+	22.2873i	1.14087	+	1.07730i
$429$		0			0
$430$	25.1673	+	16.2997i	1.21367	+	0.786040i
$431$			31.9729i			1.54008i	0.637996	+	0.770040i	$0.279764\pi$
$431$			31.9729i			1.54008i	−0.637996	+	0.770040i	$0.720236\pi$
$432$		0			0
$433$			6.15337i			0.295712i	0.989009	+	0.147856i	$0.0472372\pi$
$433$			6.15337i			0.295712i	−0.989009	+	0.147856i	$0.952763\pi$
$434$	13.8467	−	21.3798i	0.664664	−	1.02626i
$435$		0			0
$436$	−4.16674	+	0.119409i	−0.199551	+	0.00571864i
$437$	−11.8506	−	28.6098i	−0.566889	−	1.36859i
$438$		0			0
$439$	7.89620	+	7.89620i	0.376865	+	0.376865i	0.869970	−	0.493105i	$-0.164138\pi$
$439$	7.89620	+	7.89620i	0.376865	+	0.376865i	−0.493105	+	0.869970i	$0.664138\pi$
$440$	15.8164	+	2.44504i	0.754018	+	0.116563i
$441$		0			0
$442$	6.81305	−	37.0150i	0.324064	−	1.76062i
$443$	−16.7163	+	6.92410i	−0.794214	+	0.328974i	−0.742636	−	0.669695i	$-0.766425\pi$
$443$	−16.7163	+	6.92410i	−0.794214	+	0.328974i	−0.0515773	+	0.998669i	$0.516425\pi$
$444$		0			0
$445$	9.07307	−	21.9043i	0.430105	−	1.03836i
$446$	−1.93568	+	0.413940i	−0.0916570	+	0.0196006i
$447$		0			0
$448$	−8.88038	−	17.1140i	−0.419558	−	0.808563i
$449$	11.7932			0.556556			0.278278	−	0.960501i	$-0.410236\pi$
$449$	11.7932			0.556556			0.278278	+	0.960501i	$0.410236\pi$
$450$		0			0
$451$	−1.01969	+	2.46175i	−0.0480152	+	0.115919i
$452$	14.6242	+	32.6293i	0.687863	+	1.53475i
$453$		0			0
$454$	−1.68144	+	9.13516i	−0.0789137	+	0.428734i
$455$	35.0874	−	35.0874i	1.64492	−	1.64492i
$456$		0			0
$457$	4.77188	+	4.77188i	0.223219	+	0.223219i	0.809853	−	0.586633i	$-0.199547\pi$
$457$	4.77188	+	4.77188i	0.223219	+	0.223219i	−0.586633	+	0.809853i	$0.699547\pi$
$458$	15.7431	−	10.8486i	0.735627	−	0.506921i
$459$		0			0
$460$	−34.9229	+	1.00081i	−1.62829	+	0.0466628i
$461$	−6.99530	−	2.89755i	−0.325803	−	0.134952i	0.213786	−	0.976881i	$-0.431420\pi$
$461$	−6.99530	−	2.89755i	−0.325803	−	0.134952i	−0.539589	+	0.841928i	$0.681420\pi$
$462$		0			0
$463$		−	27.4835i		−	1.27727i	−0.769511	−	0.638634i	$-0.779500\pi$
$463$		−	27.4835i		−	1.27727i	0.769511	−	0.638634i	$-0.220500\pi$
$464$	11.4423	+	23.6874i	0.531195	+	1.09966i
$465$		0			0
$466$	−7.29795	−	4.72654i	−0.338071	−	0.218953i
$467$	5.37613	+	2.22687i	0.248778	+	0.103047i	0.503588	−	0.863944i	$-0.332013\pi$
$467$	5.37613	+	2.22687i	0.248778	+	0.103047i	−0.254810	+	0.966991i	$0.582013\pi$
$468$		0			0
$469$	−0.147405	−	0.355866i	−0.00680651	−	0.0164324i
$470$	−2.76090	−	4.00652i	−0.127351	−	0.184807i
$471$		0			0
$472$	−4.54912	+	7.48560i	−0.209390	+	0.344552i
$473$	−5.27394	+	5.27394i	−0.242496	+	0.242496i
$474$		0			0
$475$	72.8126	−	30.1599i	3.34087	−	1.38383i
$476$	23.3511	+	8.89756i	1.07030	+	0.407819i
$477$		0			0
$478$	0.839527	+	3.92582i	0.0383991	+	0.179563i
$479$	−8.93341			−0.408178			−0.204089	−	0.978952i	$-0.565423\pi$
$479$	−8.93341			−0.408178			−0.204089	+	0.978952i	$0.565423\pi$
$480$		0			0
$481$	−24.4874			−1.11653
$482$	−0.378692	−	1.77085i	−0.0172489	−	0.0806600i
$483$		0			0
$484$	6.41587	−	16.8381i	0.291631	−	0.765368i
$485$	−35.9787	+	14.9029i	−1.63371	+	0.676704i
$486$		0			0
$487$	5.77026	−	5.77026i	0.261475	−	0.261475i	−0.564178	−	0.825653i	$-0.690807\pi$
$487$	5.77026	−	5.77026i	0.261475	−	0.261475i	0.825653	+	0.564178i	$0.190807\pi$
$488$	−4.97644	−	20.3952i	−0.225273	−	0.923247i
$489$		0			0
$490$	−3.83428	−	5.56418i	−0.173215	−	0.251364i
$491$	−4.97702	−	12.0156i	−0.224610	−	0.542256i	0.770896	−	0.636961i	$-0.219809\pi$
$491$	−4.97702	−	12.0156i	−0.224610	−	0.542256i	−0.995505	+	0.0947058i	$0.969809\pi$
$492$		0			0
$493$	−31.4988	−	13.0472i	−1.41864	−	0.587618i
$494$	−43.3235	−	28.0586i	−1.94922	−	1.26242i
$495$		0			0
$496$	−19.8925	+	22.3136i	−0.893201	+	1.00191i
$497$		−	13.6619i		−	0.612821i
$498$		0			0
$499$	19.0776	+	7.90220i	0.854031	+	0.353751i	0.766370	−	0.642399i	$-0.222061\pi$
$499$	19.0776	+	7.90220i	0.854031	+	0.353751i	0.0876607	+	0.996150i	$0.472061\pi$
$500$	−1.39820	−	48.7899i	−0.0625294	−	2.18195i
$501$		0			0
$502$	15.9686	−	11.0040i	0.712714	−	0.491132i
