LMFDB - Embedded newform 864.2.v.a.109.5

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			109.5
Character	$\chi$	$=$	864.109
Dual form			864.2.v.a.325.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29834 - 0.560644i) q^{2} +(1.37136 + 1.45581i) q^{4} +(1.49059 - 0.617423i) q^{5} +(-3.02902 + 3.02902i) q^{7} +(-0.964291 - 2.65897i) q^{8} +O(q^{10})$	\(q+(-1.29834 - 0.560644i) q^{2} +(1.37136 + 1.45581i) q^{4} +(1.49059 - 0.617423i) q^{5} +(-3.02902 + 3.02902i) q^{7} +(-0.964291 - 2.65897i) q^{8} +(-2.28144 - 0.0340682i) q^{10} +(0.783887 + 1.89247i) q^{11} +(-2.34011 - 0.969307i) q^{13} +(5.63089 - 2.23448i) q^{14} +(-0.238764 + 3.99287i) q^{16} -0.0122868i q^{17} +(-4.36871 - 1.80958i) q^{19} +(2.94298 + 1.32331i) q^{20} +(0.0432534 - 2.89655i) q^{22} +(-4.89425 - 4.89425i) q^{23} +(-1.69489 + 1.69489i) q^{25} +(2.49482 + 2.57046i) q^{26} +(-8.56354 - 0.255811i) q^{28} +(-0.488562 + 1.17949i) q^{29} -7.33135 q^{31} +(2.54857 - 5.05022i) q^{32} +(-0.00688851 + 0.0159524i) q^{34} +(-2.64484 + 6.38521i) q^{35} +(8.98691 - 3.72250i) q^{37} +(4.65752 + 4.79873i) q^{38} +(-3.07907 - 3.36807i) q^{40} +(-0.293164 - 0.293164i) q^{41} +(0.807094 + 1.94850i) q^{43} +(-1.68009 + 3.73644i) q^{44} +(3.61045 + 9.09831i) q^{46} -10.6583i q^{47} -11.3499i q^{49} +(3.15076 - 1.25030i) q^{50} +(-1.79800 - 4.73603i) q^{52} +(-4.68985 - 11.3223i) q^{53} +(2.33691 + 2.33691i) q^{55} +(10.9749 + 5.13323i) q^{56} +(1.29559 - 1.25747i) q^{58} +(-5.64978 + 2.34021i) q^{59} +(-2.02067 + 4.87832i) q^{61} +(9.51857 + 4.11028i) q^{62} +(-6.14029 + 5.12805i) q^{64} -4.08662 q^{65} +(-3.76193 + 9.08210i) q^{67} +(0.0178872 - 0.0168496i) q^{68} +(7.01372 - 6.80734i) q^{70} +(-6.19966 + 6.19966i) q^{71} +(-0.256907 - 0.256907i) q^{73} +(-13.7550 - 0.205400i) q^{74} +(-3.35665 - 8.84158i) q^{76} +(-8.10674 - 3.35792i) q^{77} +16.9687i q^{79} +(2.10939 + 6.09915i) q^{80} +(0.216265 + 0.544985i) q^{82} +(-0.950366 - 0.393655i) q^{83} +(-0.00758614 - 0.0183146i) q^{85} +(0.0445339 - 2.98230i) q^{86} +(4.27614 - 3.90923i) q^{88} +(-7.66699 + 7.66699i) q^{89} +(10.0243 - 4.15220i) q^{91} +(0.413336 - 13.8368i) q^{92} +(-5.97552 + 13.8381i) q^{94} -7.62923 q^{95} -6.43958 q^{97} +(-6.36326 + 14.7360i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.29834	−	0.560644i	−0.918063	−	0.396435i
$2$	−1.29834	−	0.560644i	−0.918063	−	0.396435i
$3$		0			0
$3$		0			0
$4$	1.37136	+	1.45581i	0.685678	+	0.727905i
$5$	1.49059	−	0.617423i	0.666612	−	0.276120i	−0.0236057	−	0.999721i	$-0.507515\pi$
$5$	1.49059	−	0.617423i	0.666612	−	0.276120i	0.690218	+	0.723602i	$0.257515\pi$
$6$		0			0
$7$	−3.02902	+	3.02902i	−1.14486	+	1.14486i	−0.157312	+	0.987549i	$0.550283\pi$
$7$	−3.02902	+	3.02902i	−1.14486	+	1.14486i	−0.987549	+	0.157312i	$0.949717\pi$
$8$	−0.964291	−	2.65897i	−0.340928	−	0.940089i
$9$		0			0
$10$	−2.28144	−	0.0340682i	−0.721455	−	0.0107733i
$11$	0.783887	+	1.89247i	0.236351	+	0.570601i	0.996900	−	0.0786789i	$-0.0250702\pi$
$11$	0.783887	+	1.89247i	0.236351	+	0.570601i	−0.760549	+	0.649280i	$0.775070\pi$
$12$		0			0
$13$	−2.34011	−	0.969307i	−0.649031	−	0.268837i	0.0337836	−	0.999429i	$-0.489244\pi$
$13$	−2.34011	−	0.969307i	−0.649031	−	0.268837i	−0.682815	+	0.730592i	$0.739244\pi$
$14$	5.63089	−	2.23448i	1.50492	−	0.597191i
$15$		0			0
$16$	−0.238764	+	3.99287i	−0.0596910	+	0.998217i
$17$		−	0.0122868i		−	0.00297998i	−0.999999	−	0.00148999i	$-0.999526\pi$
$17$		−	0.0122868i		−	0.00297998i	0.999999	−	0.00148999i	$-0.000474279\pi$
$18$		0			0
$19$	−4.36871	−	1.80958i	−1.00225	−	0.415146i	−0.179628	−	0.983735i	$-0.557490\pi$
$19$	−4.36871	−	1.80958i	−1.00225	−	0.415146i	−0.822622	+	0.568589i	$0.807490\pi$
$20$	2.94298	+	1.32331i	0.658070	+	0.295901i
$21$		0			0
$22$	0.0432534	−	2.89655i	0.00922165	−	0.617546i
$23$	−4.89425	−	4.89425i	−1.02052	−	1.02052i	−0.999785	−	0.0207358i	$-0.993399\pi$
$23$	−4.89425	−	4.89425i	−1.02052	−	1.02052i	−0.0207358	−	0.999785i	$-0.506601\pi$
$24$		0			0
$25$	−1.69489	+	1.69489i	−0.338977	+	0.338977i
$26$	2.49482	+	2.57046i	0.489274	+	0.504108i
$27$		0			0
$28$	−8.56354	−	0.255811i	−1.61836	−	0.0483438i
$29$	−0.488562	+	1.17949i	−0.0907236	+	0.219026i	−0.962728	−	0.270472i	$-0.912820\pi$
$29$	−0.488562	+	1.17949i	−0.0907236	+	0.219026i	0.872004	+	0.489499i	$0.162820\pi$
$30$		0			0
$31$	−7.33135			−1.31675			−0.658375	−	0.752690i	$-0.728756\pi$
$31$	−7.33135			−1.31675			−0.658375	+	0.752690i	$0.728756\pi$
$32$	2.54857	−	5.05022i	0.450529	−	0.892762i
$33$		0			0
$34$	−0.00688851	+	0.0159524i	−0.00118137	+	0.00273581i
$35$	−2.64484	+	6.38521i	−0.447060	+	1.07930i
$36$		0			0
$37$	8.98691	−	3.72250i	1.47744	−	0.611975i	0.508898	−	0.860827i	$-0.330053\pi$
$37$	8.98691	−	3.72250i	1.47744	−	0.611975i	0.968542	+	0.248852i	$0.0800532\pi$
$38$	4.65752	+	4.79873i	0.755550	+	0.778457i
$39$		0			0
$40$	−3.07907	−	3.36807i	−0.486844	−	0.532538i
$41$	−0.293164	−	0.293164i	−0.0457844	−	0.0457844i	0.683844	−	0.729628i	$-0.260307\pi$
$41$	−0.293164	−	0.293164i	−0.0457844	−	0.0457844i	−0.729628	+	0.683844i	$0.760307\pi$
$42$		0			0
$43$	0.807094	+	1.94850i	0.123081	+	0.297143i	0.973396	−	0.229131i	$-0.0735885\pi$
$43$	0.807094	+	1.94850i	0.123081	+	0.297143i	−0.850315	+	0.526274i	$0.823588\pi$
$44$	−1.68009	+	3.73644i	−0.253283	+	0.563290i
$45$		0			0
$46$	3.61045	+	9.09831i	0.532332	+	1.34147i
$47$		−	10.6583i		−	1.55468i	−0.629084	−	0.777338i	$-0.716570\pi$
$47$		−	10.6583i		−	1.55468i	0.629084	−	0.777338i	$-0.283430\pi$
$48$		0			0
$49$		−	11.3499i		−	1.62141i
$50$	3.15076	−	1.25030i	0.445585	−	0.176820i
$51$		0			0
$52$	−1.79800	−	4.73603i	−0.249338	−	0.656769i
$53$	−4.68985	−	11.3223i	−0.644200	−	1.55524i	−0.820962	−	0.570983i	$-0.806562\pi$
$53$	−4.68985	−	11.3223i	−0.644200	−	1.55524i	0.176761	−	0.984254i	$-0.443438\pi$
$54$		0			0
$55$	2.33691	+	2.33691i	0.315109	+	0.315109i
$56$	10.9749	+	5.13323i	1.46659	+	0.685956i
$57$		0			0
$58$	1.29559	−	1.25747i	0.170120	−	0.165114i
$59$	−5.64978	+	2.34021i	−0.735539	+	0.304670i	−0.718826	−	0.695190i	$-0.755320\pi$
$59$	−5.64978	+	2.34021i	−0.735539	+	0.304670i	−0.0167128	+	0.999860i	$0.505320\pi$
$60$		0			0
$61$	−2.02067	+	4.87832i	−0.258720	+	0.624605i	−0.998854	−	0.0478538i	$-0.984762\pi$
$61$	−2.02067	+	4.87832i	−0.258720	+	0.624605i	0.740134	+	0.672459i	$0.234762\pi$
$62$	9.51857	+	4.11028i	1.20886	+	0.522006i
$63$		0			0
$64$	−6.14029	+	5.12805i	−0.767536	+	0.641006i
$65$	−4.08662			−0.506883
$66$		0			0
$67$	−3.76193	+	9.08210i	−0.459593	+	1.10956i	0.508970	+	0.860784i	$0.330027\pi$
$67$	−3.76193	+	9.08210i	−0.459593	+	1.10956i	−0.968562	+	0.248771i	$0.919973\pi$
$68$	0.0178872	−	0.0168496i	0.00216914	−	0.00204331i
$69$		0			0
$70$	7.01372	−	6.80734i	0.838300	−	0.813633i
$71$	−6.19966	+	6.19966i	−0.735764	+	0.735764i	−0.971755	−	0.235991i	$-0.924166\pi$
$71$	−6.19966	+	6.19966i	−0.735764	+	0.735764i	0.235991	+	0.971755i	$0.424166\pi$
$72$		0			0
$73$	−0.256907	−	0.256907i	−0.0300687	−	0.0300687i	0.691913	−	0.721981i	$-0.256768\pi$
$73$	−0.256907	−	0.256907i	−0.0300687	−	0.0300687i	−0.721981	+	0.691913i	$0.756768\pi$
$74$	−13.7550	−	0.205400i	−1.59899	−	0.0238773i
$75$		0			0
$76$	−3.35665	−	8.84158i	−0.385034	−	1.01420i
$77$	−8.10674	−	3.35792i	−0.923849	−	0.382671i
$78$		0			0
$79$			16.9687i			1.90913i	0.298010	+	0.954563i	$0.403677\pi$
$79$			16.9687i			1.90913i	−0.298010	+	0.954563i	$0.596323\pi$
$80$	2.10939	+	6.09915i	0.235837	+	0.681906i
