LMFDB - Embedded newform 864.2.w.a.107.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(107,864)]

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([4, 5, 4]))

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

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

chi := DirichletCharacter("864.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (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			107.12
Character	$\chi$	$=$	864.107
Dual form			864.2.w.a.323.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.501484 - 1.32231i) q^{2} +(-1.49703 + 1.32624i) q^{4} +(0.112585 + 0.0466342i) q^{5} +(-1.45843 + 1.45843i) q^{7} +(2.50444 + 1.31445i) q^{8} +O(q^{10})$	\(q+(-0.501484 - 1.32231i) q^{2} +(-1.49703 + 1.32624i) q^{4} +(0.112585 + 0.0466342i) q^{5} +(-1.45843 + 1.45843i) q^{7} +(2.50444 + 1.31445i) q^{8} +(0.00520548 - 0.172259i) q^{10} +(4.76670 + 1.97443i) q^{11} +(-1.35139 - 3.26255i) q^{13} +(2.65988 + 1.19712i) q^{14} +(0.482180 - 3.97083i) q^{16} -8.01284 q^{17} +(-6.25059 + 2.58908i) q^{19} +(-0.230391 + 0.0795019i) q^{20} +(0.220393 - 7.29322i) q^{22} +(-1.22164 + 1.22164i) q^{23} +(-3.52503 - 3.52503i) q^{25} +(-3.63642 + 3.42308i) q^{26} +(0.249082 - 4.11753i) q^{28} +(2.48379 + 5.99639i) q^{29} -0.180319i q^{31} +(-5.49249 + 1.35372i) q^{32} +(4.01831 + 10.5955i) q^{34} +(-0.232210 + 0.0961845i) q^{35} +(-4.49262 + 10.8462i) q^{37} +(6.55815 + 6.96686i) q^{38} +(0.220664 + 0.264780i) q^{40} +(4.14237 + 4.14237i) q^{41} +(2.37609 - 5.73640i) q^{43} +(-9.75444 + 3.36601i) q^{44} +(2.22802 + 1.00276i) q^{46} -3.20157i q^{47} +2.74597i q^{49} +(-2.89345 + 6.42895i) q^{50} +(6.35000 + 3.09186i) q^{52} +(-1.81727 + 4.38729i) q^{53} +(0.444583 + 0.444583i) q^{55} +(-5.56958 + 1.73551i) q^{56} +(6.68353 - 6.29144i) q^{58} +(2.03007 - 4.90102i) q^{59} +(-13.4598 + 5.57525i) q^{61} +(-0.238438 + 0.0904270i) q^{62} +(4.54444 + 6.58393i) q^{64} -0.430336i q^{65} +(-1.72299 - 4.15968i) q^{67} +(11.9954 - 10.6269i) q^{68} +(0.243636 + 0.258819i) q^{70} +(8.16098 + 8.16098i) q^{71} +(5.58960 - 5.58960i) q^{73} +(16.5950 + 0.501483i) q^{74} +(5.92357 - 12.1657i) q^{76} +(-9.83146 + 4.07232i) q^{77} -7.94510 q^{79} +(0.239463 - 0.424570i) q^{80} +(3.40018 - 7.55484i) q^{82} +(-2.09749 - 5.06378i) q^{83} +(-0.902125 - 0.373672i) q^{85} +(-8.77689 - 0.265228i) q^{86} +(9.34262 + 11.2104i) q^{88} +(-7.29752 + 7.29752i) q^{89} +(6.72911 + 2.78729i) q^{91} +(0.208641 - 3.44900i) q^{92} +(-4.23348 + 1.60554i) q^{94} -0.824463 q^{95} -0.728484 q^{97} +(3.63103 - 1.37706i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) $ 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

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 $

$2$	−0.501484	−	1.32231i	−0.354603	−	0.935017i
$2$	−0.501484	−	1.32231i	−0.354603	−	0.935017i
$3$		0			0
$3$		0			0
$4$	−1.49703	+	1.32624i	−0.748514	+	0.663120i
$5$	0.112585	+	0.0466342i	0.0503495	+	0.0208555i	0.407716	−	0.913109i	$-0.366325\pi$
$5$	0.112585	+	0.0466342i	0.0503495	+	0.0208555i	−0.357367	+	0.933964i	$0.616325\pi$
$6$		0			0
$7$	−1.45843	+	1.45843i	−0.551234	+	0.551234i	−0.926797	−	0.375563i	$-0.877449\pi$
$7$	−1.45843	+	1.45843i	−0.551234	+	0.551234i	0.375563	+	0.926797i	$0.377449\pi$