$503$	27.9196	+	27.9196i	1.24487	+	1.24487i	0.957956	+	0.286916i	$0.0926300\pi$
$503$	27.9196	+	27.9196i	1.24487	+	1.24487i	0.286916	+	0.957956i	$0.407370\pi$
$504$		0			0
$505$	33.3855	−	33.3855i	1.48564	−	1.48564i
$506$	1.57315	−	8.54687i	0.0699352	−	0.379955i
$507$		0			0
$508$	−1.14800	+	0.514525i	−0.0509344	+	0.0228284i
$509$	14.2624	−	34.4324i	0.632169	−	1.52619i	−0.204722	−	0.978820i	$-0.565629\pi$
$509$	14.2624	−	34.4324i	0.632169	−	1.52619i	0.836891	−	0.547370i	$-0.184371\pi$
$510$		0			0
$511$	2.22185			0.0982887
$512$	7.23099	+	21.4409i	0.319568	+	0.947563i
$513$		0			0
$514$	10.9943	−	2.35110i	0.484936	−	0.103702i
$515$	−24.4630	+	59.0590i	−1.07797	+	2.60245i
$516$		0			0
$517$	1.11818	−	0.463165i	0.0491774	−	0.0203700i
$518$	2.94310	−	15.9897i	0.129312	−	0.702548i
$519$		0			0
$520$	−46.9849	+	34.4032i	−2.06043	+	1.50868i
$521$	9.59974	+	9.59974i	0.420572	+	0.420572i	0.885401	−	0.464829i	$-0.153884\pi$
$521$	9.59974	+	9.59974i	0.420572	+	0.420572i	−0.464829	+	0.885401i	$0.653884\pi$
$522$		0			0
$523$	13.0202	+	31.4336i	0.569335	+	1.37450i	0.902116	+	0.431493i	$0.142013\pi$
$523$	13.0202	+	31.4336i	0.569335	+	1.37450i	−0.332781	+	0.943004i	$0.607987\pi$
$524$	0.0706206	+	2.46429i	0.00308508	+	0.107653i
$525$		0			0
$526$	5.73056	−	8.84819i	0.249864	−	0.385800i
$527$		−	38.7430i		−	1.68767i
$528$		0			0
$529$		−	4.02881i		−	0.175166i
$530$	41.7330	+	27.0285i	1.81276	+	1.17404i
$531$		0			0
$532$	23.5287	−	24.9170i	1.02010	−	1.08029i
$533$	−3.71027	−	8.95738i	−0.160710	−	0.387987i
$534$		0			0
$535$	46.0305	+	46.0305i	1.99007	+	1.99007i
$536$	0.107155	+	0.439159i	0.00462839	+	0.0189688i
$537$		0			0
$538$	5.39558	+	0.993122i	0.232620	+	0.0428165i
$539$	1.55290	−	0.643234i	0.0668884	−	0.0277061i
$540$		0			0
$541$	11.5070	−	27.7805i	0.494727	−	1.19438i	−0.457562	−	0.889178i	$-0.651277\pi$
$541$	11.5070	−	27.7805i	0.494727	−	1.19438i	0.952289	−	0.305198i	$-0.0987227\pi$
$542$	−0.265025	−	1.23932i	−0.0113838	−	0.0532332i
$543$		0			0
$544$	−25.4872	−	14.5060i	−1.09276	−	0.621938i
$545$	−8.35904			−0.358062
$546$		0			0
$547$	−10.4802	+	25.3015i	−0.448102	+	1.08181i	0.524930	+	0.851145i	$0.324091\pi$
$547$	−10.4802	+	25.3015i	−0.448102	+	1.08181i	−0.973032	+	0.230669i	$0.925909\pi$
$548$	−14.3298	−	5.46013i	−0.612139	−	0.233245i
$549$		0			0
$550$	21.7520	+	4.00371i	0.927508	+	0.170719i
$551$	−33.0625	+	33.0625i	−1.40851	+	1.40851i
$552$		0			0
$553$	−16.8712	−	16.8712i	−0.717434	−	0.717434i
$554$	25.2830	+	36.6898i	1.07417	+	1.55880i
$555$		0			0
$556$	−16.5258	−	15.6050i	−0.700849	−	0.661799i
$557$	13.1441	+	5.44448i	0.556935	+	0.230690i	0.643354	−	0.765569i	$-0.277542\pi$
$557$	13.1441	+	5.44448i	0.556935	+	0.230690i	−0.0864188	+	0.996259i	$0.527542\pi$
$558$		0			0
$559$		−	27.1387i		−	1.14784i
$560$	−16.8175	−	34.8150i	−0.710670	−	1.47120i
$561$		0			0
$562$	−5.25747	+	8.11772i	−0.221773	+	0.342425i
$563$	14.9009	+	6.17214i	0.627997	+	0.260125i	0.673902	−	0.738821i	$-0.264617\pi$
$563$	14.9009	+	6.17214i	0.627997	+	0.260125i	−0.0459048	+	0.998946i	$0.514617\pi$
$564$		0			0
$565$	27.4396	+	66.2451i	1.15439	+	2.78695i
$566$	30.6955	−	21.1523i	1.29023	−	0.889097i
$567$		0			0
$568$	−2.44946	+	15.8450i	−0.102777	+	0.664841i
$569$	−12.9487	+	12.9487i	−0.542836	+	0.542836i	−0.924359	−	0.381523i	$-0.875400\pi$
$569$	−12.9487	+	12.9487i	−0.542836	+	0.542836i	0.381523	+	0.924359i	$0.375400\pi$
$570$		0			0
$571$	−2.89576	+	1.19946i	−0.121184	+	0.0501959i	−0.442451	−	0.896793i	$-0.645891\pi$
$571$	−2.89576	+	1.19946i	−0.121184	+	0.0501959i	0.321268	+	0.946988i	$0.395891\pi$
$572$	−5.92437	−	13.2184i	−0.247710	−	0.552689i
$573$		0			0
$574$	6.29491	−	1.34615i	0.262745	−	0.0561873i
$575$	−48.2821			−2.01350
$576$		0			0
$577$	−2.57401			−0.107158			−0.0535788	−	0.998564i	$-0.517063\pi$
$577$	−2.57401			−0.107158			−0.0535788	+	0.998564i	$0.517063\pi$
$578$	13.6575	−	2.92063i	0.568078	−	0.121482i
$579$		0			0
$580$	21.5752	+	48.1384i	0.895862	+	1.99884i
$581$	−22.6896	+	9.39834i	−0.941324	+	0.389909i
$582$		0			0