$81$		0			0
$82$	0.216265	+	0.544985i	0.0238824	+	0.0601836i
$83$	−0.950366	−	0.393655i	−0.104316	−	0.0432092i	0.329915	−	0.944011i	$-0.392980\pi$
$83$	−0.950366	−	0.393655i	−0.104316	−	0.0432092i	−0.434231	+	0.900801i	$0.642980\pi$
$84$		0			0
$85$	−0.00758614	−	0.0183146i	−0.000822833	−	0.00198649i
$86$	0.0445339	−	2.98230i	0.00480222	−	0.321590i
$87$		0			0
$88$	4.27614	−	3.90923i	0.455838	−	0.416725i
$89$	−7.66699	+	7.66699i	−0.812699	+	0.812699i	−0.985038	−	0.172338i	$-0.944868\pi$
$89$	−7.66699	+	7.66699i	−0.812699	+	0.812699i	0.172338	+	0.985038i	$0.444868\pi$
$90$		0			0
$91$	10.0243	−	4.15220i	1.05083	−	0.435269i
$92$	0.413336	−	13.8368i	0.0430933	−	1.44259i
$93$		0			0
$94$	−5.97552	+	13.8381i	−0.616328	+	1.42729i
$95$	−7.62923			−0.782742
$96$		0			0
$97$	−6.43958			−0.653840			−0.326920	−	0.945052i	$-0.606011\pi$
$97$	−6.43958			−0.653840			−0.326920	+	0.945052i	$0.606011\pi$
$98$	−6.36326	+	14.7360i	−0.642786	+	1.48856i
$99$		0			0
$100$	−4.79172	−	0.143139i	−0.479172	−	0.0143139i
$101$	−4.84347	+	2.00623i	−0.481943	+	0.199627i	−0.610409	−	0.792087i	$-0.708995\pi$
$101$	−4.84347	+	2.00623i	−0.481943	+	0.199627i	0.128466	+	0.991714i	$0.458995\pi$
$102$		0			0
$103$	8.16767	−	8.16767i	0.804784	−	0.804784i	−0.179055	−	0.983839i	$-0.557304\pi$
$103$	8.16767	−	8.16767i	0.804784	−	0.804784i	0.983839	+	0.179055i	$0.0573039\pi$
$104$	−0.320812	+	7.15700i	−0.0314582	+	0.701801i
$105$		0			0
$106$	−0.258777	+	17.3295i	−0.0251346	+	1.68319i
$107$	5.04568	+	12.1813i	0.487784	+	1.17762i	0.955832	+	0.293912i	$0.0949574\pi$
$107$	5.04568	+	12.1813i	0.487784	+	1.17762i	−0.468048	+	0.883703i	$0.655043\pi$
$108$		0			0
$109$	−8.02210	−	3.32286i	−0.768378	−	0.318273i	−0.0361628	−	0.999346i	$-0.511513\pi$
$109$	−8.02210	−	3.32286i	−0.768378	−	0.318273i	−0.732215	+	0.681073i	$0.761513\pi$
$110$	−1.72392	−	4.34427i	−0.164369	−	0.414210i
$111$		0			0
$112$	−11.3712	−	12.8177i	−1.07448	−	1.21116i
$113$			4.84320i			0.455610i	0.973707	+	0.227805i	$0.0731549\pi$
$113$			4.84320i			0.455610i	−0.973707	+	0.227805i	$0.926845\pi$
$114$		0			0
$115$	−10.3171	−	4.27350i	−0.962078	−	0.398506i
$116$	−2.38711	+	0.906251i	−0.221637	+	0.0841433i
$117$		0			0
$118$	8.64734	+	0.129129i	0.796052	+	0.0118872i
$119$	0.0372169	+	0.0372169i	0.00341167	+	0.00341167i
$120$		0			0
$121$	4.81121	−	4.81121i	0.437382	−	0.437382i
$122$	5.35851	−	5.20083i	0.485137	−	0.470861i
$123$		0			0
$124$	−10.0539	−	10.6731i	−0.902867	−	0.958469i
$125$	−4.56703	+	11.0258i	−0.408488	+	0.986177i
$126$		0			0
$127$	−10.4541			−0.927656			−0.463828	−	0.885925i	$-0.653524\pi$
$127$	−10.4541			−0.927656			−0.463828	+	0.885925i	$0.653524\pi$
$128$	10.8472	−	3.21542i	0.958763	−	0.284205i
$129$		0			0
$130$	5.30581	+	2.29114i	0.465351	+	0.200946i
$131$	4.27726	−	10.3262i	0.373706	−	0.902206i	−0.619410	−	0.785068i	$-0.712628\pi$
$131$	4.27726	−	10.3262i	0.373706	−	0.902206i	0.993116	−	0.117138i	$-0.0373719\pi$
$132$		0			0
$133$	18.7141	−	7.75165i	1.62272	−	0.672153i
$134$	9.97608	−	9.68252i	0.861802	−	0.836442i
$135$		0			0
$136$	−0.0326702	+	0.0118480i	−0.00280145	+	0.00101596i
$137$	0.0273619	+	0.0273619i	0.00233769	+	0.00233769i	0.708275	−	0.705937i	$-0.249474\pi$
$137$	0.0273619	+	0.0273619i	0.00233769	+	0.00233769i	−0.705937	+	0.708275i	$0.749474\pi$
$138$		0			0
$139$	6.16027	+	14.8722i	0.522507	+	1.26144i	0.936341	+	0.351092i	$0.114189\pi$
$139$	6.16027	+	14.8722i	0.522507	+	1.26144i	−0.413834	+	0.910352i	$0.635811\pi$
$140$	−12.9227	+	4.90601i	−1.09216	+	0.414634i
$141$		0			0
$142$	11.5250	−	4.57344i	0.967161	−	0.383795i
$143$		−	5.18843i		−	0.433878i
$144$		0			0
$145$			2.05979i			0.171056i
$146$	0.189518	+	0.477585i	0.0156846	+	0.0395252i
$147$		0			0
$148$	17.7435	+	7.97836i	1.45851	+	0.655817i
$149$	3.55854	+	8.59108i	0.291527	+	0.703808i	0.999998	−	0.00193144i	$-0.000614797\pi$
$149$	3.55854	+	8.59108i	0.291527	+	0.703808i	−0.708471	+	0.705740i	$0.750615\pi$
$150$		0			0
$151$	6.63546	+	6.63546i	0.539986	+	0.539986i	0.923525	−	0.383539i	$-0.125295\pi$
$151$	6.63546	+	6.63546i	0.539986	+	0.539986i	−0.383539	+	0.923525i	$0.625295\pi$
$152$	−0.598916	+	13.3612i	−0.0485785	+	1.08374i
$153$		0			0
$154$	8.64268	+	8.90471i	0.696447	+	0.717562i
$155$	−10.9280	+	4.52654i	−0.877762	+	0.363581i
$156$		0			0
$157$	1.78115	−	4.30007i	0.142151	−	0.343183i	−0.836729	−	0.547616i	$-0.815535\pi$
$157$	1.78115	−	4.30007i	0.142151	−	0.343183i	0.978880	+	0.204434i	$0.0655353\pi$
$158$	9.51339	−	22.0311i	0.756845	−	1.75270i
$159$		0			0
$160$	0.680756	−	9.10136i	0.0538185	−	0.719526i
$161$	29.6495			2.33671
$162$		0			0
$163$	0.338465	−	0.817126i	0.0265106	−	0.0640022i	−0.910070	−	0.414455i	$-0.863972\pi$
$163$	0.338465	−	0.817126i	0.0265106	−	0.0640022i	0.936580	+	0.350453i	$0.113972\pi$
$164$	0.0247587	−	0.828822i	0.00193333	−	0.0647201i
$165$		0			0
$166$	1.01320	+	1.04391i	0.0786392	+	0.0810234i
$167$	14.4237	−	14.4237i	1.11614	−	1.11614i	0.123835	−	0.992303i	$-0.460481\pi$
$167$	14.4237	−	14.4237i	1.11614	−	1.11614i	0.992303	−	0.123835i	$-0.0395193\pi$
$168$		0			0
$169$	−4.65581	−	4.65581i	−0.358139	−	0.358139i
$170$	−0.000418589		0.0280316i	−3.21043e−5		0.00214993i
$171$		0			0
$172$	−1.72983	+	3.84706i	−0.131898	+	0.293336i
$173$	−16.4485	−	6.81319i	−1.25056	−	0.517997i	−0.343558	−	0.939131i	$-0.611632\pi$
$173$	−16.4485	−	6.81319i	−1.25056	−	0.517997i	−0.906998	+	0.421134i	$0.861632\pi$
$174$		0			0
$175$		−	10.2677i		−	0.776163i
$176$	−7.74355	+	2.67810i	−0.583692	+	0.201870i
$177$		0			0
$178$	14.2528	−	5.65588i	1.06829	−	0.423926i
$179$	−12.1054	−	5.01421i	−0.904798	−	0.374780i	−0.118735	−	0.992926i	$-0.537884\pi$
$179$	−12.1054	−	5.01421i	−0.904798	−	0.374780i	−0.786063	+	0.618146i	$0.787884\pi$
$180$		0			0
$181$	−1.92854	−	4.65590i	−0.143347	−	0.346070i	0.835857	−	0.548947i	$-0.184971\pi$
$181$	−1.92854	−	4.65590i	−0.143347	−	0.346070i	−0.979204	+	0.202876i	$0.934971\pi$
$182$	−15.3428	−	0.229110i	−1.13729	−	0.0169828i
$183$		0			0
$184$	−8.29420	+	17.7331i	−0.611456	+	1.30731i
$185$	11.0974	−	11.0974i	0.815901	−	0.815901i
$186$		0			0
$187$	0.0232524	−	0.00963145i	0.00170038	−	0.000704322i
$188$	15.5165	−	14.6163i	1.13166	−	1.06601i
$189$		0			0
$190$	9.90530	+	4.27728i	0.718606	+	0.310307i
$191$	26.2786			1.90145			0.950726	−	0.310034i	$-0.100340\pi$
$191$	26.2786			1.90145			0.950726	+	0.310034i	$0.100340\pi$
$192$		0			0
$193$	19.9124			1.43333			0.716664	−	0.697419i	$-0.245668\pi$
$193$	19.9124			1.43333			0.716664	+	0.697419i	$0.245668\pi$
$194$	8.36074	+	3.61031i	0.600267	+	0.259205i
$195$		0			0
$196$	16.5233	−	15.5648i	1.18024	−	1.11177i
$197$	−21.2125	+	8.78651i	−1.51133	+	0.626013i	−0.975832	−	0.218524i	$-0.929876\pi$
$197$	−21.2125	+	8.78651i	−1.51133	+	0.626013i	−0.535497	+	0.844537i	$0.679876\pi$
$198$		0			0
$199$	−2.52269	+	2.52269i	−0.178829	+	0.178829i	−0.790845	−	0.612016i	$-0.790359\pi$
$199$	−2.52269	+	2.52269i	−0.178829	+	0.178829i	0.612016	+	0.790845i	$0.290359\pi$
$200$	6.14102	+	2.87229i	0.434236	+	0.203102i
$201$		0			0
$202$	7.41323	+	0.110700i	0.521593	+	0.00778882i
$203$	−2.09284	−	5.05257i	−0.146889	−	0.354621i
$204$		0			0
$205$	−0.617993	−	0.255981i	−0.0431625	−	0.0178785i
$206$	−15.1835	+	6.02523i	−1.05789	+	0.419798i
$207$		0			0
$208$	4.42905	−	9.11233i	0.307099	−	0.631826i
$209$		−	9.68616i		−	0.670005i
$210$		0			0
$211$	5.59080	+	2.31579i	0.384887	+	0.159425i	0.566733	−	0.823902i	$-0.308207\pi$