$8$	2.50444	+	1.31445i	0.885453	+	0.464729i
$9$		0			0
$10$	0.00520548	−	0.172259i	0.00164612	−	0.0544731i
$11$	4.76670	+	1.97443i	1.43721	+	0.595313i	0.959121	−	0.282996i	$-0.0913283\pi$
$11$	4.76670	+	1.97443i	1.43721	+	0.595313i	0.478093	+	0.878309i	$0.341328\pi$
$12$		0			0
$13$	−1.35139	−	3.26255i	−0.374809	−	0.904869i	−0.992921	−	0.118779i	$-0.962102\pi$
$13$	−1.35139	−	3.26255i	−0.374809	−	0.904869i	0.618112	−	0.786090i	$-0.287898\pi$
$14$	2.65988	+	1.19712i	0.710883	+	0.319944i
$15$		0			0
$16$	0.482180	−	3.97083i	0.120545	−	0.992708i
$17$	−8.01284			−1.94340			−0.971699	−	0.236220i	$-0.924091\pi$
$17$	−8.01284			−1.94340			−0.971699	+	0.236220i	$0.924091\pi$
$18$		0			0
$19$	−6.25059	+	2.58908i	−1.43398	+	0.593976i	−0.958332	−	0.285657i	$-0.907788\pi$
$19$	−6.25059	+	2.58908i	−1.43398	+	0.593976i	−0.475653	+	0.879633i	$0.657788\pi$
$20$	−0.230391	+	0.0795019i	−0.0515170	+	0.0177772i
$21$		0			0
$22$	0.220393	−	7.29322i	0.0469879	−	1.55492i
$23$	−1.22164	+	1.22164i	−0.254729	+	0.254729i	−0.822906	−	0.568177i	$-0.807649\pi$
$23$	−1.22164	+	1.22164i	−0.254729	+	0.254729i	0.568177	+	0.822906i	$0.307649\pi$
$24$		0			0
$25$	−3.52503	−	3.52503i	−0.705007	−	0.705007i
$26$	−3.63642	+	3.42308i	−0.713160	+	0.671322i
$27$		0			0
$28$	0.249082	−	4.11753i	0.0470721	−	0.778141i
$29$	2.48379	+	5.99639i	0.461228	+	1.11350i	0.967894	+	0.251359i	$0.0808776\pi$
$29$	2.48379	+	5.99639i	0.461228	+	1.11350i	−0.506666	+	0.862142i	$0.669122\pi$
$30$		0			0
$31$		−	0.180319i		−	0.0323862i	−0.999869	−	0.0161931i	$-0.994845\pi$
$31$		−	0.180319i		−	0.0323862i	0.999869	−	0.0161931i	$-0.00515465\pi$
$32$	−5.49249	+	1.35372i	−0.970944	+	0.239306i
$33$		0			0
$34$	4.01831	+	10.5955i	0.689135	+	1.81711i
$35$	−0.232210	+	0.0961845i	−0.0392506	+	0.0162581i
$36$		0			0
$37$	−4.49262	+	10.8462i	−0.738583	+	1.78310i	−0.127021	+	0.991900i	$0.540542\pi$
$37$	−4.49262	+	10.8462i	−0.738583	+	1.78310i	−0.611562	+	0.791197i	$0.709458\pi$
$38$	6.55815	+	6.96686i	1.06387	+	1.13017i
$39$		0			0
$40$	0.220664	+	0.264780i	0.0348900	+	0.0418654i
$41$	4.14237	+	4.14237i	0.646929	+	0.646929i	0.952250	−	0.305321i	$-0.0987637\pi$
$41$	4.14237	+	4.14237i	0.646929	+	0.646929i	−0.305321	+	0.952250i	$0.598764\pi$
$42$		0			0
$43$	2.37609	−	5.73640i	0.362351	−	0.874793i	−0.632604	−	0.774475i	$-0.718014\pi$
$43$	2.37609	−	5.73640i	0.362351	−	0.874793i	0.994955	−	0.100318i	$-0.0319859\pi$
$44$	−9.75444	+	3.36601i	−1.47054	+	0.507444i
$45$		0			0
$46$	2.22802	+	1.00276i	0.328503	+	0.147848i
$47$		−	3.20157i		−	0.466997i	−0.972357	−	0.233499i	$-0.924983\pi$
$47$		−	3.20157i		−	0.466997i	0.972357	−	0.233499i	$-0.0750174\pi$
$48$		0			0
$49$			2.74597i			0.392281i
$50$	−2.89345	+	6.42895i	−0.409196	+	0.909191i
$51$		0			0
$52$	6.35000	+	3.09186i	0.880586	+	0.428764i
$53$	−1.81727	+	4.38729i	−0.249622	+	0.602640i	−0.998172	−	0.0604378i	$-0.980750\pi$
$53$	−1.81727	+	4.38729i	−0.249622	+	0.602640i	0.748550	+	0.663078i	$0.230750\pi$
$54$		0			0
$55$	0.444583	+	0.444583i	0.0599475	+	0.0599475i
$56$	−5.56958	+	1.73551i	−0.744267	+	0.231918i
$57$		0			0
$58$	6.68353	−	6.29144i	0.877590	−	0.826107i
$59$	2.03007	−	4.90102i	0.264292	−	0.638058i	−0.734903	−	0.678172i	$-0.762772\pi$