$583$	−8.74537	+	8.74537i	−0.362196	+	0.362196i
$584$	−2.57688	−	0.398357i	−0.106632	−	0.0164841i
$585$		0			0
$586$	18.6864	−	12.8768i	0.771929	−	0.531937i
$587$	1.75203	+	4.22979i	0.0723142	+	0.174582i	0.955904	−	0.293681i	$-0.0948802\pi$
$587$	1.75203	+	4.22979i	0.0723142	+	0.174582i	−0.883589	+	0.468262i	$0.844880\pi$
$588$		0			0
$589$	−49.0886	−	20.3332i	−2.02266	−	0.837814i
$590$	−9.54865	+	14.7435i	−0.393112	+	0.606979i
$591$		0			0
$592$	−6.28020	+	18.0171i	−0.258115	+	0.740498i
$593$			3.34507i			0.137365i	0.997639	+	0.0686827i	$0.0218796\pi$
$593$			3.34507i			0.137365i	−0.997639	+	0.0686827i	$0.978120\pi$
$594$		0			0
$595$	46.2960	+	19.1764i	1.89795	+	0.786157i
$596$	−26.5218	−	25.0440i	−1.08637	−	1.02584i
$597$		0			0
$598$	17.9427	+	26.0378i	0.733731	+	1.06477i
$599$	24.9663	+	24.9663i	1.02010	+	1.02010i	0.999794	+	0.0203034i	$0.00646321\pi$
$599$	24.9663	+	24.9663i	1.02010	+	1.02010i	0.0203034	+	0.999794i	$0.493537\pi$
$600$		0			0
$601$	26.4859	−	26.4859i	1.08038	−	1.08038i	0.0839074	−	0.996474i	$-0.473260\pi$
$601$	26.4859	−	26.4859i	1.08038	−	1.08038i	0.996474	−	0.0839074i	$-0.0267400\pi$
$602$	17.7210	+	3.26176i	0.722253	+	0.132939i
$603$		0			0
$604$	−25.8128	−	9.83552i	−1.05031	−	0.400201i
$605$	13.8278	−	33.3832i	0.562179	−	1.35722i
$606$		0			0
$607$	16.7034			0.677970			0.338985	−	0.940792i	$-0.389916\pi$
$607$	16.7034			0.677970			0.338985	+	0.940792i	$0.389916\pi$
$608$	−31.7558	+	24.6801i	−1.28787	+	1.00091i
$609$		0			0
$610$	−8.80363	−	41.1678i	−0.356449	−	1.66684i
$611$	−1.68529	+	4.06864i	−0.0681794	+	0.164600i
$612$		0			0
$613$	−28.6301	+	11.8590i	−1.15636	+	0.478980i	−0.876662	−	0.481107i	$-0.840235\pi$
$613$	−28.6301	+	11.8590i	−1.15636	+	0.478980i	−0.279699	+	0.960088i	$0.590235\pi$
$614$	42.0141	+	7.73321i	1.69555	+	0.312087i
$615$		0			0
$616$	9.34337	−	2.27979i	0.376455	−	0.0918552i
$617$	−15.0897	−	15.0897i	−0.607488	−	0.607488i	0.334801	−	0.942289i	$-0.391331\pi$
$617$	−15.0897	−	15.0897i	−0.607488	−	0.607488i	−0.942289	+	0.334801i	$0.891331\pi$
$618$		0			0
$619$	0.0105920	+	0.0255713i	0.000425727	+	0.00102780i	0.924092	−	0.382169i	$-0.124823\pi$
$619$	0.0105920	+	0.0255713i	0.000425727	+	0.00102780i	−0.923667	+	0.383197i	$0.874823\pi$
$620$	−41.1561	+	43.5846i	−1.65287	+	1.75040i
$621$		0			0
$622$	−14.8591	−	9.62356i	−0.595797	−	0.385870i
$623$		−	14.2475i		−	0.570815i
$624$		0			0
$625$		−	42.4536i		−	1.69815i
$626$	−4.11379	+	6.35184i	−0.164420	+	0.253871i
$627$		0			0
$628$	−0.270565	−	9.44132i	−0.0107967	−	0.376750i
$629$	−9.46332	−	22.8465i	−0.377327	−	0.910949i
$630$		0			0
$631$	−25.9511	−	25.9511i	−1.03310	−	1.03310i	−0.999433	−	0.0336656i	$-0.989282\pi$
$631$	−25.9511	−	25.9511i	−1.03310	−	1.03310i	−0.0336656	−	0.999433i	$-0.510718\pi$
$632$	16.5422	+	22.5919i	0.658013	+	0.898657i
$633$		0			0
$634$	−2.07111	+	11.2523i	−0.0822545	+	0.446884i
$635$	−2.33071	+	0.965414i	−0.0924916	+	0.0383113i
$636$		0			0
$637$	−2.34049	+	5.65045i	−0.0927337	+	0.223879i
$638$	−12.8317	+	2.74403i	−0.508012	+	0.108637i
$639$		0			0
$640$	13.2628	+	43.3934i	0.524258	+	1.71528i
$641$	−48.5136			−1.91617			−0.958085	−	0.286483i	$-0.907514\pi$
$641$	−48.5136			−1.91617			−0.958085	+	0.286483i	$0.907514\pi$
$642$		0			0
$643$	−15.1986	+	36.6927i	−0.599374	+	1.44702i	0.274846	+	0.961488i	$0.411373\pi$
$643$	−15.1986	+	36.6927i	−0.599374	+	1.44702i	−0.874220	+	0.485529i	$0.838627\pi$
$644$	−19.1586	+	8.58674i	−0.754956	+	0.338365i
$645$		0			0
$646$	9.43574	−	51.2639i	0.371244	−	2.01695i
$647$	9.68089	−	9.68089i	0.380595	−	0.380595i	−0.490721	−	0.871316i	$-0.663267\pi$
$647$	9.68089	−	9.68089i	0.380595	−	0.380595i	0.871316	+	0.490721i	$0.163267\pi$
$648$		0			0
$649$	−3.08957	−	3.08957i	−0.121276	−	0.121276i
$650$	−66.2669	+	45.6645i	−2.59920	+	1.79111i
$651$		0			0
$652$	0.795411	+	27.7557i	0.0311507	+	1.08700i
$653$	−46.6877	−	19.3387i	−1.82703	−	0.756781i	−0.970675	−	0.240397i	$-0.922722\pi$
$653$	−46.6877	−	19.3387i	−1.82703	−	0.756781i	−0.856357	−	0.516384i	$-0.827278\pi$
$654$		0			0