$211$	5.59080	+	2.31579i	0.384887	+	0.159425i	−0.181846	+	0.983327i	$0.558207\pi$
$212$	10.0517	−	22.3544i	0.690351	−	1.53531i
$213$		0			0
$214$	0.278411	−	18.6443i	0.0190318	−	1.27450i
$215$	2.40609	+	2.40609i	0.164094	+	0.164094i
$216$		0			0
$217$	22.2068	−	22.2068i	1.50750	−	1.50750i
$218$	8.55245	+	8.81174i	0.579245	+	0.596806i
$219$		0			0
$220$	−0.197360	+	6.60683i	−0.0133060	+	0.445432i
$221$	−0.0119097	+	0.0287525i	−0.000801131	+	0.00193410i
$222$		0			0
$223$	−11.6742			−0.781760			−0.390880	−	0.920442i	$-0.627829\pi$
$223$	−11.6742			−0.781760			−0.390880	+	0.920442i	$0.627829\pi$
$224$	7.57755	+	23.0169i	0.506296	+	1.53788i
$225$		0			0
$226$	2.71531	−	6.28811i	0.180620	−	0.418279i
$227$	−10.1668	+	24.5449i	−0.674797	+	1.62910i	0.0985583	+	0.995131i	$0.468577\pi$
$227$	−10.1668	+	24.5449i	−0.674797	+	1.62910i	−0.773355	+	0.633973i	$0.781423\pi$
$228$		0			0
$229$	12.1386	−	5.02796i	0.802139	−	0.332257i	0.0563262	−	0.998412i	$-0.482061\pi$
$229$	12.1386	−	5.02796i	0.802139	−	0.332257i	0.745813	+	0.666156i	$0.232061\pi$
$230$	10.9992	+	11.3327i	0.725266	+	0.747255i
$231$		0			0
$232$	3.60735	+	0.161699i	0.236834	+	0.0106161i
$233$	−1.12226	−	1.12226i	−0.0735217	−	0.0735217i	0.669390	−	0.742911i	$-0.266556\pi$
$233$	−1.12226	−	1.12226i	−0.0735217	−	0.0735217i	−0.742911	+	0.669390i	$0.766556\pi$
$234$		0			0
$235$	−6.58069	−	15.8872i	−0.429277	−	1.03637i
$236$	−11.1548	−	5.01573i	−0.726113	−	0.326497i
$237$		0			0
$238$	−0.0274546	−	0.0691855i	−0.00177962	−	0.00448463i
$239$		−	9.71183i		−	0.628206i	−0.949389	−	0.314103i	$-0.898296\pi$
$239$		−	9.71183i		−	0.628206i	0.949389	−	0.314103i	$-0.101704\pi$
$240$		0			0
$241$			16.7316i			1.07778i	0.842376	+	0.538890i	$0.181156\pi$
$241$			16.7316i			1.07778i	−0.842376	+	0.538890i	$0.818844\pi$
$242$	−8.94394	+	3.54919i	−0.574938	+	0.228151i
$243$		0			0
$244$	−9.87296	+	3.74821i	−0.632052	+	0.239955i
$245$	−7.00769	−	16.9181i	−0.447705	−	1.08086i
$246$		0			0
$247$	8.46924	+	8.46924i	0.538885	+	0.538885i
$248$	7.06956	+	19.4939i	0.448917	+	1.23786i
$249$		0			0
$250$	12.1111	−	11.7547i	0.765973	−	0.743433i
$251$	20.9306	−	8.66974i	1.32113	−	0.547229i	0.393017	−	0.919531i	$-0.371432\pi$
$251$	20.9306	−	8.66974i	1.32113	−	0.547229i	0.928112	+	0.372302i	$0.121432\pi$
$252$		0			0
$253$	5.42568	−	13.0988i	0.341110	−	0.823512i
$254$	13.5730	+	5.86106i	0.851646	+	0.367755i
$255$		0			0
$256$	−15.8860	−	1.90671i	−0.992874	−	0.119169i
$257$	21.1681			1.32043			0.660216	−	0.751076i	$-0.270465\pi$
$257$	21.1681			1.32043			0.660216	+	0.751076i	$0.270465\pi$
$258$		0			0
$259$	−15.9460	+	38.4970i	−0.990836	+	2.39209i
$260$	−5.60422	−	5.94935i	−0.347559	−	0.368963i
$261$		0			0
$262$	−11.3427	+	11.0089i	−0.700751	+	0.680131i
$263$	0.424755	−	0.424755i	0.0261915	−	0.0261915i	−0.693890	−	0.720081i	$-0.744105\pi$
$263$	0.424755	−	0.424755i	0.0261915	−	0.0261915i	0.720081	+	0.693890i	$0.244105\pi$
$264$		0			0
$265$	−13.9813	−	13.9813i	−0.858864	−	0.858864i
$266$	−28.6432	−	0.427721i	−1.75623	−	0.0262253i
$267$		0			0
$268$	−18.3808	+	6.97814i	−1.12278	+	0.426258i
$269$	6.87535	+	2.84786i	0.419198	+	0.173637i	0.582304	−	0.812971i	$-0.302151\pi$
$269$	6.87535	+	2.84786i	0.419198	+	0.173637i	−0.163106	+	0.986608i	$0.552151\pi$
$270$		0			0
$271$			1.04359i			0.0633937i	0.999498	+	0.0316969i	$0.0100911\pi$
$271$			1.04359i			0.0633937i	−0.999498	+	0.0316969i	$0.989909\pi$
$272$	0.0490595	+	0.00293364i	0.00297467	+	0.000177878i
$273$		0			0
$274$	−0.0201847	−	0.0508653i	−0.00121940	−	0.00307288i
$275$	−4.53612	−	1.87892i	−0.273538	−	0.113303i
$276$		0			0
$277$	−0.702477	−	1.69593i	−0.0422077	−	0.101898i	0.901370	−	0.433050i	$-0.142563\pi$
$277$	−0.702477	−	1.69593i	−0.0422077	−	0.101898i	−0.943577	+	0.331152i	$0.892563\pi$
$278$	0.339912	−	22.7629i	0.0203866	−	1.36523i
$279$		0			0
$280$	19.5285	+	0.875363i	1.16705	+	0.0523129i
$281$	21.1976	−	21.1976i	1.26454	−	1.26454i	0.315676	−	0.948867i	$-0.397769\pi$
$281$	21.1976	−	21.1976i	1.26454	−	1.26454i	0.948867	−	0.315676i	$-0.102231\pi$
$282$		0			0
$283$	−21.6319	+	8.96024i	−1.28588	+	0.532631i	−0.917756	−	0.397144i	$-0.870001\pi$
$283$	−21.6319	+	8.96024i	−1.28588	+	0.532631i	−0.368128	+	0.929775i	$0.620001\pi$
$284$	−17.5275	−	0.523583i	−1.04006	−	0.0310689i
$285$		0			0
$286$	−2.90886	+	6.73632i	−0.172005	+	0.398327i
$287$	1.77600			0.104834
$288$		0			0
$289$	16.9998			0.999991
$290$	1.15481	−	2.67430i	0.0678127	−	0.157040i
$291$		0			0
$292$	0.0216967	−	0.726318i	0.00126970	−	0.0425046i
$293$	−8.06247	+	3.33958i	−0.471015	+	0.195101i	−0.605549	−	0.795808i	$-0.707046\pi$
$293$	−8.06247	+	3.33958i	−0.471015	+	0.195101i	0.134534	+	0.990909i	$0.457046\pi$
$294$		0			0
$295$	−6.97660	+	6.97660i	−0.406194	+	0.406194i
$296$	−18.5640	−	20.3064i	−1.07901	−	1.18029i
$297$		0			0
$298$	0.196353	−	13.1492i	0.0113744	−	0.761712i
$299$	6.70907	+	16.1971i	0.387995	+	0.936704i
$300$		0			0
$301$	−8.34674	−	3.45733i	−0.481098	−	0.199277i
$302$	−4.89493	−	12.3352i	−0.281672	−	0.709811i
$303$		0			0
$304$	8.26849	−	17.0116i	0.474231	−	0.975683i
$305$			8.51919i			0.487807i
$306$		0			0
$307$	6.75688	+	2.79879i	0.385635	+	0.159735i	0.567074	−	0.823667i	$-0.308075\pi$
$307$	6.75688	+	2.79879i	0.385635	+	0.159735i	−0.181439	+	0.983402i	$0.558075\pi$
$308$	−6.22873	−	16.4068i	−0.354915	−	0.934863i
$309$		0			0
$310$	16.7261	+	0.249766i	0.949977	+	0.0141858i
$311$	−18.0585	−	18.0585i	−1.02400	−	1.02400i	−0.999705	−	0.0243000i	$-0.992264\pi$
$311$	−18.0585	−	18.0585i	−1.02400	−	1.02400i	−0.0243000	−	0.999705i	$-0.507736\pi$
$312$		0			0
$313$	9.87000	−	9.87000i	0.557885	−	0.557885i	−0.370819	−	0.928705i	$-0.620923\pi$
$313$	9.87000	−	9.87000i	0.557885	−	0.557885i	0.928705	+	0.370819i	$0.120923\pi$
$314$	−4.72333	+	4.58434i	−0.266553	+	0.258710i
$315$		0			0
$316$	−24.7032	+	23.2701i	−1.38966	+	1.30905i
$317$	−4.41727	+	10.6642i	−0.248099	+	0.598964i	−0.998043	−	0.0625381i	$-0.980081\pi$
$317$	−4.41727	+	10.6642i	−0.248099	+	0.598964i	0.749944	+	0.661502i	$0.230081\pi$
$318$		0			0
$319$	−2.61513			−0.146419
$320$	−5.98648	+	11.4350i	−0.334654	+	0.639234i
$321$		0			0
$322$	−38.4951	−	16.6228i	−2.14525	−	0.926354i
$323$	−0.0222339	+	0.0536774i	−0.00123713	+	0.00298669i
$324$		0			0
$325$	5.60909	−	2.32336i	0.311136	−	0.128877i
$326$	−0.897558	+	0.871146i	−0.0497111	+	0.0482483i
$327$		0			0
$328$	−0.496819	+	1.06221i	−0.0274323	+	0.0586507i
$329$	32.2842	+	32.2842i	1.77989	+	1.77989i
$330$		0			0
$331$	−7.92492	−	19.1324i	−0.435593	−	1.05161i	−0.977454	−	0.211146i	$-0.932280\pi$
$331$	−7.92492	−	19.1324i	−0.435593	−	1.05161i	0.541862	−	0.840468i	$-0.317720\pi$
$332$	−0.730204	−	1.92339i	−0.0400752	−	0.105560i
$333$		0			0
$334$	−26.8133	+	10.6402i	−1.46716	+	0.582208i
$335$			15.8604i			0.866546i
$336$		0			0
$337$			27.7111i			1.50952i	0.656000	+	0.754761i	$0.272247\pi$
$337$			27.7111i			1.50952i	−0.656000	+	0.754761i	$0.727753\pi$
$338$	3.43456	+	8.65506i	0.186815	+	0.470773i
$339$		0			0
$340$	0.0162592	−	0.0361598i	0.000881780	−	0.00196104i
$341$	−5.74695	−	13.8744i	−0.311215	−	0.751340i
$342$		0			0
$343$	13.1759	+	13.1759i	0.711434	+	0.711434i
$344$	4.40273	−	4.02496i	0.237379	−	0.217011i
$345$		0			0
$346$	17.5359	+	18.0676i	0.942737	+	0.971319i
$347$	−10.7311	+	4.44498i	−0.576077	+	0.238619i	−0.651648	−	0.758521i	$-0.725922\pi$
$347$	−10.7311	+	4.44498i	−0.576077	+	0.238619i	0.0755707	+	0.997140i	$0.475922\pi$