$59$	2.03007	−	4.90102i	0.264292	−	0.638058i	0.999195	+	0.0401145i	$0.0127723\pi$
$60$		0			0
$61$	−13.4598	+	5.57525i	−1.72336	+	0.713838i	−0.723637	+	0.690181i	$0.757531\pi$
$61$	−13.4598	+	5.57525i	−1.72336	+	0.713838i	−0.999720	+	0.0236567i	$0.992469\pi$
$62$	−0.238438	+	0.0904270i	−0.0302817	+	0.0114842i
$63$		0			0
$64$	4.54444	+	6.58393i	0.568054	+	0.822991i
$65$		−	0.430336i		−	0.0533766i
$66$		0			0
$67$	−1.72299	−	4.15968i	−0.210497	−	0.508185i	0.783003	−	0.622018i	$-0.213687\pi$
$67$	−1.72299	−	4.15968i	−0.210497	−	0.508185i	−0.993500	+	0.113833i	$0.963687\pi$
$68$	11.9954	−	10.6269i	1.45466	−	1.28871i
$69$		0			0
$70$	0.243636	+	0.258819i	0.0291200	+	0.0309348i
$71$	8.16098	+	8.16098i	0.968530	+	0.968530i	0.999520	−	0.0309893i	$-0.00986577\pi$
$71$	8.16098	+	8.16098i	0.968530	+	0.968530i	−0.0309893	+	0.999520i	$0.509866\pi$
$72$		0			0
$73$	5.58960	−	5.58960i	0.654213	−	0.654213i	−0.299791	−	0.954005i	$-0.596917\pi$
$73$	5.58960	−	5.58960i	0.654213	−	0.654213i	0.954005	+	0.299791i	$0.0969171\pi$
$74$	16.5950	+	0.501483i	1.92913	+	0.0582962i
$75$		0			0
$76$	5.92357	−	12.1657i	0.679480	−	1.39550i
$77$	−9.83146	+	4.07232i	−1.12040	+	0.464084i
$78$		0			0
$79$	−7.94510			−0.893894			−0.446947	−	0.894560i	$-0.647489\pi$
$79$	−7.94510			−0.893894			−0.446947	+	0.894560i	$0.647489\pi$
$80$	0.239463	−	0.424570i	0.0267728	−	0.0474683i
$81$		0			0
$82$	3.40018	−	7.55484i	0.375487	−	0.834292i
$83$	−2.09749	−	5.06378i	−0.230229	−	0.555822i	0.765975	−	0.642870i	$-0.222257\pi$
$83$	−2.09749	−	5.06378i	−0.230229	−	0.555822i	−0.996204	+	0.0870480i	$0.972257\pi$
$84$		0			0
$85$	−0.902125	−	0.373672i	−0.0978492	−	0.0405305i
$86$	−8.77689	−	0.265228i	−0.946437	−	0.0286003i
$87$		0			0
$88$	9.34262	+	11.2104i	0.995926	+	1.19504i
$89$	−7.29752	+	7.29752i	−0.773536	+	0.773536i	−0.978723	−	0.205187i	$-0.934220\pi$
$89$	−7.29752	+	7.29752i	−0.773536	+	0.773536i	0.205187	+	0.978723i	$0.434220\pi$
$90$		0			0
$91$	6.72911	+	2.78729i	0.705403	+	0.292187i
$92$	0.208641	−	3.44900i	0.0217523	−	0.359584i
$93$		0			0
$94$	−4.23348	+	1.60554i	−0.436650	+	0.165599i
$95$	−0.824463			−0.0845881
$96$		0			0
$97$	−0.728484			−0.0739663			−0.0369832	−	0.999316i	$-0.511775\pi$
$97$	−0.728484			−0.0739663			−0.0369832	+	0.999316i	$0.511775\pi$
$98$	3.63103	−	1.37706i	0.366790	−	0.139104i
$99$		0			0
$100$	9.95211	+	0.602033i	0.995211	+	0.0602033i
$101$	−9.21853	−	3.81844i	−0.917278	−	0.379949i	−0.126440	−	0.991974i	$-0.540355\pi$
$101$	−9.21853	−	3.81844i	−0.917278	−	0.379949i	−0.790838	+	0.612026i	$0.790355\pi$
$102$		0			0
$103$	−9.17377	+	9.17377i	−0.903918	+	0.903918i	−0.995772	−	0.0918540i	$-0.970721\pi$
$103$	−9.17377	+	9.17377i	−0.903918	+	0.903918i	0.0918540	+	0.995772i	$0.470721\pi$
$104$	0.903983	−	9.94721i	0.0886428	−	0.975404i
$105$		0			0
$106$	6.71271	+	0.202851i	0.651996	+	0.0197026i
$107$	−4.20725	−	1.74270i	−0.406730	−	0.168473i	0.169932	−	0.985456i	$-0.445645\pi$
$107$	−4.20725	−	1.74270i	−0.406730	−	0.168473i	−0.576662	+	0.816983i	$0.695645\pi$
$108$		0			0
$109$	0.168187	+	0.406039i	0.0161094	+	0.0388915i	0.931730	−	0.363153i	$-0.118300\pi$
$109$	0.168187	+	0.406039i	0.0161094	+	0.0388915i	−0.915620	+	0.402044i	$0.868300\pi$
$110$	0.364926	−	0.810829i	0.0347944	−	0.0773095i
$111$		0			0