$655$			4.94370i			0.193166i
$656$	−7.54214	+	0.432634i	−0.294471	+	0.0168915i
$657$		0			0
$658$	−2.45418	−	1.58946i	−0.0956740	−	0.0619636i
$659$	41.0194	+	16.9908i	1.59789	+	0.661867i	0.991115	−	0.133009i	$-0.0424640\pi$
$659$	41.0194	+	16.9908i	1.59789	+	0.661867i	0.606772	+	0.794876i	$0.292464\pi$
$660$		0			0
$661$	3.50729	+	8.46734i	0.136418	+	0.329341i	0.977295	−	0.211885i	$-0.0679602\pi$
$661$	3.50729	+	8.46734i	0.136418	+	0.329341i	−0.840877	+	0.541226i	$0.817960\pi$
$662$	6.98603	+	10.1379i	0.271520	+	0.394020i
$663$		0			0
$664$	28.0003	−	6.83208i	1.08662	−	0.265136i
$665$	48.5943	−	48.5943i	1.88441	−	1.88441i
$666$		0			0
$667$	26.4644	−	10.9619i	1.02470	−	0.424447i
$668$	−4.37440	+	11.4804i	−0.169251	+	0.444189i
$669$		0			0
$670$	0.189564	+	0.886445i	0.00732350	+	0.0342463i
$671$	10.4718			0.404259
$672$		0			0
$673$	−31.1260			−1.19982			−0.599910	−	0.800068i	$-0.704797\pi$
$673$	−31.1260			−1.19982			−0.599910	+	0.800068i	$0.704797\pi$
$674$	−9.60972	−	44.9372i	−0.370152	−	1.73092i
$675$		0			0
$676$	24.9564	+	9.50921i	0.959861	+	0.365739i
$677$	26.3347	−	10.9082i	1.01212	−	0.419235i	0.185895	−	0.982570i	$-0.440482\pi$
$677$	26.3347	−	10.9082i	1.01212	−	0.419235i	0.826229	+	0.563334i	$0.190482\pi$
$678$		0			0
$679$	−16.5478	+	16.5478i	−0.635046	+	0.635046i
$680$	−50.2555	−	30.5411i	−1.92721	−	1.17120i
$681$		0			0
$682$	−8.46088	−	12.2781i	−0.323984	−	0.470154i
$683$	12.1985	+	29.4498i	0.466763	+	1.12686i	0.965568	+	0.260151i	$0.0837722\pi$
$683$	12.1985	+	29.4498i	0.466763	+	1.12686i	−0.498805	+	0.866714i	$0.666228\pi$
$684$		0			0
$685$	−28.4103	−	11.7679i	−1.08550	−	0.449629i
$686$	−23.4341	−	15.1772i	−0.894717	−	0.579466i
$687$		0			0
$688$	−19.9678	−	6.96017i	−0.761266	−	0.265354i
$689$		−	45.0019i		−	1.71444i
$690$		0			0
$691$	21.0826	+	8.73270i	0.802020	+	0.332208i	0.745765	−	0.666209i	$-0.232084\pi$
$691$	21.0826	+	8.73270i	0.802020	+	0.332208i	0.0562550	+	0.998416i	$0.482084\pi$
$692$	−29.4114	+	0.842861i	−1.11806	+	0.0320408i
$693$		0			0
$694$	−11.6406	+	8.02153i	−0.441870	+	0.304493i
$695$	−32.2293	−	32.2293i	−1.22253	−	1.22253i
$696$		0			0
$697$	6.92329	−	6.92329i	0.262238	−	0.262238i
$698$	1.03227	−	5.60830i	0.0390722	−	0.212277i
$699$		0			0
$700$	−21.8534	−	48.7592i	−0.825983	−	1.84292i
$701$	−1.94437	+	4.69413i	−0.0734379	+	0.177295i	−0.956336	−	0.292270i	$-0.905589\pi$
$701$	−1.94437	+	4.69413i	−0.0734379	+	0.177295i	0.882898	+	0.469565i	$0.155589\pi$
$702$		0			0
$703$	−33.9138			−1.27908
$704$	−11.2451	+	0.968895i	−0.423816	+	0.0365166i
$705$		0			0
$706$	−3.42252	+	0.731899i	−0.128808	+	0.0275454i
$707$	10.8577	−	26.2128i	0.408346	−	0.985834i
$708$		0			0
$709$	25.1332	−	10.4105i	0.943898	−	0.390975i	0.142964	−	0.989728i	$-0.454337\pi$
$709$	25.1332	−	10.4105i	0.943898	−	0.390975i	0.800934	+	0.598753i	$0.204337\pi$
$710$	−5.82011	+	31.6204i	−0.218425	+	1.18669i
$711$		0			0
$712$	−2.55445	+	16.5242i	−0.0957322	+	0.619269i
$713$	23.0168	+	23.0168i	0.861987	+	0.861987i
$714$		0			0
$715$	−11.1160	−	26.8364i	−0.415715	−	1.00363i
$716$	−6.64538	+	0.190441i	−0.248350	+	0.00711710i
$717$		0			0
$718$	−19.7138	+	30.4389i	−0.735714	+	1.13597i
$719$			43.0777i			1.60653i	0.595623	+	0.803264i	$0.296905\pi$
$719$			43.0777i			1.60653i	−0.595623	+	0.803264i	$0.703095\pi$
$720$		0			0
$721$			38.4145i			1.43063i
$722$	−37.4478	−	24.2532i	−1.39366	−	0.902610i
$723$		0			0
$724$	8.67219	+	8.18899i	0.322300	+	0.304342i
$725$	27.8983	+	67.3524i	1.03612	+	2.50141i
$726$		0			0
$727$	−3.41768	−	3.41768i	−0.126755	−	0.126755i	0.640883	−	0.767638i	$-0.278568\pi$
$727$	−3.41768	−	3.41768i	−0.126755	−	0.126755i	−0.767638	+	0.640883i	$0.778568\pi$
$728$	−18.1739	+	29.9052i	−0.673569	+	1.10836i
$729$		0			0
$730$	−5.14244	−	0.946528i	−0.190330	−	0.0350326i
$731$	25.3201	−	10.4879i	0.936498	−	0.387910i
$732$		0			0
$733$	−18.1666	+	43.8581i	−0.670999	+	1.61994i	0.108916	+	0.994051i	$0.465262\pi$
$733$	−18.1666	+	43.8581i	−0.670999	+	1.61994i	−0.779916	+	0.625885i	$0.784738\pi$