$348$		0			0
$349$	−4.27551	+	10.3220i	−0.228863	+	0.552524i	−0.996039	−	0.0889122i	$-0.971661\pi$
$349$	−4.27551	+	10.3220i	−0.228863	+	0.552524i	0.767177	+	0.641436i	$0.221661\pi$
$350$	−5.75651	+	13.3309i	−0.307699	+	0.712567i
$351$		0			0
$352$	11.5552	+	0.864296i	0.615894	+	0.0460672i
$353$	−2.71287			−0.144391			−0.0721957	−	0.997390i	$-0.523001\pi$
$353$	−2.71287			−0.144391			−0.0721957	+	0.997390i	$0.523001\pi$
$354$		0			0
$355$	−5.41334	+	13.0690i	−0.287310	+	0.693629i
$356$	−21.6759	−	0.647504i	−1.14882	−	0.0343177i
$357$		0			0
$358$	12.9057	+	13.2969i	0.682085	+	0.702765i
$359$	10.6633	−	10.6633i	0.562787	−	0.562787i	−0.367311	−	0.930098i	$-0.619722\pi$
$359$	10.6633	−	10.6633i	0.562787	−	0.562787i	0.930098	+	0.367311i	$0.119722\pi$
$360$		0			0
$361$	2.37600	+	2.37600i	0.125053	+	0.125053i
$362$	−0.106413	+	7.12615i	−0.00559294	+	0.374542i
$363$		0			0
$364$	19.7917	+	8.89932i	1.03737	+	0.466451i
$365$	−0.541563	−	0.224323i	−0.0283467	−	0.0117416i
$366$		0			0
$367$		−	29.3315i		−	1.53109i	−0.643380	−	0.765547i	$-0.722469\pi$
$367$		−	29.3315i		−	1.53109i	0.643380	−	0.765547i	$-0.277531\pi$
$368$	20.7106	−	18.3735i	1.07962	−	0.957785i
$369$		0			0
$370$	−20.6299	+	8.18650i	−1.07250	+	0.425596i
$371$	48.5011	+	20.0898i	2.51805	+	1.04301i
$372$		0			0
$373$	9.86170	+	23.8082i	0.510619	+	1.23274i	0.943524	+	0.331304i	$0.107489\pi$
$373$	9.86170	+	23.8082i	0.510619	+	1.23274i	−0.432904	+	0.901440i	$0.642511\pi$
$374$	−0.0355892		0.000531445i	−0.00184028		2.74804e-5i
$375$		0			0
$376$	−28.3402	+	10.2777i	−1.46153	+	0.530033i
$377$	2.28658	−	2.28658i	0.117765	−	0.117765i
$378$		0			0
$379$	30.4953	−	12.6316i	1.56644	−	0.648840i	0.580246	−	0.814441i	$-0.302956\pi$
$379$	30.4953	−	12.6316i	1.56644	−	0.648840i	0.986193	+	0.165601i	$0.0529563\pi$
$380$	−10.4624	−	11.1067i	−0.536709	−	0.569762i
$381$		0			0
$382$	−34.1184	−	14.7329i	−1.74565	−	0.753802i
$383$	0.534607			0.0273172			0.0136586	−	0.999907i	$-0.495652\pi$
$383$	0.534607			0.0273172			0.0136586	+	0.999907i	$0.495652\pi$
$384$		0			0
$385$	−14.1571			−0.721512
$386$	−25.8530	−	11.1638i	−1.31588	−	0.568222i
$387$		0			0
$388$	−8.83096	−	9.37481i	−0.448324	−	0.475934i
$389$	22.1347	−	9.16850i	1.12227	−	0.464861i	0.257127	−	0.966378i	$-0.417224\pi$
$389$	22.1347	−	9.16850i	1.12227	−	0.464861i	0.865148	+	0.501516i	$0.167224\pi$
$390$		0			0
$391$	−0.0601346	+	0.0601346i	−0.00304113	+	0.00304113i
$392$	−30.1791	+	10.9446i	−1.52427	+	0.552786i
$393$		0			0
$394$	32.4671	+	0.484823i	1.63567	+	0.0244250i
$395$	10.4768	+	25.2933i	0.527147	+	1.27265i
$396$		0			0
$397$	−32.3523	−	13.4008i	−1.62371	−	0.672565i	−0.629208	−	0.777237i	$-0.716621\pi$
$397$	−32.3523	−	13.4008i	−1.62371	−	0.672565i	−0.994507	+	0.104673i	$0.966621\pi$
$398$	4.68964	−	1.86097i	0.235070	−	0.0932821i
$399$		0			0
$400$	−6.36277	−	7.17213i	−0.318139	−	0.358607i
$401$			30.5352i			1.52485i	0.647075	+	0.762426i	$0.275992\pi$
$401$			30.5352i			1.52485i	−0.647075	+	0.762426i	$0.724008\pi$
$402$		0			0
$403$	17.1562	+	7.10633i	0.854611	+	0.353992i
$404$	−9.56281	−	4.29991i	−0.475767	−	0.213929i
$405$		0			0
$406$	−0.115479	+	7.73327i	−0.00573112	+	0.383796i
$407$	14.0895	+	14.0895i	0.698388	+	0.698388i
$408$		0			0
$409$	−8.90088	+	8.90088i	−0.440120	+	0.440120i	−0.892052	−	0.451932i	$-0.850735\pi$
$409$	−8.90088	+	8.90088i	−0.440120	+	0.440120i	0.451932	+	0.892052i	$0.350735\pi$
$410$	0.658848	+	0.678823i	0.0325382	+	0.0335247i
$411$		0			0
$412$	23.0914	+	0.689788i	1.13763	+	0.0339834i
$413$	10.0247	−	24.2018i	0.493285	−	1.19089i
$414$		0			0
$415$	−1.65966			−0.0814694
$416$	−10.8592	+	9.34775i	−0.532415	+	0.458311i
$417$		0			0
$418$	−5.43049	+	12.5759i	−0.265614	+	0.615107i
$419$	−12.0294	+	29.0416i	−0.587676	+	1.41878i	0.298043	+	0.954553i	$0.403666\pi$
$419$	−12.0294	+	29.0416i	−0.587676	+	1.41878i	−0.885719	+	0.464223i	$0.846334\pi$
$420$		0			0
$421$	−28.6809	+	11.8800i	−1.39782	+	0.578996i	−0.949185	−	0.314720i	$-0.898089\pi$
$421$	−28.6809	+	11.8800i	−1.39782	+	0.578996i	−0.448634	+	0.893715i	$0.648089\pi$
$422$	−5.96041	−	6.14112i	−0.290148	−	0.298945i
$423$		0			0
$424$	−25.5833	+	23.3882i	−1.24244	+	1.13583i
$425$	0.0208247	+	0.0208247i	0.00101015	+	0.00101015i
$426$		0			0
$427$	−8.65589	−	20.8972i	−0.418888	−	1.01128i
$428$	−10.8143	+	24.0505i	−0.522729	+	1.16253i
$429$		0			0
$430$	−1.77496	−	4.47288i	−0.0855961	−	0.215702i
$431$		−	28.8965i		−	1.39190i	−0.718092	−	0.695948i	$-0.754984\pi$
$431$		−	28.8965i		−	1.39190i	0.718092	−	0.695948i	$-0.245016\pi$
$432$		0			0
$433$			27.0871i			1.30172i	0.759197	+	0.650861i	$0.225592\pi$
$433$			27.0871i			1.30172i	−0.759197	+	0.650861i	$0.774408\pi$
$434$	−41.2820	+	16.3818i	−1.98160	+	0.786351i
$435$		0			0
$436$	−6.16370	−	16.2355i	−0.295188	−	0.777539i
$437$	12.5250	+	30.2380i	0.599152	+	1.44648i
$438$		0			0
$439$	1.24520	+	1.24520i	0.0594304	+	0.0594304i	0.736197	−	0.676767i	$-0.236620\pi$
$439$	1.24520	+	1.24520i	0.0594304	+	0.0594304i	−0.676767	+	0.736197i	$0.736620\pi$
$440$	3.96032	−	8.46724i	0.188801	−	0.403660i
$441$		0			0
$442$	0.0315827	−	0.0306533i	0.00150223	−	0.00145803i
$443$	−18.5275	+	7.67436i	−0.880270	+	0.364620i	−0.776601	−	0.629992i	$-0.783058\pi$
$443$	−18.5275	+	7.67436i	−0.880270	+	0.364620i	−0.103668	+	0.994612i	$0.533058\pi$
$444$		0			0
$445$	−6.69457	+	16.1621i	−0.317353	+	0.766158i
$446$	15.1570	+	6.54505i	0.717704	+	0.309917i
$447$		0			0
$448$	3.06609	−	34.1320i	0.144859	−	1.61259i
$449$	5.62045			0.265245			0.132623	−	0.991167i	$-0.457660\pi$
$449$	5.62045			0.265245			0.132623	+	0.991167i	$0.457660\pi$
$450$		0			0
$451$	0.324996	−	0.784611i	0.0153035	−	0.0369459i
$452$	−7.05078	+	6.64176i	−0.331641	+	0.312402i
$453$		0			0
$454$	26.9610	−	26.1676i	1.26534	−	1.22811i
$455$	12.3785	−	12.3785i	0.580311	−	0.580311i
$456$		0			0
$457$	−10.0331	−	10.0331i	−0.469329	−	0.469329i	0.432368	−	0.901697i	$-0.357678\pi$
$457$	−10.0331	−	10.0331i	−0.469329	−	0.469329i	−0.901697	+	0.432368i	$0.857678\pi$
$458$	−18.5788	−	0.277433i	−0.868132	−	0.0129636i
$459$		0			0
$460$	−7.92707	−	20.8803i	−0.369601	−	0.973548i
$461$	−8.07495	−	3.34475i	−0.376088	−	0.155781i	0.186629	−	0.982430i	$-0.440244\pi$
$461$	−8.07495	−	3.34475i	−0.376088	−	0.155781i	−0.562717	+	0.826650i	$0.690244\pi$
$462$		0			0
$463$		−	36.7220i		−	1.70662i	−0.521406	−	0.853309i	$-0.674592\pi$
$463$		−	36.7220i		−	1.70662i	0.521406	−	0.853309i	$-0.325408\pi$
$464$	−4.59290	−	2.23238i	−0.213220	−	0.103636i
$465$		0			0
$466$	0.827883	+	2.08626i	0.0383509	+	0.0966441i
$467$	−23.1570	−	9.59193i	−1.07158	−	0.443862i	−0.224030	−	0.974582i	$-0.571921\pi$
$467$	−23.1570	−	9.59193i	−1.07158	−	0.443862i	−0.847547	+	0.530721i	$0.821921\pi$
$468$		0			0
$469$	−16.1149	−	38.9048i	−0.744117	−	1.79646i
$470$	−0.363110	+	24.3163i	−0.0167490	+	1.12163i
$471$		0			0
$472$	11.6706	+	12.7660i	0.537183	+	0.587601i
$473$	−3.05481	+	3.05481i	−0.140460	+	0.140460i
$474$		0			0
$475$	10.4715	−	4.33743i	0.480465	−	0.199015i
$476$	−0.00314310	+	0.105218i	−0.000144064	+	0.00482268i
$477$		0			0
$478$	−5.44488	+	12.6092i	−0.249043	+	0.576732i
$479$	−30.6819			−1.40189			−0.700945	−	0.713215i	$-0.747238\pi$
$479$	−30.6819			−1.40189			−0.700945	+	0.713215i	$0.747238\pi$
$480$		0			0
$481$	−24.6386			−1.12343
$482$	9.38050	−	21.7233i	0.427270	−	0.989469i
$483$		0			0
$484$	13.6021	+	0.406323i	0.618276	+	0.0184692i