$112$	5.08795	+	6.49440i	0.480766	+	0.613663i
$113$	6.90293			0.649373			0.324686	−	0.945822i	$-0.394741\pi$
$113$	6.90293			0.649373			0.324686	+	0.945822i	$0.394741\pi$
$114$		0			0
$115$	−0.194508	+	0.0805678i	−0.0181380	+	0.00751299i
$116$	−11.6709	−	5.68266i	−1.08362	−	0.527622i
$117$		0			0
$118$	−7.49873	−	0.226603i	−0.690314	−	0.0208605i
$119$	11.6862	−	11.6862i	1.07127	−	1.07127i
$120$		0			0
$121$	11.0449	+	11.0449i	1.00408	+	1.00408i
$122$	14.1221	+	15.0022i	1.27856	+	1.35824i
$123$		0			0
$124$	0.239146	+	0.269942i	0.0214759	+	0.0242415i
$125$	−0.465650	−	1.12418i	−0.0416490	−	0.100550i
$126$		0			0
$127$			12.4524i			1.10498i	0.833521	+	0.552488i	$0.186321\pi$
$127$			12.4524i			1.10498i	−0.833521	+	0.552488i	$0.813679\pi$
$128$	6.42705	−	9.31091i	0.568077	−	0.822976i
$129$		0			0
$130$	−0.569039	+	0.215806i	−0.0499080	+	0.0189275i
$131$	11.8423	−	4.90523i	1.03466	−	0.428572i	0.200270	−	0.979741i	$-0.435818\pi$
$131$	11.8423	−	4.90523i	1.03466	−	0.428572i	0.834394	+	0.551169i	$0.185818\pi$
$132$		0			0
$133$	5.34006	−	12.8920i	0.463042	−	1.11788i
$134$	−4.63634	+	4.36435i	−0.400519	+	0.377023i
$135$		0			0
$136$	−20.0677	−	10.5325i	−1.72079	−	0.903153i
$137$	6.55386	+	6.55386i	0.559934	+	0.559934i	0.929289	−	0.369354i	$-0.120421\pi$
$137$	6.55386	+	6.55386i	0.559934	+	0.559934i	−0.369354	+	0.929289i	$0.620421\pi$
$138$		0			0
$139$	−1.20358	+	2.90571i	−0.102087	+	0.246459i	−0.966668	−	0.256034i	$-0.917584\pi$
$139$	−1.20358	+	2.90571i	−0.102087	+	0.246459i	0.864581	+	0.502494i	$0.167584\pi$
$140$	0.220061	−	0.451957i	0.0185985	−	0.0381973i
$141$		0			0
$142$	6.69877	−	14.8840i	0.562149	−	1.24904i
$143$		−	18.2198i		−	1.52362i
$144$		0			0
$145$			0.790933i			0.0656834i
$146$	−10.1943	−	4.58811i	−0.843686	−	0.379715i
$147$		0			0
$148$	−7.65901	−	22.1953i	−0.629567	−	1.82444i
$149$	5.63924	−	13.6143i	0.461985	−	1.11533i	−0.505597	−	0.862770i	$-0.668728\pi$
$149$	5.63924	−	13.6143i	0.461985	−	1.11533i	0.967581	−	0.252560i	$-0.0812725\pi$
$150$		0			0
$151$	8.71225	+	8.71225i	0.708993	+	0.708993i	0.966324	−	0.257330i	$-0.0828428\pi$
$151$	8.71225	+	8.71225i	0.708993	+	0.708993i	−0.257330	+	0.966324i	$0.582843\pi$
$152$	−19.0575	−	1.73190i	−1.54576	−	0.140476i
$153$		0			0
$154$	10.3152	+	10.9581i	0.831223	+	0.883026i
$155$	0.00840903	−	0.0203012i	0.000675429	−	0.00163063i
$156$		0			0
$157$	−2.89512	+	1.19920i	−0.231056	+	0.0957065i	−0.495208	−	0.868775i	$-0.664908\pi$
$157$	−2.89512	+	1.19920i	−0.231056	+	0.0957065i	0.264152	+	0.964481i	$0.414908\pi$
$158$	3.98434	+	10.5059i	0.316977	+	0.835806i
$159$		0			0
$160$	−0.681501	−	0.103730i	−0.0538774	−	0.00820056i
$161$		−	3.56334i		−	0.280831i
$162$		0			0
$163$	−3.77764	−	9.12003i	−0.295888	−	0.714336i	−0.999991	−	0.00423837i	$-0.998651\pi$
$163$	−3.77764	−	9.12003i	−0.295888	−	0.714336i	0.704103	−	0.710097i	$-0.251349\pi$
$164$	−11.6950	−	0.707466i	−0.913226	−	0.0552438i
$165$		0			0
$166$	−5.64405	+	5.31294i	−0.438063	+	0.412364i
$167$	−2.16120	−	2.16120i	−0.167239	−	0.167239i	0.618526	−	0.785765i	$-0.287730\pi$
$167$	−2.16120	−	2.16120i	−0.167239	−	0.167239i	−0.785765	+	0.618526i	$0.787730\pi$
$168$		0			0
$169$	0.374404	−	0.374404i	0.0288003	−	0.0288003i
$170$	−0.0417106	+	1.38028i	−0.00319906	+	0.105863i