$734$	−3.43744	−	16.0743i	−0.126878	−	0.593312i
$735$		0			0
$736$	23.7596	−	6.52386i	0.875790	−	0.240473i
$737$	−0.225483			−0.00830579
$738$		0			0
$739$	−6.42479	+	15.5108i	−0.236340	+	0.570575i	−0.996899	−	0.0786942i	$-0.974925\pi$
$739$	−6.42479	+	15.5108i	−0.236340	+	0.570575i	0.760559	+	0.649269i	$0.224925\pi$
$740$	−13.6236	+	35.7543i	−0.500812	+	1.31435i
$741$		0			0
$742$	29.3853	+	5.40872i	1.07877	+	0.198560i
$743$	23.2111	−	23.2111i	0.851532	−	0.851532i	−0.138790	−	0.990322i	$-0.544321\pi$
$743$	23.2111	−	23.2111i	0.851532	−	0.851532i	0.990322	+	0.138790i	$0.0443212\pi$
$744$		0			0
$745$	−51.7240	−	51.7240i	−1.89502	−	1.89502i
$746$	−27.1960	−	39.4659i	−0.995715	−	1.44495i
$747$		0			0
$748$	10.0431	−	10.6357i	0.367213	−	0.388881i
$749$	36.1411	+	14.9701i	1.32057	+	0.546996i
$750$		0			0
$751$			28.3909i			1.03600i	0.855381	+	0.517999i	$0.173323\pi$
$751$			28.3909i			1.03600i	−0.855381	+	0.517999i	$0.826677\pi$
$752$	2.56137	+	2.28346i	0.0934034	+	0.0832691i
$753$		0			0
$754$	25.9546	−	40.0748i	0.945210	−	1.45944i
$755$	−51.1764	−	21.1980i	−1.86250	−	0.771472i
$756$		0			0
$757$	−12.8053	−	30.9146i	−0.465415	−	1.12361i	−0.966143	−	0.258006i	$-0.916934\pi$
$757$	−12.8053	−	30.9146i	−0.465415	−	1.12361i	0.500728	−	0.865604i	$-0.333066\pi$
$758$	−14.2578	+	9.82509i	−0.517868	+	0.356863i
$759$		0			0
$760$	−65.0718	+	47.6467i	−2.36040	+	1.72833i
$761$	−5.26876	+	5.26876i	−0.190993	+	0.190993i	−0.796125	−	0.605132i	$-0.793120\pi$
$761$	−5.26876	+	5.26876i	−0.190993	+	0.190993i	0.605132	+	0.796125i	$0.293120\pi$
$762$		0			0
$763$	−4.64084	+	1.92230i	−0.168010	+	0.0695919i
$764$	38.1909	−	17.1168i	1.38170	−	0.619264i
$765$		0			0
$766$	20.0388	−	4.28525i	0.724031	−	0.154832i
$767$	15.8983			0.574056
$768$		0			0
$769$	48.6047			1.75273			0.876365	−	0.481647i	$-0.159961\pi$
$769$	48.6047			1.75273			0.876365	+	0.481647i	$0.159961\pi$
$770$	18.8596	−	4.03308i	0.679654	−	0.145342i
$771$		0			0
$772$	45.4114	−	20.3530i	1.63439	−	0.732521i
$773$	−40.1091	+	16.6138i	−1.44263	+	0.597555i	−0.960433	−	0.278510i	$-0.910159\pi$
$773$	−40.1091	+	16.6138i	−1.44263	+	0.597555i	−0.482192	+	0.876065i	$0.660159\pi$
$774$		0			0
$775$	−58.5784	+	58.5784i	−2.10420	+	2.10420i
$776$	22.1589	−	16.2251i	0.795457	−	0.582448i
$777$		0			0
$778$	−1.10788	+	0.763441i	−0.0397194	+	0.0273707i
$779$	−5.13854	−	12.4055i	−0.184107	−	0.444474i
$780$		0			0
$781$	−7.38873	−	3.06051i	−0.264390	−	0.109514i
$782$	−17.3590	+	26.8029i	−0.620755	+	0.958468i
$783$		0			0
$784$	3.55718	+	3.17122i	0.127042	+	0.113258i
$785$		−	18.9405i		−	0.676017i
$786$		0			0
$787$	−36.0672	−	14.9395i	−1.28566	−	0.532536i	−0.367968	−	0.929838i	$-0.619947\pi$
$787$	−36.0672	−	14.9395i	−1.28566	−	0.532536i	−0.917688	+	0.397302i	$0.869947\pi$
$788$	23.5760	−	24.9671i	0.839859	−	0.889416i
$789$		0			0
$790$	31.8608	+	46.2354i	1.13356	+	1.64498i
$791$	30.4683	+	30.4683i	1.08333	+	1.08333i
$792$		0			0
$793$	−26.9429	+	26.9429i	−0.956769	+	0.956769i
$794$	10.8513	+	1.99732i	0.385099	+	0.0708822i
$795$		0			0
$796$	−8.11833	+	21.3061i	−0.287747	+	0.755175i
$797$	12.6091	−	30.4411i	0.446638	−	1.07828i	−0.526935	−	0.849905i	$-0.676659\pi$
$797$	12.6091	−	30.4411i	0.446638	−	1.07828i	0.973573	−	0.228375i	$-0.0733411\pi$
$798$		0			0
$799$	−4.44729			−0.157334
$800$	16.6034	+	60.4687i	0.587018	+	2.13789i
$801$		0			0
$802$	−4.58829	−	21.4559i	−0.162018	−	0.757634i
$803$	0.497733	−	1.20163i	0.0175646	−	0.0424048i
$804$		0			0
$805$	−38.8965	+	16.1115i	−1.37092	+	0.567855i
$806$	53.3595	+	9.82145i	1.87951	+	0.345946i
$807$		0			0
$808$	−17.2924	+	28.4547i	−0.608344	+	1.00103i
$809$	−18.4126	−	18.4126i	−0.647354	−	0.647354i	0.304999	−	0.952353i	$-0.401344\pi$
$809$	−18.4126	−	18.4126i	−0.647354	−	0.647354i	−0.952353	+	0.304999i	$0.901344\pi$
$810$		0			0
$811$	1.08349	+	2.61577i	0.0380464	+	0.0918520i	0.941761	−	0.336284i	$-0.109170\pi$
$811$	1.08349	+	2.61577i	0.0380464	+	0.0918520i	−0.903714	+	0.428136i	$0.859170\pi$
$812$	23.0485	+	21.7643i	0.808845	+	0.763777i
$813$		0			0