$485$	−9.59878	+	3.97594i	−0.435858	+	0.180538i
$486$		0			0
$487$	−22.0916	+	22.0916i	−1.00107	+	1.00107i	−0.00106586	+	0.999999i	$0.500339\pi$
$487$	−22.0916	+	22.0916i	−1.00107	+	1.00107i	−0.999999	+	0.00106586i	$0.999661\pi$
$488$	14.9198	+	0.668780i	0.675390	+	0.0302743i
$489$		0			0
$490$	−0.386671	+	25.8942i	−0.0174680	+	1.16978i
$491$	−5.40731	−	13.0544i	−0.244029	−	0.589137i	0.753647	−	0.657279i	$-0.228293\pi$
$491$	−5.40731	−	13.0544i	−0.244029	−	0.589137i	−0.997676	+	0.0681423i	$0.978293\pi$
$492$		0			0
$493$	0.0144922	+	0.00600285i	0.000652694	+	0.000270355i
$494$	−6.24769	−	15.7441i	−0.281097	−	0.708363i
$495$		0			0
$496$	1.75046	−	29.2731i	0.0785982	−	1.31440i
$497$		−	37.5578i		−	1.68470i
$498$		0			0
$499$	−10.1263	−	4.19445i	−0.453316	−	0.187770i	0.144330	−	0.989530i	$-0.453897\pi$
$499$	−10.1263	−	4.19445i	−0.453316	−	0.187770i	−0.597646	+	0.801760i	$0.703897\pi$
$500$	−22.3145	+	8.47156i	−0.997934	+	0.378860i
$501$		0			0
$502$	−32.0356	−	0.478380i	−1.42982	−	0.0213511i
$503$	−6.84191	−	6.84191i	−0.305066	−	0.305066i	0.537926	−	0.842992i	$-0.319208\pi$
$503$	−6.84191	−	6.84191i	−0.305066	−	0.305066i	−0.842992	+	0.537926i	$0.819208\pi$
$504$		0			0
$505$	−5.98093	+	5.98093i	−0.266148	+	0.266148i
$506$	−14.3881	+	13.9647i	−0.639629	+	0.620807i
$507$		0			0
$508$	−14.3364	−	15.2193i	−0.636073	−	0.675245i
$509$	3.85781	−	9.31357i	0.170994	−	0.412817i	−0.815030	−	0.579419i	$-0.803280\pi$
$509$	3.85781	−	9.31357i	0.170994	−	0.412817i	0.986024	+	0.166602i	$0.0532795\pi$
$510$		0			0
$511$	1.55635			0.0688489
$512$	19.5564	+	11.3819i	0.864278	+	0.503015i
$513$		0			0
$514$	−27.4834	−	11.8678i	−1.21224	−	0.523466i
$515$	7.13174	−	17.2176i	0.314262	−	0.758696i
$516$		0			0
$517$	20.1706	−	8.35492i	0.887100	−	0.367449i
$518$	42.2864	−	41.0421i	1.85796	−	1.80329i
$519$		0			0
$520$	3.94069	+	10.8662i	0.172811	+	0.476516i
$521$	−1.36138	−	1.36138i	−0.0596431	−	0.0596431i	0.676656	−	0.736299i	$-0.263428\pi$
$521$	−1.36138	−	1.36138i	−0.0596431	−	0.0596431i	−0.736299	+	0.676656i	$0.763428\pi$
$522$		0			0
$523$	−8.74729	−	21.1178i	−0.382492	−	0.923418i	−0.991482	−	0.130240i	$-0.958425\pi$
$523$	−8.74729	−	21.1178i	−0.382492	−	0.923418i	0.608990	−	0.793178i	$-0.291575\pi$
$524$	20.8986	−	7.93404i	0.912962	−	0.346600i
$525$		0			0
$526$	−0.789611	+	0.313338i	−0.0344287	+	0.0136622i
$527$			0.0900788i			0.00392389i
$528$		0			0
$529$			24.9073i			1.08293i
$530$	10.3139	+	25.9909i	0.448007	+	1.12897i
$531$		0			0
$532$	36.9487	+	16.6140i	1.60193	+	0.720306i
$533$	0.401871	+	0.970202i	0.0174069	+	0.0420241i
$534$		0			0
$535$	15.0421	+	15.0421i	0.650326	+	0.650326i
$536$	27.7767	+	1.24509i	1.19977	+	0.0537795i
$537$		0			0
$538$	−7.32988	−	7.55211i	−0.316014	−	0.325595i
$539$	21.4794	−	8.89704i	0.925182	−	0.383223i
$540$		0			0
$541$	−10.1239	+	24.4413i	−0.435261	+	1.05081i	0.542305	+	0.840182i	$0.317552\pi$
$541$	−10.1239	+	24.4413i	−0.435261	+	1.05081i	−0.977566	+	0.210630i	$0.932448\pi$
$542$	0.585084	−	1.35493i	0.0251315	−	0.0581994i
$543$		0			0
$544$	−0.0620510	−	0.0313138i	−0.00266042	−	0.00134257i
$545$	−14.0093			−0.600092
$546$		0			0
$547$	−8.67168	+	20.9353i	−0.370774	+	0.895128i	0.622845	+	0.782345i	$0.285977\pi$
$547$	−8.67168	+	20.9353i	−0.370774	+	0.895128i	−0.993620	+	0.112783i	$0.964023\pi$
$548$	−0.00231081	+	0.0773567i	−9.87129e−5	+	0.00330451i
$549$		0			0
$550$	4.83600	+	4.98262i	0.206208	+	0.212460i
$551$	4.26876	−	4.26876i	0.181855	−	0.181855i
$552$		0			0
$553$	−51.3984	−	51.3984i	−2.18568	−	2.18568i
$554$	−0.0387613	+	2.59573i	−0.00164681	+	0.110282i
$555$		0			0
$556$	−13.2032	+	29.3633i	−0.559940	+	1.24528i
$557$	1.53435	+	0.635548i	0.0650124	+	0.0269290i	0.414953	−	0.909843i	$-0.363798\pi$
$557$	1.53435	+	0.635548i	0.0650124	+	0.0269290i	−0.349940	+	0.936772i	$0.613798\pi$
$558$		0			0
$559$		−	5.34203i		−	0.225944i
$560$	−24.8638	−	12.0851i	−1.05069	−	0.510687i
$561$		0			0
$562$	−39.4059	+	15.6373i	−1.66224	+	0.659620i
$563$	22.2053	+	9.19776i	0.935844	+	0.387639i	0.797892	−	0.602800i	$-0.205948\pi$
$563$	22.2053	+	9.19776i	0.935844	+	0.387639i	0.137951	+	0.990439i	$0.455948\pi$
$564$		0			0
$565$	2.99030	+	7.21923i	0.125803	+	0.303715i
$566$	33.1090	+	0.494409i	1.39168	+	0.0207815i
$567$		0			0
$568$	22.4630	+	10.5065i	0.942527	+	0.440841i
$569$	−32.4716	+	32.4716i	−1.36128	+	1.36128i	−0.488988	+	0.872291i	$0.662634\pi$
$569$	−32.4716	+	32.4716i	−1.36128	+	1.36128i	−0.872291	+	0.488988i	$0.837366\pi$
$570$		0			0
$571$	13.7402	−	5.69137i	0.575008	−	0.238176i	−0.0761778	−	0.997094i	$-0.524272\pi$
$571$	13.7402	−	5.69137i	0.575008	−	0.238176i	0.651186	+	0.758918i	$0.274272\pi$
$572$	7.55336	−	7.11518i	0.315822	−	0.297501i
$573$		0			0
$574$	−2.30584	−	0.995701i	−0.0962439	−	0.0415598i
$575$	16.5904			0.691866
$576$		0			0
$577$	29.7504			1.23853			0.619263	−	0.785184i	$-0.287432\pi$
$577$	29.7504			1.23853			0.619263	+	0.785184i	$0.287432\pi$
$578$	−22.0715	−	9.53087i	−0.918055	−	0.396432i
$579$		0			0
$580$	−2.99866	+	2.82470i	−0.124513	+	0.117289i
$581$	4.07106	−	1.68629i	0.168896	−	0.0699591i
$582$		0			0
$583$	17.7508	−	17.7508i	0.735163	−	0.735163i
$584$	−0.435376	+	0.930842i	−0.0180160	+	0.0385185i
$585$		0			0
$586$	12.3401	+	0.184272i	0.509766	+	0.00761220i
$587$	−0.708534	−	1.71055i	−0.0292443	−	0.0706021i	0.908583	−	0.417705i	$-0.137165\pi$
$587$	−0.708534	−	1.71055i	−0.0292443	−	0.0706021i	−0.937827	+	0.347103i	$0.887165\pi$
$588$		0			0
$589$	32.0285	+	13.2667i	1.31971	+	0.546643i
$590$	12.9694	−	5.14659i	0.533941	−	0.211882i
$591$		0			0
$592$	12.7177	+	36.7723i	0.522694	+	1.51133i
$593$		−	2.64654i		−	0.108680i	−0.998522	−	0.0543401i	$-0.982694\pi$
$593$		−	2.64654i		−	0.108680i	0.998522	−	0.0543401i	$-0.0173055\pi$
$594$		0			0
$595$	0.0784537	+	0.0324966i	0.00321629	+	0.00133223i
$596$	−7.62695	+	16.9620i	−0.312412	+	0.694790i
$597$		0			0
$598$	0.370193	−	24.7907i	0.0151383	−	1.01377i
$599$	−9.56784	−	9.56784i	−0.390931	−	0.390931i	0.484088	−	0.875019i	$-0.339151\pi$
$599$	−9.56784	−	9.56784i	−0.390931	−	0.390931i	−0.875019	+	0.484088i	$0.839151\pi$
$600$		0			0
$601$	0.0361940	−	0.0361940i	0.00147639	−	0.00147639i	−0.706368	−	0.707845i	$-0.749668\pi$
$601$	0.0361940	−	0.0361940i	0.00147639	−	0.00147639i	0.707845	+	0.706368i	$0.249668\pi$
$602$	8.89855	+	9.16833i	0.362678	+	0.373673i
$603$		0			0
$604$	−0.560388	+	18.7595i	−0.0228019	+	0.763315i
$605$	4.20099	−	10.1421i	0.170795	−	0.412334i
$606$		0			0
$607$	−1.23893			−0.0502868			−0.0251434	−	0.999684i	$-0.508004\pi$
$607$	−1.23893			−0.0502868			−0.0251434	+	0.999684i	$0.508004\pi$
$608$	−20.2727	+	17.4511i	−0.822168	+	0.707736i
$609$		0			0
$610$	4.77623	−	11.0608i	0.193384	−	0.447838i
$611$	−10.3312	+	24.9417i	−0.417955	+	1.00903i
$612$		0			0
$613$	−19.4410	+	8.05272i	−0.785214	+	0.325246i	−0.739018	−	0.673686i	$-0.764710\pi$
$613$	−19.4410	+	8.05272i	−0.785214	+	0.325246i	−0.0461965	+	0.998932i	$0.514710\pi$
$614$	−7.20357	−	7.42197i	−0.290713	−	0.299527i
$615$		0			0
$616$	−1.11137	+	24.7936i	−0.0447784	+	0.998963i
$617$	−6.76482	−	6.76482i	−0.272341	−	0.272341i	0.557701	−	0.830042i	$-0.311684\pi$
$617$	−6.76482	−	6.76482i	−0.272341	−	0.272341i	−0.830042	+	0.557701i	$0.811684\pi$
$618$		0			0
$619$	3.68250	+	8.89034i	0.148012	+	0.357333i	0.980445	−	0.196793i	$-0.0630526\pi$
$619$	3.68250	+	8.89034i	0.148012	+	0.357333i	−0.832433	+	0.554126i	$0.813053\pi$
$620$	−21.5760	−	9.70165i	−0.866514	−	0.389628i