$171$		0			0
$172$	4.05076	+	11.7388i	0.308868	+	0.895076i
$173$	3.14700	−	1.30353i	0.239262	−	0.0991057i	−0.259830	−	0.965654i	$-0.583667\pi$
$173$	3.14700	−	1.30353i	0.239262	−	0.0991057i	0.499093	+	0.866549i	$0.333667\pi$
$174$		0			0
$175$	10.2820			0.777248
$176$	10.1385	−	17.9757i	0.764221	−	1.35497i
$177$		0			0
$178$	13.3092	+	5.99002i	0.997567	+	0.448971i
$179$	4.94524	+	11.9389i	0.369624	+	0.892352i	0.993812	+	0.111077i	$0.0354302\pi$
$179$	4.94524	+	11.9389i	0.369624	+	0.892352i	−0.624187	+	0.781275i	$0.714570\pi$
$180$		0			0
$181$	−18.0743	−	7.48660i	−1.34345	−	0.556475i	−0.408988	−	0.912540i	$-0.634118\pi$
$181$	−18.0743	−	7.48660i	−1.34345	−	0.556475i	−0.934461	+	0.356065i	$0.884118\pi$
$182$	0.311127	−	10.2958i	0.0230623	−	0.763174i
$183$		0			0
$184$	−4.66530	+	1.45373i	−0.343930	+	0.107171i
$185$	−1.01160	+	1.01160i	−0.0743746	+	0.0743746i
$186$		0			0
$187$	−38.1948	−	15.8208i	−2.79308	−	1.15693i
$188$	4.24605	+	4.79284i	0.309675	+	0.349554i
$189$		0			0
$190$	0.413455	+	1.09020i	0.0299952	+	0.0790913i
$191$	5.66758			0.410092			0.205046	−	0.978752i	$-0.434266\pi$
$191$	5.66758			0.410092			0.205046	+	0.978752i	$0.434266\pi$
$192$		0			0
$193$	−1.52588			−0.109835			−0.0549174	−	0.998491i	$-0.517490\pi$
$193$	−1.52588			−0.109835			−0.0549174	+	0.998491i	$0.517490\pi$
$194$	0.365323	+	0.963284i	0.0262287	+	0.0691598i
$195$		0			0
$196$	−3.64181	−	4.11079i	−0.260129	−	0.293628i
$197$	−17.9164	−	7.42122i	−1.27649	−	0.528740i	−0.361560	−	0.932349i	$-0.617756\pi$
$197$	−17.9164	−	7.42122i	−1.27649	−	0.528740i	−0.914932	+	0.403609i	$0.867756\pi$
$198$		0			0
$199$	5.43647	−	5.43647i	0.385381	−	0.385381i	−0.487655	−	0.873036i	$-0.662148\pi$
$199$	5.43647	−	5.43647i	0.385381	−	0.385381i	0.873036	+	0.487655i	$0.162148\pi$
$200$	−4.19475	−	13.4617i	−0.296614	−	0.951887i
$201$		0			0
$202$	−0.426228	+	14.1047i	−0.0299893	+	0.992401i
$203$	−12.3677	−	5.12288i	−0.868045	−	0.359556i
$204$		0			0
$205$	0.273192	+	0.659544i	0.0190806	+	0.0460645i
$206$	16.7311	+	7.53010i	1.16571	+	0.524647i
$207$		0			0
$208$	−13.6067	+	3.79302i	−0.943452	+	0.262999i
$209$	−34.9067			−2.41454
$210$		0			0
$211$	14.3300	−	5.93566i	0.986515	−	0.408628i	0.169680	−	0.985499i	$-0.445727\pi$
$211$	14.3300	−	5.93566i	0.986515	−	0.408628i	0.816835	+	0.576871i	$0.195727\pi$
$212$	−3.09808	−	8.97803i	−0.212777	−	0.616614i
$213$		0			0
$214$	−0.194526	+	6.43724i	−0.0132975	+	0.440041i
$215$	0.535025	−	0.535025i	0.0364884	−	0.0364884i
$216$		0			0
$217$	0.262982	+	0.262982i	0.0178524	+	0.0178524i
$218$	0.452568	−	0.426018i	0.0306518	−	0.0288536i
$219$		0			0
$220$	−1.25517	−	0.0759293i	−0.0846239	−	0.00511915i
$221$	10.8285	+	26.1423i	0.728404	+	1.75852i
$222$		0			0
$223$			1.71374i			0.114760i	0.998352	+	0.0573802i	$0.0182747\pi$
$223$			1.71374i			0.114760i	−0.998352	+	0.0573802i	$0.981725\pi$
$224$	6.03611	−	9.98471i	0.403304	−	0.667131i
$225$		0			0
$226$	−3.46171	−	9.12784i	−0.230270	−	0.607175i
$227$	17.5958	−	7.28843i	1.16788	−	0.483750i	0.287386	−	0.957815i	$-0.407214\pi$
$227$	17.5958	−	7.28843i	1.16788	−	0.483750i	0.880490	+	0.474064i	$0.157214\pi$
$228$		0			0
$229$	−2.36650	+	5.71324i	−0.156383	+	0.377541i	−0.982580	−	0.185839i	$-0.940500\pi$