$814$	−7.98837	−	5.17369i	−0.279992	−	0.181338i
$815$			55.6817i			1.95044i
$816$		0			0
$817$		−	37.5857i		−	1.31496i
$818$	−5.96759	+	9.21418i	−0.208652	+	0.322166i
$819$		0			0
$820$	−15.1430	+	0.433961i	−0.528816	+	0.0151546i
$821$	−0.0926235	−	0.223613i	−0.00323258	−	0.00780414i	0.922255	−	0.386582i	$-0.126344\pi$
$821$	−0.0926235	−	0.223613i	−0.00323258	−	0.00780414i	−0.925488	+	0.378778i	$0.876344\pi$
$822$		0			0
$823$	5.08560	+	5.08560i	0.177273	+	0.177273i	0.790166	−	0.612893i	$-0.209994\pi$
$823$	5.08560	+	5.08560i	0.177273	+	0.177273i	−0.612893	+	0.790166i	$0.709994\pi$
$824$	6.88738	−	44.5529i	0.239933	−	1.55207i
$825$		0			0
$826$	−1.91080	+	10.3813i	−0.0664851	+	0.361211i
$827$	15.5066	−	6.42303i	0.539216	−	0.223351i	−0.0964180	−	0.995341i	$-0.530739\pi$
$827$	15.5066	−	6.42303i	0.539216	−	0.223351i	0.635634	+	0.771990i	$0.280739\pi$
$828$		0			0
$829$	5.67512	−	13.7009i	0.197105	−	0.475853i	−0.794165	−	0.607702i	$-0.792091\pi$
$829$	5.67512	−	13.7009i	0.197105	−	0.475853i	0.991270	+	0.131849i	$0.0420914\pi$
$830$	56.5187	−	12.0864i	1.96179	−	0.419524i
$831$		0			0
$832$	26.4397	−	31.4254i	0.916631	−	1.08948i
$833$	−6.17632			−0.213997
$834$		0			0
$835$	−9.42790	+	22.7610i	−0.326266	+	0.787676i
$836$	−8.20495	−	18.3068i	−0.283774	−	0.633154i
$837$		0			0
$838$	−3.16500	+	17.1953i	−0.109333	+	0.594002i
$839$	−7.26802	+	7.26802i	−0.250920	+	0.250920i	−0.821348	−	0.570428i	$-0.806777\pi$
$839$	−7.26802	+	7.26802i	−0.250920	+	0.250920i	0.570428	+	0.821348i	$0.306777\pi$
$840$		0			0
$841$	−10.0771	−	10.0771i	−0.347487	−	0.347487i
$842$	−10.8022	+	7.44380i	−0.372268	+	0.256530i
$843$		0			0
$844$	−26.2253	+	0.751554i	−0.902713	+	0.0258696i
$845$	49.4785	+	20.4947i	1.70211	+	0.705039i
$846$		0			0
$847$		−	21.7139i		−	0.746098i
$848$	−33.1111	−	11.5415i	−1.13704	−	0.396337i
$849$		0			0
$850$	−68.2139	−	44.1790i	−2.33972	−	1.51533i
$851$	19.1949	+	7.95081i	0.657994	+	0.272550i
$852$		0			0
$853$	−11.5073	−	27.7811i	−0.394002	−	0.951206i	−0.989059	−	0.147522i	$-0.952870\pi$
$853$	−11.5073	−	27.7811i	−0.394002	−	0.951206i	0.595057	−	0.803684i	$-0.297130\pi$
$854$	−14.3549	−	20.8313i	−0.491214	−	0.712834i
$855$		0			0
$856$	−39.2321	−	23.8420i	−1.34093	−	0.814903i
$857$	−3.34719	+	3.34719i	−0.114338	+	0.114338i	−0.761961	−	0.647623i	$-0.775763\pi$
$857$	−3.34719	+	3.34719i	−0.114338	+	0.114338i	0.647623	+	0.761961i	$0.275763\pi$
$858$		0			0
$859$	−7.18610	+	2.97658i	−0.245186	+	0.101560i	−0.501893	−	0.864930i	$-0.667363\pi$
$859$	−7.18610	+	2.97658i	−0.245186	+	0.101560i	0.256706	+	0.966489i	$0.417363\pi$
$860$	−39.6255	−	15.0986i	−1.35122	−	0.514858i
$861$		0			0
$862$	−9.45565	−	44.2167i	−0.322061	−	1.50603i
$863$	41.7004			1.41950			0.709749	−	0.704454i	$-0.248808\pi$
$863$	41.7004			1.41950			0.709749	+	0.704454i	$0.248808\pi$
$864$		0			0
$865$	−59.0033			−2.00617
$866$	−1.81979	−	8.50977i	−0.0618391	−	0.289174i
$867$		0			0
$868$	−12.8264	+	33.6622i	−0.435356	+	1.14257i
$869$	−12.9038	+	5.34494i	−0.437732	+	0.181315i
$870$		0			0
$871$	0.580147	−	0.580147i	0.0196575	−	0.0196575i
$872$	5.72706	−	1.39741i	0.193943	−	0.0473221i
$873$		0			0
$874$	24.8497	+	36.0611i	0.840555	+	1.21978i
$875$	−22.5089	−	54.3413i	−0.760940	−	1.83707i
$876$		0			0
$877$	26.4086	+	10.9388i	0.891755	+	0.369377i	0.781044	−	0.624476i	$-0.214687\pi$
$877$	26.4086	+	10.9388i	0.891755	+	0.369377i	0.110710	+	0.993853i	$0.464687\pi$
$878$	−13.2552	−	8.58480i	−0.447343	−	0.289723i
$879$		0			0
$880$	−22.5963	+	1.29618i	−0.761722	+	0.0436941i
$881$		−	11.0118i		−	0.370995i	−0.982645	−	0.185498i	$-0.940610\pi$
$881$		−	11.0118i		−	0.370995i	0.982645	−	0.185498i	$-0.0593897\pi$
$882$		0			0
$883$	32.1953	+	13.3357i	1.08346	+	0.448783i	0.851721	−	0.523996i	$-0.175559\pi$
$883$	32.1953	+	13.3357i	1.08346	+	0.448783i	0.231736	+	0.972779i	$0.425559\pi$
$884$	1.52471	+	53.2046i	0.0512817	+	1.78946i
$885$		0			0
$886$	21.0699	−	14.5193i	0.707859	−	0.487786i
$887$	−15.6911	−	15.6911i	−0.526854	−	0.526854i	0.392779	−	0.919633i	$-0.371514\pi$