$621$		0			0
$622$	13.3216	+	33.5704i	0.534149	+	1.34605i
$623$		−	46.4469i		−	1.86086i
$624$		0			0
$625$			7.27008i			0.290803i
$626$	−18.3481	+	7.28103i	−0.733339	+	0.291008i
$627$		0			0
$628$	8.70266	−	3.30391i	0.347274	−	0.131840i
$629$	−0.0457376	−	0.110420i	−0.00182368	−	0.00440274i
$630$		0			0
$631$	16.5654	+	16.5654i	0.659458	+	0.659458i	0.955252	−	0.295794i	$-0.0955841\pi$
$631$	16.5654	+	16.5654i	0.659458	+	0.659458i	−0.295794	+	0.955252i	$0.595584\pi$
$632$	45.1193	−	16.3627i	1.79475	−	0.650875i
$633$		0			0
$634$	11.7140	−	11.3693i	0.465221	−	0.451531i
$635$	−15.5829	+	6.45463i	−0.618387	+	0.256144i
$636$		0			0
$637$	−11.0015	+	26.5601i	−0.435897	+	1.05235i
$638$	3.39532	+	1.46616i	0.134422	+	0.0580458i
$639$		0			0
$640$	14.1834	−	11.4902i	0.560649	−	0.454188i
$641$	−4.08383			−0.161302			−0.0806508	−	0.996742i	$-0.525700\pi$
$641$	−4.08383			−0.161302			−0.0806508	+	0.996742i	$0.525700\pi$
$642$		0			0
$643$	6.54688	−	15.8056i	0.258184	−	0.623310i	−0.740635	−	0.671908i	$-0.765475\pi$
$643$	6.54688	−	15.8056i	0.258184	−	0.623310i	0.998818	+	0.0485974i	$0.0154751\pi$
$644$	40.6601	+	43.1641i	1.60223	+	1.70090i
$645$		0			0
$646$	0.0589610	−	0.0572260i	0.00231979	−	0.00225153i
$647$	21.0598	−	21.0598i	0.827946	−	0.827946i	−0.159286	−	0.987232i	$-0.550919\pi$
$647$	21.0598	−	21.0598i	0.827946	−	0.827946i	0.987232	+	0.159286i	$0.0509192\pi$
$648$		0			0
$649$	−8.85758	−	8.85758i	−0.347690	−	0.347690i
$650$	−8.58506	−	0.128199i	−0.336734	−	0.00502836i
$651$		0			0
$652$	1.65373	−	0.627830i	0.0647653	−	0.0245877i
$653$	10.5944	+	4.38835i	0.414591	+	0.171729i	0.580222	−	0.814459i	$-0.302966\pi$
$653$	10.5944	+	4.38835i	0.414591	+	0.171729i	−0.165630	+	0.986188i	$0.552966\pi$
$654$		0			0
$655$		−	18.0330i		−	0.704609i
$656$	1.24056	−	1.10057i	0.0484357	−	0.0429699i
$657$		0			0
$658$	−23.8158	−	60.0158i	−0.928438	−	2.33966i
$659$	27.0318	+	11.1969i	1.05301	+	0.436170i	0.840965	−	0.541090i	$-0.181988\pi$
$659$	27.0318	+	11.1969i	1.05301	+	0.436170i	0.212044	+	0.977260i	$0.431988\pi$
$660$		0			0
$661$	14.1399	+	34.1368i	0.549980	+	1.32777i	0.917493	+	0.397751i	$0.130209\pi$
$661$	14.1399	+	34.1368i	0.549980	+	1.32777i	−0.367513	+	0.930018i	$0.619791\pi$
$662$	−0.437282	+	29.2834i	−0.0169954	+	1.13813i
$663$		0			0
$664$	−0.130288	+	2.90660i	−0.00505615	+	0.112798i
$665$	23.1091	−	23.1091i	0.896131	−	0.896131i
$666$		0			0
$667$	8.16386	−	3.38158i	0.316106	−	0.130935i
$668$	40.7781	+	1.21813i	1.57775	+	0.0471309i
$669$		0			0
$670$	8.89204	−	20.5921i	0.343529	−	0.795543i
$671$	−10.8161			−0.417549
$672$		0			0
$673$	18.3131			0.705918			0.352959	−	0.935639i	$-0.385175\pi$
$673$	18.3131			0.705918			0.352959	+	0.935639i	$0.385175\pi$
$674$	15.5361	−	35.9784i	0.598428	−	1.38584i
$675$		0			0
$676$	0.393200	−	13.1627i	0.0151231	−	0.506260i
$677$	−12.4693	+	5.16497i	−0.479236	+	0.198506i	−0.609206	−	0.793012i	$-0.708512\pi$
$677$	−12.4693	+	5.16497i	−0.479236	+	0.198506i	0.129970	+	0.991518i	$0.458512\pi$
$678$		0			0
$679$	19.5056	−	19.5056i	0.748557	−	0.748557i
$680$	−0.0413827	+	0.0378319i	−0.00158695	+	0.00145079i
$681$		0			0
$682$	−0.317106	+	21.2356i	−0.0121426	+	0.813153i
$683$	−2.63508	−	6.36164i	−0.100828	−	0.243421i	0.865413	−	0.501059i	$-0.167056\pi$
$683$	−2.63508	−	6.36164i	−0.100828	−	0.243421i	−0.966242	+	0.257637i	$0.917056\pi$
$684$		0			0
$685$	0.0576793	+	0.0238915i	0.00220381	+	0.000912848i
$686$	−9.71979	−	24.4938i	−0.371103	−	0.935178i
$687$		0			0
$688$	−7.97280	+	2.75739i	−0.303960	+	0.105124i
$689$			31.0414i			1.18258i
$690$		0			0
$691$	−7.45340	−	3.08730i	−0.283541	−	0.117446i	0.236381	−	0.971661i	$-0.424039\pi$
$691$	−7.45340	−	3.08730i	−0.283541	−	0.117446i	−0.519921	+	0.854214i	$0.674039\pi$
$692$	−12.6380	−	33.2892i	−0.480426	−	1.26547i
$693$		0			0
$694$	16.4247	+	0.245266i	0.623472	+	0.00931015i
$695$	18.3649	+	18.3649i	0.696620	+	0.696620i
$696$		0			0
$697$	−0.00360204	+	0.00360204i	−0.000136437	+	0.000136437i
$698$	11.3380	−	11.0044i	0.429150	−	0.416522i
$699$		0			0
$700$	14.9478	−	14.0806i	0.564973	−	0.532198i
$701$	8.61858	−	20.8071i	0.325519	−	0.785873i	−0.673395	−	0.739283i	$-0.735165\pi$
$701$	8.61858	−	20.8071i	0.325519	−	0.785873i	0.998914	−	0.0465897i	$-0.0148353\pi$
$702$		0			0
$703$	−45.9973			−1.73482
$704$	−14.5180	−	7.60050i	−0.547167	−	0.286455i
$705$		0			0
$706$	3.52222	+	1.52095i	0.132560	+	0.0572419i
$707$	8.59404	−	20.7479i	0.323212	−	0.780303i
$708$		0			0
$709$	32.5471	−	13.4815i	1.22233	−	0.506307i	0.324182	−	0.945995i	$-0.394911\pi$
$709$	32.5471	−	13.4815i	1.22233	−	0.506307i	0.898151	+	0.439688i	$0.144911\pi$
$710$	14.3554	−	13.9330i	0.538748	−	0.522895i
$711$		0			0
$712$	27.7795	+	12.9931i	1.04108	+	0.486938i
$713$	35.8814	+	35.8814i	1.34377	+	1.34377i
$714$		0			0
$715$	−3.20345	−	7.73382i	−0.119802	−	0.289228i
$716$	−9.30104	−	24.4994i	−0.347596	−	0.915585i
$717$		0			0
$718$	−19.8228	+	7.86622i	−0.739782	+	0.293565i
$719$			50.0351i			1.86600i	0.359882	+	0.932998i	$0.382817\pi$
$719$			50.0351i			1.86600i	−0.359882	+	0.932998i	$0.617183\pi$
$720$		0			0
$721$			49.4800i			1.84273i
$722$	−1.75276	−	4.41694i	−0.0652309	−	0.164381i
$723$		0			0
$724$	4.13339	−	9.19248i	0.153616	−	0.341636i
$725$	−1.17105	−	2.82716i	−0.0434916	−	0.104998i
$726$		0			0
$727$	0.324541	+	0.324541i	0.0120366	+	0.0120366i	0.713099	−	0.701063i	$-0.247291\pi$
$727$	0.324541	+	0.324541i	0.0120366	+	0.0120366i	−0.701063	+	0.713099i	$0.747291\pi$
$728$	−20.7069	−	22.6504i	−0.767450	−	0.839480i
$729$		0			0
$730$	0.577366	+	0.594871i	0.0213693	+	0.0220172i
$731$	0.0239408	−	0.00991660i	0.000885482	−	0.000366779i
$732$		0			0
$733$	7.06222	−	17.0497i	0.260849	−	0.629745i	−0.738143	−	0.674645i	$-0.764297\pi$
$733$	7.06222	−	17.0497i	0.260849	−	0.629745i	0.998991	+	0.0448997i	$0.0142968\pi$
$734$	−16.4446	+	38.0822i	−0.606979	+	1.40564i
$735$		0			0
$736$	−37.1904	+	12.2437i	−1.37086	+	0.451309i
$737$	−20.1365			−0.741739
$738$		0			0
$739$	0.895156	−	2.16110i	0.0329288	−	0.0794972i	−0.906560	−	0.422078i	$-0.861301\pi$
$739$	0.895156	−	2.16110i	0.0329288	−	0.0794972i	0.939488	+	0.342580i	$0.111301\pi$
$740$	31.3743	+	0.937219i	1.15334	+	0.0344528i
$741$		0			0
$742$	−51.7075	−	53.2752i	−1.89824	−	1.95579i
$743$	−19.4229	+	19.4229i	−0.712556	+	0.712556i	−0.967069	−	0.254513i	$-0.918085\pi$
$743$	−19.4229	+	19.4229i	−0.712556	+	0.712556i	0.254513	+	0.967069i	$0.418085\pi$
$744$		0			0
$745$	10.6086	+	10.6086i	0.388671	+	0.388671i
$746$	0.544150	−	36.4400i	0.0199227	−	1.33416i
$747$		0			0
$748$	0.0459089	+	0.0206429i	0.00167859	+	0.000754779i
$749$	−52.1810	−	21.6141i	−1.90665	−	0.789761i
$750$		0			0
$751$		−	16.5933i		−	0.605500i	−0.953070	−	0.302750i	$-0.902095\pi$
$751$		−	16.5933i		−	0.605500i	0.953070	−	0.302750i	$-0.0979047\pi$
$752$	42.5572	+	2.54482i	1.55190	+	0.0928002i
$753$		0			0
$754$	−4.25071	+	1.68679i	−0.154802	+	0.0614294i
$755$	13.9876	+	5.79387i	0.509062	+	0.210860i
$756$		0			0
$757$	13.4579	+	32.4903i	0.489136	+	1.18088i	0.955155	+	0.296105i	$0.0956878\pi$
$757$	13.4579	+	32.4903i	0.489136	+	1.18088i	−0.466019	+	0.884775i	$0.654312\pi$
$758$	−46.6750	−	0.696986i	−1.69531	−	0.0253157i
$759$		0			0
$760$	7.35679	+	20.2859i	0.266859	+	0.735848i
$761$	15.3310	−	15.3310i	0.555750	−	0.555750i	−0.372345	−	0.928095i	$-0.621446\pi$
$761$	15.3310	−	15.3310i	0.555750	−	0.555750i	0.928095	+	0.372345i	$0.121446\pi$