$229$	−2.36650	+	5.71324i	−0.156383	+	0.377541i	0.826197	+	0.563381i	$0.190500\pi$
$230$	0.204079	+	0.216797i	0.0134565	+	0.0142952i
$231$		0			0
$232$	−1.66147	+	18.2824i	−0.109081	+	1.20030i
$233$	−9.63587	−	9.63587i	−0.631267	−	0.631267i	0.317119	−	0.948386i	$-0.397285\pi$
$233$	−9.63587	−	9.63587i	−0.631267	−	0.631267i	−0.948386	+	0.317119i	$0.897285\pi$
$234$		0			0
$235$	0.149303	−	0.360449i	0.00973944	−	0.0235131i
$236$	3.46085	+	10.0293i	0.225282	+	0.652852i
$237$		0			0
$238$	−21.3132	−	9.59234i	−1.38153	−	0.621779i
$239$		−	20.8820i		−	1.35075i	−0.737477	−	0.675373i	$-0.763983\pi$
$239$		−	20.8820i		−	1.35075i	0.737477	−	0.675373i	$-0.236017\pi$
$240$		0			0
$241$		−	18.0182i		−	1.16066i	−0.814383	−	0.580328i	$-0.802924\pi$
$241$		−	18.0182i		−	1.16066i	0.814383	−	0.580328i	$-0.197076\pi$
$242$	9.06595	−	20.1436i	0.582781	−	1.29488i
$243$		0			0
$244$	12.7556	−	26.1973i	0.816596	−	1.67711i
$245$	−0.128056	+	0.309155i	−0.00818121	+	0.0197512i
$246$		0			0
$247$	16.8940	+	16.8940i	1.07494	+	1.07494i
$248$	0.237020	−	0.451597i	0.0150508	−	0.0286765i
$249$		0			0
$250$	−1.25300	+	1.17949i	−0.0792467	+	0.0745976i
$251$	−2.98953	+	7.21736i	−0.188697	+	0.455556i	−0.989709	−	0.143093i	$-0.954295\pi$
$251$	−2.98953	+	7.21736i	−0.188697	+	0.455556i	0.801012	+	0.598648i	$0.204295\pi$
$252$		0			0
$253$	−8.23521	+	3.41114i	−0.517743	+	0.214456i
$254$	16.4660	−	6.24470i	1.03317	−	0.391828i
$255$		0			0
$256$	−15.5350	−	3.82931i	−0.970938	−	0.239332i
$257$			17.6818i			1.10296i	0.834188	+	0.551480i	$0.185937\pi$
$257$			17.6818i			1.10296i	−0.834188	+	0.551480i	$0.814063\pi$
$258$		0			0
$259$	−9.26617	−	22.3705i	−0.575772	−	1.39004i
$260$	0.570728	+	0.644224i	0.0353950	+	0.0399531i
$261$		0			0
$262$	−12.4250	−	13.1993i	−0.767617	−	0.815455i
$263$	16.2323	+	16.2323i	1.00093	+	1.00093i	1.00000		0.000928003i	$0.000295393\pi$
$263$	16.2323	+	16.2323i	1.00093	+	1.00093i	0.000928003		1.00000i	$0.499705\pi$
$264$		0			0
$265$	−0.409195	+	0.409195i	−0.0251367	+	0.0251367i
$266$	−19.7253	−	0.596076i	−1.20943	−	0.0365478i
$267$		0			0
$268$	8.09610	+	3.94205i	0.494548	+	0.240799i
$269$	−19.7245	+	8.17017i	−1.20263	+	0.498144i	−0.891846	−	0.452338i	$-0.850590\pi$
$269$	−19.7245	+	8.17017i	−1.20263	+	0.498144i	−0.310779	+	0.950482i	$0.600590\pi$
$270$		0			0
$271$	1.66527			0.101158			0.0505790	−	0.998720i	$-0.483893\pi$
$271$	1.66527			0.101158			0.0505790	+	0.998720i	$0.483893\pi$
$272$	−3.86363	+	31.8176i	−0.234267	+	1.92923i
$273$		0			0
$274$	5.37960	−	11.9529i	0.324994	−	0.722102i
$275$	−9.84284	−	23.7627i	−0.593545	−	1.43295i
$276$		0			0
$277$	−13.6184	−	5.64093i	−0.818251	−	0.338931i	−0.0660102	−	0.997819i	$-0.521027\pi$
$277$	−13.6184	−	5.64093i	−0.818251	−	0.338931i	−0.752241	+	0.658888i	$0.771027\pi$
$278$	4.44584	+	0.134348i	0.266644	+	0.00805768i
$279$		0			0
$280$	−0.707985	−	0.0643403i	−0.0423102	−	0.00384507i
$281$	7.90436	−	7.90436i	0.471535	−	0.471535i	−0.430876	−	0.902411i	$-0.641795\pi$
$281$	7.90436	−	7.90436i	0.471535	−	0.471535i	0.902411	+	0.430876i	$0.141795\pi$
$282$		0			0
$283$	−1.61230	−	0.667835i	−0.0958411	−	0.0396987i	0.334248	−	0.942485i	$-0.391518\pi$
$283$	−1.61230	−	0.667835i	−0.0958411	−	0.0396987i	−0.430089	+	0.902787i	$0.641518\pi$