$887$	−15.6911	−	15.6911i	−0.526854	−	0.526854i	−0.919633	+	0.392779i	$0.871514\pi$
$888$		0			0
$889$	−1.07197	+	1.07197i	−0.0359528	+	0.0359528i
$890$	−6.06958	+	32.9757i	−0.203453	+	1.10535i
$891$		0			0
$892$	2.55452	−	1.14491i	0.0855316	−	0.0383345i
$893$	−2.33404	+	5.63486i	−0.0781056	+	0.188564i
$894$		0			0
$895$	−13.3315			−0.445624
$896$	17.3424	+	21.0415i	0.579368	+	0.702948i
$897$		0			0
$898$	−16.3094	+	3.48772i	−0.544251	+	0.116387i
$899$	18.8084	−	45.4075i	0.627296	−	1.51443i
$900$		0			0
$901$	41.9864	−	17.3913i	1.39877	−	0.579389i
$902$	0.682138	−	3.70602i	0.0227127	−	0.123397i
$903$		0			0
$904$	−29.8742	−	40.7996i	−0.993601	−	1.35697i
$905$	16.9129	+	16.9129i	0.562204	+	0.562204i
$906$		0			0
$907$	17.8670	+	43.1348i	0.593264	+	1.43227i	0.880333	+	0.474357i	$0.157319\pi$
$907$	17.8670	+	43.1348i	0.593264	+	1.43227i	−0.287068	+	0.957910i	$0.592681\pi$
$908$	−0.376294	−	13.1307i	−0.0124877	−	0.435757i
$909$		0			0
$910$	−38.1472	+	58.9007i	−1.26457	+	1.95254i
$911$		−	57.8948i		−	1.91814i	−0.283168	−	0.959070i	$-0.591385\pi$
$911$		−	57.8948i		−	1.91814i	0.283168	−	0.959070i	$-0.408615\pi$
$912$		0			0
$913$			14.3766i			0.475795i
$914$	−8.01048	−	5.18801i	−0.264963	−	0.171604i
$915$		0			0
$916$	−18.5635	+	19.6589i	−0.613355	+	0.649547i
$917$	1.13688	+	2.74468i	0.0375432	+	0.0906374i
$918$		0			0
$919$	10.8436	+	10.8436i	0.357698	+	0.357698i	0.862964	−	0.505266i	$-0.168606\pi$
$919$	10.8436	+	10.8436i	0.357698	+	0.357698i	−0.505266	+	0.862964i	$0.668606\pi$
$920$	48.0005	−	11.7122i	1.58253	−	0.386138i
$921$		0			0
$922$	10.5310	+	1.93836i	0.346821	+	0.0638366i
$923$	26.8849	−	11.1361i	0.884927	−	0.366549i
$924$		0			0
$925$	−20.2350	+	48.8516i	−0.665322	+	1.60623i
$926$	8.12797	+	38.0082i	0.267102	+	1.24903i
$927$		0			0
$928$	−22.8294	−	29.3745i	−0.749410	−	0.964264i
$929$	42.1538			1.38302			0.691510	−	0.722367i	$-0.256946\pi$
$929$	42.1538			1.38302			0.691510	+	0.722367i	$0.256946\pi$
$930$		0			0
$931$	−3.24147	+	7.82559i	−0.106235	+	0.256473i
$932$	11.4905	+	4.37826i	0.376384	+	0.143415i
$933$		0			0
$934$	−8.09346	−	1.48970i	−0.264826	−	0.0487444i
$935$	20.7423	−	20.7423i	0.678344	−	0.678344i
$936$		0			0
$937$	−41.0343	−	41.0343i	−1.34053	−	1.34053i	−0.895528	−	0.445006i	$-0.853202\pi$
$937$	−41.0343	−	41.0343i	−1.34053	−	1.34053i	−0.445006	−	0.895528i	$-0.646798\pi$
$938$	0.309096	+	0.448550i	0.0100924	+	0.0146457i
$939$		0			0
$940$	5.00306	+	4.72429i	0.163182	+	0.154089i
$941$	37.2060	+	15.4112i	1.21288	+	0.502391i	0.895139	−	0.445786i	$-0.147076\pi$
$941$	37.2060	+	15.4112i	1.21288	+	0.502391i	0.317741	+	0.948178i	$0.397076\pi$
$942$		0			0
$943$			8.22612i			0.267879i
$944$	4.07740	−	11.6975i	0.132708	−	0.380722i
$945$		0			0
$946$	5.73386	−	8.85329i	0.186424	−	0.287845i
$947$	27.6776	+	11.4644i	0.899401	+	0.372544i	0.783990	−	0.620774i	$-0.213181\pi$
$947$	27.6776	+	11.4644i	0.899401	+	0.372544i	0.115411	+	0.993318i	$0.463181\pi$
$948$		0			0
$949$	1.81107	+	4.37231i	0.0587898	+	0.141931i
$950$	−91.7763	+	63.2431i	−2.97762	+	2.05188i
$951$		0			0
$952$	−34.9247	−	5.39898i	−1.13192	−	0.174982i
$953$	35.9881	−	35.9881i	1.16577	−	1.16577i	0.182578	−	0.983191i	$-0.441556\pi$
$953$	35.9881	−	35.9881i	1.16577	−	1.16577i	0.983191	−	0.182578i	$-0.0584443\pi$
$954$		0			0
$955$	77.5363	−	32.1166i	2.50902	−	1.03927i
$956$	−2.32204	−	5.18092i	−0.0751002	−	0.167563i
$957$		0			0
$958$	12.3544	−	2.64196i	0.399153	−	0.0853579i
$959$	−18.4793			−0.596727
$960$		0			0
$961$	24.8505			0.801628
$962$	33.8647	−	7.24188i	1.09184	−	0.233488i
$963$		0			0
$964$	1.04742	+	2.33699i	0.0337351	+	0.0752695i
$965$	92.1958	−	38.1888i	2.96789	−	1.22934i
$966$		0			0
$967$	32.2074	−	32.2074i	1.03572	−	1.03572i	0.0363823	−	0.999338i	$-0.488417\pi$
$967$	32.2074	−	32.2074i	1.03572	−	1.03572i	0.999338	−	0.0363823i	$-0.0115834\pi$
$968$	−3.89311	+	25.1836i	−0.125129	+	0.809432i
$969$		0			0
$970$	45.3492	−	31.2502i	1.45607	−	1.00338i
$971$	21.6824	+	52.3459i	0.695820	+	1.67986i	0.732712	+	0.680539i	$0.238254\pi$