$762$		0			0
$763$	34.3641	−	14.2341i	1.24406	−	0.515308i
$764$	36.0373	+	38.2566i	1.30378	+	1.38408i
$765$		0			0
$766$	−0.694100	−	0.299725i	−0.0250789	−	0.0108295i
$767$	15.4895			0.559294
$768$		0			0
$769$	−28.5024			−1.02782			−0.513911	−	0.857844i	$-0.671804\pi$
$769$	−28.5024			−1.02782			−0.513911	+	0.857844i	$0.671804\pi$
$770$	18.3807	+	7.93709i	0.662393	+	0.286033i
$771$		0			0
$772$	27.3070	+	28.9887i	0.982801	+	1.04333i
$773$	−0.206772	+	0.0856477i	−0.00743706	+	0.00308053i	−0.386399	−	0.922332i	$-0.626281\pi$
$773$	−0.206772	+	0.0856477i	−0.00743706	+	0.00308053i	0.378962	+	0.925412i	$0.376281\pi$
$774$		0			0
$775$	12.4258	−	12.4258i	0.446348	−	0.446348i
$776$	6.20963	+	17.1227i	0.222913	+	0.614668i
$777$		0			0
$778$	−33.8786	−	0.505900i	−1.21461	−	0.0181374i
$779$	0.750243	+	1.81125i	0.0268803	+	0.0648947i
$780$		0			0
$781$	−16.5925	−	6.87284i	−0.593727	−	0.245930i
$782$	0.111789	−	0.0443608i	0.00399757	−	0.00158634i
$783$		0			0
$784$	45.3187	+	2.70995i	1.61852	+	0.0967839i
$785$		−	7.50936i		−	0.268020i
$786$		0			0
$787$	−22.5388	−	9.33588i	−0.803421	−	0.332788i	−0.0570955	−	0.998369i	$-0.518184\pi$
$787$	−22.5388	−	9.33588i	−0.803421	−	0.332788i	−0.746326	+	0.665581i	$0.768184\pi$
$788$	−41.8814	−	18.8319i	−1.49196	−	0.670860i
$789$		0			0
$790$	0.578092	−	38.7131i	0.0205676	−	1.37735i
$791$	−14.6701	−	14.6701i	−0.521610	−	0.521610i
$792$		0			0
$793$	9.45718	−	9.45718i	0.335834	−	0.335834i
$794$	34.4911	+	35.5368i	1.22404	+	1.26115i
$795$		0			0
$796$	−7.13207	−	0.213050i	−0.252790	−	0.00755137i
$797$	−19.6655	+	47.4766i	−0.696586	+	1.68171i	0.0344830	+	0.999405i	$0.489022\pi$
$797$	−19.6655	+	47.4766i	−0.696586	+	1.68171i	−0.731069	+	0.682303i	$0.760978\pi$
$798$		0			0
$799$	−0.130956			−0.00463291
$800$	4.24001	+	12.8791i	0.149907	+	0.455345i
$801$		0			0
$802$	17.1194	−	39.6449i	0.604505	−	1.39991i
$803$	0.284803	−	0.687575i	0.0100505	−	0.0242640i
$804$		0			0
$805$	44.1953	−	18.3063i	1.55768	−	0.645212i
$806$	−18.2904	−	18.8449i	−0.644252	−	0.663785i
$807$		0			0
$808$	10.0050	+	10.9441i	0.351976	+	0.385011i
$809$	−30.5369	−	30.5369i	−1.07362	−	1.07362i	−0.997065	−	0.0765539i	$-0.975608\pi$
$809$	−30.5369	−	30.5369i	−1.07362	−	1.07362i	−0.0765539	−	0.997065i	$-0.524392\pi$
$810$		0			0
$811$	−9.01221	−	21.7574i	−0.316461	−	0.764006i	−0.999437	−	0.0335639i	$-0.989314\pi$
$811$	−9.01221	−	21.7574i	−0.316461	−	0.764006i	0.682975	−	0.730442i	$-0.260686\pi$
$812$	4.48554	−	9.97564i	0.157412	−	0.350077i
$813$		0			0
$814$	−10.3937	−	26.1920i	−0.364298	−	0.918030i
$815$		−	1.42698i		−	0.0499848i
$816$		0			0
$817$		−	9.97292i		−	0.348908i
$818$	16.5466	−	6.56611i	0.578537	−	0.229579i
$819$		0			0
$820$	−0.474828	−	1.25072i	−0.0165817	−	0.0436771i
$821$	−9.71365	−	23.4508i	−0.339009	−	0.818439i	−0.997811	−	0.0661237i	$-0.978937\pi$
$821$	−9.71365	−	23.4508i	−0.339009	−	0.818439i	0.658803	−	0.752316i	$-0.271063\pi$
$822$		0			0
$823$	25.4141	+	25.4141i	0.885881	+	0.885881i	0.994124	−	0.108243i	$-0.0345225\pi$
$823$	25.4141	+	25.4141i	0.885881	+	0.885881i	−0.108243	+	0.994124i	$0.534522\pi$
$824$	−29.5936	−	13.8416i	−1.03094	−	0.482195i
$825$		0			0
$826$	−26.5841	+	25.8018i	−0.924979	+	0.897760i
$827$	−26.8438	+	11.1190i	−0.933449	+	0.386647i	−0.796986	−	0.603998i	$-0.793573\pi$
$827$	−26.8438	+	11.1190i	−0.933449	+	0.386647i	−0.136463	+	0.990645i	$0.543573\pi$
$828$		0			0
$829$	−2.83838	+	6.85246i	−0.0985811	+	0.237996i	−0.965474	−	0.260498i	$-0.916113\pi$
$829$	−2.83838	+	6.85246i	−0.0985811	+	0.237996i	0.866893	+	0.498494i	$0.166113\pi$
$830$	2.15479	+	0.930478i	0.0747940	+	0.0322973i
$831$		0			0
$832$	19.3396	−	6.04840i	0.670481	−	0.209690i
$833$	−0.139454			−0.00483179
$834$		0			0
$835$	12.5943	−	30.4053i	0.435843	−	1.05222i
$836$	14.1012	−	13.2832i	0.487700	−	0.459408i
$837$		0			0
$838$	31.9003	−	30.9616i	1.10198	−	1.06955i
$839$	−24.7209	+	24.7209i	−0.853460	+	0.853460i	−0.990558	−	0.137097i	$-0.956223\pi$
$839$	−24.7209	+	24.7209i	−0.853460	+	0.853460i	0.137097	+	0.990558i	$0.456223\pi$
$840$		0			0
$841$	19.3536	+	19.3536i	0.667365	+	0.667365i
$842$	43.8979	+	0.655515i	1.51282	+	0.0225906i
$843$		0			0
$844$	4.29564	+	11.3149i	0.147862	+	0.389475i
$845$	−9.81451	−	4.06530i	−0.337629	−	0.139851i
$846$		0			0
$847$			29.1465i			1.00148i
$848$	46.3282	−	16.0226i	1.59092	−	0.550218i
$849$		0			0
$850$	−0.0153622	−	0.0387127i	−0.000526920	−	0.00132783i
$851$	−62.2030	−	25.7653i	−2.13229	−	0.883224i
$852$		0			0
$853$	0.593767	+	1.43348i	0.0203302	+	0.0490814i	0.933719	−	0.358008i	$-0.116544\pi$
$853$	0.593767	+	1.43348i	0.0203302	+	0.0490814i	−0.913388	+	0.407089i	$0.866544\pi$
$854$	−0.477615	+	31.9844i	−0.0163437	+	1.09448i
$855$		0			0
$856$	27.5244	−	25.1627i	0.940764	−	0.860043i
$857$	−4.97247	+	4.97247i	−0.169856	+	0.169856i	−0.786916	−	0.617060i	$-0.788324\pi$
$857$	−4.97247	+	4.97247i	−0.169856	+	0.169856i	0.617060	+	0.786916i	$0.288324\pi$
$858$		0			0
$859$	48.7865	−	20.2080i	1.66457	−	0.689488i	0.666160	−	0.745809i	$-0.267937\pi$
$859$	48.7865	−	20.2080i	1.66457	−	0.689488i	0.998413	+	0.0563206i	$0.0179369\pi$
$860$	−0.203203	+	6.80243i	−0.00692917	+	0.231961i
$861$		0			0
$862$	−16.2007	+	37.5174i	−0.551797	+	1.27785i
$863$	−46.7185			−1.59031			−0.795157	−	0.606403i	$-0.792612\pi$
$863$	−46.7185			−1.59031			−0.795157	+	0.606403i	$0.792612\pi$
$864$		0			0
$865$	−28.7246			−0.976666
$866$	15.1862	−	35.1681i	0.516048	−	1.19506i
$867$		0			0
$868$	62.7823	+	1.87544i	2.13097	+	0.0636567i
$869$	−32.1127	+	13.3015i	−1.08935	+	0.451224i
$870$		0			0
$871$	17.6067	−	17.6067i	0.596580	−	0.596580i
$872$	−1.09977	+	24.5348i	−0.0372429	+	0.830852i
$873$		0			0
$874$	0.691106	−	46.2812i	0.0233770	−	1.56549i
$875$	−19.5637	−	47.2310i	−0.661374	−	1.59670i
$876$		0			0
$877$	−22.3579	−	9.26093i	−0.754971	−	0.312719i	−0.0282030	−	0.999602i	$-0.508978\pi$
$877$	−22.3579	−	9.26093i	−0.754971	−	0.312719i	−0.726768	+	0.686883i	$0.758978\pi$
$878$	−0.918578	−	2.31481i	−0.0310005	−	0.0781211i
$879$		0			0
$880$	−9.88894	+	8.77300i	−0.333356	+	0.295738i
$881$		−	23.9642i		−	0.807373i	−0.914897	−	0.403687i	$-0.867729\pi$
$881$		−	23.9642i		−	0.807373i	0.914897	−	0.403687i	$-0.132271\pi$
$882$		0			0
$883$	22.7801	+	9.43583i	0.766612	+	0.317541i	0.731499	−	0.681842i	$-0.238821\pi$
$883$	22.7801	+	9.43583i	0.766612	+	0.317541i	0.0351126	+	0.999383i	$0.488821\pi$
$884$	−0.0581905	+	0.0220917i	−0.00195716	+	0.000743024i
$885$		0			0
$886$	28.3576	+	0.423456i	0.952691	+	0.0142263i
$887$	1.11052	+	1.11052i	0.0372876	+	0.0372876i	0.725505	−	0.688217i	$-0.241606\pi$
$887$	1.11052	+	1.11052i	0.0372876	+	0.0372876i	−0.688217	+	0.725505i	$0.741606\pi$
$888$		0			0
$889$	31.6658	−	31.6658i	1.06204	−	1.06204i
$890$	17.7530	−	17.2306i	0.595082	−	0.577571i
$891$		0			0
$892$	−16.0094	−	16.9954i	−0.536035	−	0.569047i
$893$	−19.2870	+	46.5631i	−0.645417	+	1.55817i
$894$		0			0
$895$	−21.1400			−0.706634
$896$	−23.1167	+	42.5958i	−0.772275	+	1.42303i
$897$		0			0
$898$	−7.29723	−	3.15107i	−0.243512	−	0.105153i
$899$	3.58182	−	8.64727i	0.119460	−	0.288403i
$900$		0			0
$901$	−0.139115	+	0.0576232i	−0.00463458	+	0.00191971i
$902$	−0.861842	+	0.836481i	−0.0286962	+	0.0278518i
$903$		0			0
$904$	12.8779	−	4.67026i	0.428314	−	0.155330i
$905$	−5.74932	−	5.74932i	−0.191114	−	0.191114i
$906$		0			0
$907$	−0.322193	−	0.777842i	−0.0106982	−	0.0258278i	0.918440	−	0.395560i	$-0.129449\pi$