$284$	−23.0406	−	1.39380i	−1.36721	−	0.0827067i
$285$		0			0
$286$	−24.0923	+	9.13696i	−1.42461	+	0.540280i
$287$	−12.0827			−0.713219
$288$		0			0
$289$	47.2056			2.77680
$290$	1.04586	−	0.396640i	0.0614151	−	0.0232915i
$291$		0			0
$292$	−0.954636	+	15.7809i	−0.0558659	+	0.923509i
$293$	19.8242	+	8.21146i	1.15814	+	0.479718i	0.877256	−	0.480022i	$-0.159371\pi$
$293$	19.8242	+	8.21146i	1.15814	+	0.479718i	0.280887	+	0.959741i	$0.409371\pi$
$294$		0			0
$295$	0.457110	−	0.457110i	0.0266140	−	0.0266140i
$296$	−25.5082	+	21.2582i	−1.48264	+	1.23561i
$297$		0			0
$298$	−20.8304	−	0.629472i	−1.20667	−	0.0364643i
$299$	5.63656	+	2.33474i	0.325971	+	0.135022i
$300$		0			0
$301$	4.90077	+	11.8315i	0.282475	+	0.681956i
$302$	7.15128	−	15.8894i	0.411510	−	0.914332i
$303$		0			0
$304$	7.26689	+	26.0685i	0.416785	+	1.49513i
$305$	−1.77537			−0.101658
$306$		0			0
$307$	15.0549	−	6.23596i	0.859231	−	0.355905i	0.0908245	−	0.995867i	$-0.471050\pi$
$307$	15.0549	−	6.23596i	0.859231	−	0.355905i	0.768407	+	0.639962i	$0.221050\pi$
$308$	9.31708	−	19.1352i	0.530890	−	1.09033i
$309$		0			0
$310$	−0.0310615		0.000938645i	−0.00176418		5.33115e-5i
$311$	4.52683	−	4.52683i	0.256693	−	0.256693i	−0.567015	−	0.823708i	$-0.691902\pi$
$311$	4.52683	−	4.52683i	0.256693	−	0.256693i	0.823708	+	0.567015i	$0.191902\pi$
$312$		0			0
$313$	7.32857	+	7.32857i	0.414235	+	0.414235i	0.883211	−	0.468976i	$-0.155377\pi$
$313$	7.32857	+	7.32857i	0.414235	+	0.414235i	−0.468976	+	0.883211i	$0.655377\pi$
$314$	3.03758	+	3.22688i	0.171420	+	0.182103i
$315$		0			0
$316$	11.8940	−	10.5371i	0.669092	−	0.592758i
$317$	−5.30033	−	12.7961i	−0.297696	−	0.718703i	−0.999977	−	0.00680237i	$-0.997835\pi$
$317$	−5.30033	−	12.7961i	−0.297696	−	0.718703i	0.702280	−	0.711900i	$-0.252165\pi$
$318$		0			0
$319$			33.4871i			1.87491i
$320$	0.204599	+	0.953177i	0.0114374	+	0.0532842i
$321$		0			0
$322$	−4.71185	+	1.78696i	−0.262581	+	0.0995833i
$323$	50.0850	−	20.7459i	2.78680	−	1.15433i
$324$		0			0
$325$	−6.73690	+	16.2643i	−0.373696	+	0.902182i
$326$	−10.1651	+	9.56878i	−0.562993	+	0.529965i
$327$		0			0
$328$	4.92937	+	15.8192i	0.272179	+	0.873471i
$329$	4.66926	+	4.66926i	0.257425	+	0.257425i
$330$		0			0
$331$	7.53511	−	18.1914i	0.414167	−	0.999888i	−0.569839	−	0.821756i	$-0.692995\pi$
$331$	7.53511	−	18.1914i	0.414167	−	0.999888i	0.984007	−	0.178132i	$-0.0570054\pi$
$332$	9.85578	+	4.79885i	0.540906	+	0.263371i
$333$		0			0
$334$	−1.77398	+	3.94160i	−0.0970678	+	0.215675i
$335$		−	0.548668i		−	0.0299769i
$336$		0			0
$337$		−	4.94510i		−	0.269377i	−0.990888	−	0.134688i	$-0.956997\pi$
$337$		−	4.94510i		−	0.269377i	0.990888	−	0.134688i	$-0.0430034\pi$
$338$	−0.682837	−	0.307322i	−0.0371414	−	0.0167161i
$339$		0			0
$340$	1.84608	−	0.637036i	0.100118	−	0.0345481i
$341$	0.356027	−	0.859525i	0.0192799	−	0.0465459i
$342$		0			0
$343$	−14.2138	−	14.2138i	−0.767473	−	0.767473i
$344$	13.4910	−	11.2432i	0.727386	−	0.606193i
$345$		0			0
$346$	−3.30185	−	3.50763i	−0.177509	−	0.188571i
$347$	−7.14620	+	17.2524i	−0.383628	+	0.926160i	0.607630	+	0.794220i	$0.292120\pi$
$347$	−7.14620	+	17.2524i	−0.383628	+	0.926160i	−0.991258	+	0.131939i	$0.957880\pi$
$348$		0			0
$349$	17.4196	−	7.21544i	0.932451	−	0.386234i	0.135843	−	0.990730i	$-0.456626\pi$