$971$	21.6824	+	52.3459i	0.695820	+	1.67986i	−0.0368916	+	0.999319i	$0.511746\pi$
$972$		0			0
$973$	−25.3050	−	10.4817i	−0.811241	−	0.336027i
$974$	−6.27346	+	9.68644i	−0.201015	+	0.310374i
$975$		0			0
$976$	12.9138	+	26.7337i	0.413361	+	0.855726i
$977$			15.5425i			0.497247i	0.968600	+	0.248624i	$0.0799782\pi$
$977$			15.5425i			0.497247i	−0.968600	+	0.248624i	$0.920022\pi$
$978$		0			0
$979$	−7.70545	−	3.19170i	−0.246267	−	0.102007i
$980$	6.94815	+	6.56101i	0.221950	+	0.209584i
$981$		0			0
$982$	10.4364	+	15.1450i	0.333040	+	0.483296i
$983$	−18.6056	−	18.6056i	−0.593425	−	0.593425i	0.345130	−	0.938555i	$-0.387835\pi$
$983$	−18.6056	−	18.6056i	−0.593425	−	0.593425i	−0.938555	+	0.345130i	$0.887835\pi$
$984$		0			0
$985$	48.6919	−	48.6919i	1.55145	−	1.55145i
$986$	47.4197	+	8.72817i	1.51015	+	0.277962i
$987$		0			0
$988$	68.2122	+	25.9911i	2.17012	+	0.826886i
$989$	−8.81166	+	21.2732i	−0.280194	+	0.676449i
$990$		0			0
$991$	39.3281			1.24930			0.624649	−	0.780906i	$-0.285242\pi$
$991$	39.3281			1.24930			0.624649	+	0.780906i	$0.285242\pi$
$992$	20.9113	−	36.7414i	0.663934	−	1.16654i
$993$		0			0
$994$	4.04037	+	18.8937i	0.128153	+	0.599271i
$995$	−17.4970	+	42.2415i	−0.554692	+	1.33915i
$996$		0			0
$997$	−30.1578	+	12.4918i	−0.955108	+	0.395619i	−0.805148	−	0.593074i	$-0.797914\pi$
$997$	−30.1578	+	12.4918i	−0.955108	+	0.395619i	−0.149959	+	0.988692i	$0.547914\pi$
$998$	−28.7203	−	5.28631i	−0.909125	−	0.167335i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.a.109.3	✓	128
3.2	odd	2	inner	864.2.v.a.109.30	yes	128
32.5	even	8	inner	864.2.v.a.325.3	yes	128
96.5	odd	8	inner	864.2.v.a.325.30	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.a.109.3	✓	128	1.1	even	1	trivial
864.2.v.a.109.30	yes	128	3.2	odd	2	inner
864.2.v.a.325.3	yes	128	32.5	even	8	inner
864.2.v.a.325.30	yes	128	96.5	odd	8	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38295 + 0.295740i) q^{2} +(1.82508 - 0.817983i) q^{4} +(3.70533 - 1.53480i) q^{5} +(1.70420 - 1.70420i) q^{7} +(-2.28207 + 1.67097i) q^{8} +O(q^{10})\)	\(q+(-1.38295 + 0.295740i) q^{2} +(1.82508 - 0.817983i) q^{4} +(3.70533 - 1.53480i) q^{5} +(1.70420 - 1.70420i) q^{7} +(-2.28207 + 1.67097i) q^{8} +(-4.67037 + 3.21836i) q^{10} +(-0.539908 - 1.30345i) q^{11} +(4.74278 + 1.96452i) q^{13} +(-1.85282 + 2.86082i) q^{14} +(2.66181 - 2.98576i) q^{16} +5.18418i q^{17} +(6.56852 + 2.72077i) q^{19} +(5.50707 - 5.83202i) q^{20} +(1.13215 + 1.64293i) q^{22} +(-3.07987 - 3.07987i) q^{23} +(7.83834 - 7.83834i) q^{25} +(-7.14000 - 1.31420i) q^{26} +(1.71629 - 4.50431i) q^{28} +(-2.51674 + 6.07595i) q^{29} -7.47332 q^{31} +(-2.79812 + 4.91635i) q^{32} +(-1.53317 - 7.16943i) q^{34} +(3.69903 - 8.93025i) q^{35} +(-4.40696 + 1.82542i) q^{37} +(-9.88854 - 1.82010i) q^{38} +(-5.89122 + 9.69403i) q^{40} +(-1.33547 - 1.33547i) q^{41} +(-2.02307 - 4.88412i) q^{43} +(-2.05157 - 1.93726i) q^{44} +(5.17013 + 3.34845i) q^{46} +0.857860i q^{47} +1.19138i q^{49} +(-8.52189 + 13.1581i) q^{50} +(10.2629 - 0.294109i) q^{52} +(-3.35470 - 8.09895i) q^{53} +(-4.00107 - 4.00107i) q^{55} +(-1.04143 + 6.73679i) q^{56} +(1.68362 - 9.14701i) q^{58} +(2.86121 - 1.18515i) q^{59} +(-2.84041 + 6.85735i) q^{61} +(10.3352 - 2.21016i) q^{62} +(2.41569 - 7.62656i) q^{64} +20.5887 q^{65} +(0.0611610 - 0.147656i) q^{67} +(4.24057 + 9.46152i) q^{68} +(-2.47453 + 13.4440i) q^{70} +(4.00830 - 4.00830i) q^{71} +(0.651872 + 0.651872i) q^{73} +(5.55474 - 3.82778i) q^{74} +(14.2136 - 0.407327i) q^{76} +(-3.14146 - 1.30124i) q^{77} -9.89973i q^{79} +(5.28033 - 15.1486i) q^{80} +(2.24183 + 1.45193i) q^{82} +(-9.41435 - 3.89955i) q^{83} +(7.95666 + 19.2091i) q^{85} +(4.24222 + 6.15617i) q^{86} +(3.41014 + 2.07240i) q^{88} +(4.18011 - 4.18011i) q^{89} +(11.4306 - 4.73472i) q^{91} +(-8.14028 - 3.10171i) q^{92} +(-0.253703 - 1.18637i) q^{94} +28.5144 q^{95} -9.70998 q^{97} +(-0.352338 - 1.64761i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) \) 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

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