$907$	−0.322193	−	0.777842i	−0.0106982	−	0.0258278i	−0.929138	+	0.369732i	$0.879449\pi$
$908$	−49.6751	+	18.8589i	−1.64853	+	0.625853i
$909$		0			0
$910$	−23.0113	+	9.13150i	−0.762818	+	0.302706i
$911$			9.60293i			0.318159i	0.987266	+	0.159080i	$0.0508526\pi$
$911$			9.60293i			0.318159i	−0.987266	+	0.159080i	$0.949147\pi$
$912$		0			0
$913$		−	2.10712i		−	0.0697355i
$914$	7.40135	+	18.6514i	0.244815	+	0.616932i
$915$		0			0
$916$	23.9660	+	10.7763i	0.791861	+	0.356060i
$917$	18.3224	+	44.2342i	0.605059	+	1.46074i
$918$		0			0
$919$	−13.5414	−	13.5414i	−0.446690	−	0.446690i	0.447563	−	0.894253i	$-0.352292\pi$
$919$	−13.5414	−	13.5414i	−0.446690	−	0.446690i	−0.894253	+	0.447563i	$0.852292\pi$
$920$	−1.41440	+	31.5539i	−0.0466314	+	1.04030i
$921$		0			0
$922$	8.60878	+	8.86979i	0.283515	+	0.292111i
$923$	20.5173	−	8.49854i	0.675335	−	0.279733i
$924$		0			0
$925$	−8.92257	+	21.5410i	−0.293372	+	0.708264i
$926$	−20.5880	+	47.6776i	−0.676563	+	1.56678i
$927$		0			0
$928$	4.71156	+	5.47337i	0.154665	+	0.179672i
$929$	−39.9230			−1.30983			−0.654916	−	0.755701i	$-0.727296\pi$
$929$	−39.9230			−1.30983			−0.654916	+	0.755701i	$0.727296\pi$
$930$		0			0
$931$	−20.5385	+	49.5844i	−0.673123	+	1.62506i
$932$	0.0947788	−	3.17281i	0.00310458	−	0.103929i
$933$		0			0
$934$	24.6879	+	25.4364i	0.807812	+	0.832304i
$935$	0.0287131	−	0.0287131i	0.000939019	−	0.000939019i
$936$		0			0
$937$	39.2438	+	39.2438i	1.28204	+	1.28204i	0.939505	+	0.342535i	$0.111286\pi$
$937$	39.2438	+	39.2438i	1.28204	+	1.28204i	0.342535	+	0.939505i	$0.388714\pi$
$938$	−0.889189	+	59.5462i	−0.0290330	+	1.94425i
$939$		0			0
$940$	14.1042	−	31.3672i	0.460030	−	1.02309i
$941$	39.0223	+	16.1636i	1.27209	+	0.526917i	0.913599	−	0.406616i	$-0.133291\pi$
$941$	39.0223	+	16.1636i	1.27209	+	0.526917i	0.358491	+	0.933533i	$0.383291\pi$
$942$		0			0
$943$			2.86963i			0.0934480i
$944$	−7.99520	−	23.1176i	−0.260222	−	0.752413i
$945$		0			0
$946$	5.67883	−	2.25351i	0.184635	−	0.0732678i
$947$	−29.2371	−	12.1104i	−0.950078	−	0.393535i	−0.146818	−	0.989164i	$-0.546903\pi$
$947$	−29.2371	−	12.1104i	−0.950078	−	0.393535i	−0.803260	+	0.595628i	$0.796903\pi$
$948$		0			0
$949$	0.352170	+	0.850213i	0.0114319	+	0.0275991i
$950$	−16.0273	−	0.239331i	−0.519993	−	0.00776492i
$951$		0			0
$952$	0.0630709	−	0.134847i	0.00204414	−	0.00437041i
$953$	−3.99976	+	3.99976i	−0.129565	+	0.129565i	−0.768915	−	0.639351i	$-0.779203\pi$
$953$	−3.99976	+	3.99976i	−0.129565	+	0.129565i	0.639351	+	0.768915i	$0.279203\pi$
$954$		0			0
$955$	39.1706	−	16.2250i	1.26753	−	0.525028i
$956$	14.1386	−	13.3184i	0.457274	−	0.430747i
$957$		0			0
$958$	39.8354	+	17.2016i	1.28702	+	0.555759i
$959$	−0.165759			−0.00535265
$960$		0			0
$961$	22.7487			0.733831
$962$	31.9893	+	13.8135i	1.03138	+	0.445366i
$963$		0			0
$964$	−24.3581	+	22.9450i	−0.784521	+	0.739010i
$965$	29.6813	−	12.2944i	0.955474	−	0.395770i
$966$		0			0
$967$	20.0348	−	20.0348i	0.644276	−	0.644276i	−0.307327	−	0.951604i	$-0.599435\pi$
$967$	20.0348	−	20.0348i	0.644276	−	0.644276i	0.951604	+	0.307327i	$0.0994347\pi$
$968$	−17.4323	−	8.15347i	−0.560295	−	0.262063i
$969$		0			0
$970$	14.6915	+	0.219385i	0.471717	+	0.00704403i
$971$	−11.5251	−	27.8241i	−0.369859	−	0.892919i	−0.993773	−	0.111426i	$-0.964458\pi$
$971$	−11.5251	−	27.8241i	−0.369859	−	0.892919i	0.623913	−	0.781493i	$-0.285542\pi$
$972$		0			0
$973$	−63.7078	−	26.3886i	−2.04238	−	0.845980i
$974$	41.0678	−	16.2968i	1.31590	−	0.522183i
$975$		0			0
$976$	−18.9960	−	9.23303i	−0.608048	−	0.295542i
$977$		−	50.5040i		−	1.61577i	−0.589343	−	0.807883i	$-0.700613\pi$
$977$		−	50.5040i		−	1.61577i	0.589343	−	0.807883i	$-0.299387\pi$
$978$		0			0
$979$	−20.5196	−	8.49950i	−0.655810	−	0.271645i
$980$	15.0194	−	33.4025i	0.479778	−	1.06701i
$981$		0			0
$982$	−0.298365	+	19.9806i	−0.00952121	+	0.637606i
$983$	9.33417	+	9.33417i	0.297714	+	0.297714i	0.840118	−	0.542404i	$-0.182486\pi$
$983$	9.33417	+	9.33417i	0.297714	+	0.297714i	−0.542404	+	0.840118i	$0.682486\pi$
$984$		0			0
$985$	−26.1942	+	26.1942i	−0.834616	+	0.834616i
$986$	−0.0154502	−	0.0159187i	−0.000492036	−	0.000506954i
$987$		0			0
$988$	−0.715257	+	23.9439i	−0.0227554	+	0.761758i
$989$	5.58631	−	13.4865i	0.177634	−	0.428847i
$990$		0			0
$991$	6.09661			0.193665			0.0968327	−	0.995301i	$-0.469129\pi$
$991$	6.09661			0.193665			0.0968327	+	0.995301i	$0.469129\pi$
$992$	−18.6845	+	37.0250i	−0.593233	+	1.17554i
$993$		0			0
$994$	−21.0565	+	48.7626i	−0.667873	+	1.54666i
$995$	−2.20273	+	5.31787i	−0.0698314	+	0.168588i
$996$		0			0
$997$	33.9849	−	14.0770i	1.07631	−	0.445824i	0.227099	−	0.973872i	$-0.427076\pi$
$997$	33.9849	−	14.0770i	1.07631	−	0.445824i	0.849214	+	0.528048i	$0.177076\pi$
$998$	10.7958	+	11.1231i	0.341734	+	0.352095i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.a.109.5	✓	128
3.2	odd	2	inner	864.2.v.a.109.28	yes	128
32.5	even	8	inner	864.2.v.a.325.5	yes	128
96.5	odd	8	inner	864.2.v.a.325.28	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.a.109.5	✓	128	1.1	even	1	trivial
864.2.v.a.109.28	yes	128	3.2	odd	2	inner
864.2.v.a.325.5	yes	128	32.5	even	8	inner
864.2.v.a.325.28	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)

\(f(q)\)	\(=\)	\(q+(-1.29834 - 0.560644i) q^{2} +(1.37136 + 1.45581i) q^{4} +(1.49059 - 0.617423i) q^{5} +(-3.02902 + 3.02902i) q^{7} +(-0.964291 - 2.65897i) q^{8} +O(q^{10})\)	\(q+(-1.29834 - 0.560644i) q^{2} +(1.37136 + 1.45581i) q^{4} +(1.49059 - 0.617423i) q^{5} +(-3.02902 + 3.02902i) q^{7} +(-0.964291 - 2.65897i) q^{8} +(-2.28144 - 0.0340682i) q^{10} +(0.783887 + 1.89247i) q^{11} +(-2.34011 - 0.969307i) q^{13} +(5.63089 - 2.23448i) q^{14} +(-0.238764 + 3.99287i) q^{16} -0.0122868i q^{17} +(-4.36871 - 1.80958i) q^{19} +(2.94298 + 1.32331i) q^{20} +(0.0432534 - 2.89655i) q^{22} +(-4.89425 - 4.89425i) q^{23} +(-1.69489 + 1.69489i) q^{25} +(2.49482 + 2.57046i) q^{26} +(-8.56354 - 0.255811i) q^{28} +(-0.488562 + 1.17949i) q^{29} -7.33135 q^{31} +(2.54857 - 5.05022i) q^{32} +(-0.00688851 + 0.0159524i) q^{34} +(-2.64484 + 6.38521i) q^{35} +(8.98691 - 3.72250i) q^{37} +(4.65752 + 4.79873i) q^{38} +(-3.07907 - 3.36807i) q^{40} +(-0.293164 - 0.293164i) q^{41} +(0.807094 + 1.94850i) q^{43} +(-1.68009 + 3.73644i) q^{44} +(3.61045 + 9.09831i) q^{46} -10.6583i q^{47} -11.3499i q^{49} +(3.15076 - 1.25030i) q^{50} +(-1.79800 - 4.73603i) q^{52} +(-4.68985 - 11.3223i) q^{53} +(2.33691 + 2.33691i) q^{55} +(10.9749 + 5.13323i) q^{56} +(1.29559 - 1.25747i) q^{58} +(-5.64978 + 2.34021i) q^{59} +(-2.02067 + 4.87832i) q^{61} +(9.51857 + 4.11028i) q^{62} +(-6.14029 + 5.12805i) q^{64} -4.08662 q^{65} +(-3.76193 + 9.08210i) q^{67} +(0.0178872 - 0.0168496i) q^{68} +(7.01372 - 6.80734i) q^{70} +(-6.19966 + 6.19966i) q^{71} +(-0.256907 - 0.256907i) q^{73} +(-13.7550 - 0.205400i) q^{74} +(-3.35665 - 8.84158i) q^{76} +(-8.10674 - 3.35792i) q^{77} +16.9687i q^{79} +(2.10939 + 6.09915i) q^{80} +(0.216265 + 0.544985i) q^{82} +(-0.950366 - 0.393655i) q^{83} +(-0.00758614 - 0.0183146i) q^{85} +(0.0445339 - 2.98230i) q^{86} +(4.27614 - 3.90923i) q^{88} +(-7.66699 + 7.66699i) q^{89} +(10.0243 - 4.15220i) q^{91} +(0.413336 - 13.8368i) q^{92} +(-5.97552 + 13.8381i) q^{94} -7.62923 q^{95} -6.43958 q^{97} +(-6.36326 + 14.7360i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 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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