$349$	17.4196	−	7.21544i	0.932451	−	0.386234i	0.796608	+	0.604497i	$0.206626\pi$
$350$	−5.15627	−	13.5961i	−0.275614	−	0.726740i
$351$		0			0
$352$	−28.8539	−	4.39178i	−1.53792	−	0.234083i
$353$		−	19.5356i		−	1.03978i	−0.854234	−	0.519888i	$-0.825974\pi$
$353$		−	19.5356i		−	1.03978i	0.854234	−	0.519888i	$-0.174026\pi$
$354$		0			0
$355$	0.538223	+	1.29938i	0.0285659	+	0.0689642i
$356$	1.24633	−	20.6028i	0.0660553	−	1.09195i
$357$		0			0
$358$	13.3070	−	12.5263i	0.703294	−	0.662036i
$359$	18.9311	+	18.9311i	0.999144	+	0.999144i	1.00000		0.000855334i	$-0.000272261\pi$
$359$	18.9311	+	18.9311i	0.999144	+	0.999144i	−0.000855334		1.00000i	$0.500272\pi$
$360$		0			0
$361$	18.9316	−	18.9316i	0.996398	−	0.996398i
$362$	−0.835681	+	27.6542i	−0.0439224	+	1.45347i
$363$		0			0
$364$	−13.7703	+	4.75176i	−0.721759	+	0.249060i
$365$	0.889972	−	0.368638i	0.0465832	−	0.0192954i
$366$		0			0
$367$	29.9760			1.56474			0.782368	−	0.622817i	$-0.214012\pi$
$367$	29.9760			1.56474			0.782368	+	0.622817i	$0.214012\pi$
$368$	4.26186	+	5.43996i	0.222165	+	0.283578i
$369$		0			0
$370$	1.84496	+	0.830354i	0.0959150	+	0.0431681i
$371$	−3.74818	−	9.04891i	−0.194596	−	0.469796i
$372$		0			0
$373$	4.66594	+	1.93269i	0.241593	+	0.100071i	0.500195	−	0.865913i	$-0.333262\pi$
$373$	4.66594	+	1.93269i	0.241593	+	0.100071i	−0.258602	+	0.965984i	$0.583262\pi$
$374$	−1.76597	+	58.4394i	−0.0913163	+	3.02183i
$375$		0			0
$376$	4.20831	−	8.01814i	0.217027	−	0.413504i
$377$	16.2070	−	16.2070i	0.834701	−	0.834701i
$378$		0			0
$379$	18.0310	+	7.46866i	0.926188	+	0.383640i	0.794231	−	0.607616i	$-0.207874\pi$
$379$	18.0310	+	7.46866i	0.926188	+	0.383640i	0.131957	+	0.991255i	$0.457874\pi$
$380$	1.23424	−	1.09343i	0.0633153	−	0.0560920i
$381$		0			0
$382$	−2.84220	−	7.49432i	−0.145420	−	0.383443i
$383$	−30.1958			−1.54293			−0.771466	−	0.636270i	$-0.780476\pi$
$383$	−30.1958			−1.54293			−0.771466	+	0.636270i	$0.780476\pi$
$384$		0			0
$385$	−1.29678			−0.0660902
$386$	0.765202	+	2.01769i	0.0389478	+	0.102697i
$387$		0			0
$388$	1.09056	−	0.966144i	0.0553648	−	0.0490485i
$389$	7.21945	+	2.99039i	0.366040	+	0.151619i	0.558120	−	0.829761i	$-0.311523\pi$
$389$	7.21945	+	2.99039i	0.366040	+	0.151619i	−0.192079	+	0.981379i	$0.561523\pi$
$390$		0			0
$391$	9.78878	−	9.78878i	0.495040	−	0.495040i
$392$	−3.60944	+	6.87712i	−0.182304	+	0.347347i
$393$		0			0
$394$	−0.828383	+	27.4127i	−0.0417333	+	1.38103i
$395$	−0.894499	−	0.370514i	−0.0450071	−	0.0186426i
$396$		0			0
$397$	3.97647	+	9.60005i	0.199573	+	0.481813i	0.991705	−	0.128538i	$-0.0410284\pi$
$397$	3.97647	+	9.60005i	0.199573	+	0.481813i	−0.792131	+	0.610351i	$0.791028\pi$
$398$	−9.91502	−	4.46241i	−0.496995	−	0.223681i
$399$		0			0
$400$	−15.6970	+	12.2976i	−0.784851	+	0.614881i
$401$	−17.1468			−0.856270			−0.428135	−	0.903715i	$-0.640829\pi$
$401$	−17.1468			−0.856270			−0.428135	+	0.903715i	$0.640829\pi$
$402$		0			0
$403$	−0.588299	+	0.243682i	−0.0293053	+	0.0121386i
$404$	18.8645	−	6.50966i	0.938546	−	0.323868i
$405$		0			0
$406$	−0.571834	+	18.9231i	−0.0283797	+	0.939136i
$407$	−42.8300	+	42.8300i	−2.12300	+	2.12300i
$408$		0			0
$409$	1.46166	+	1.46166i	0.0722746	+	0.0722746i	0.742320	−	0.670045i	$-0.233725\pi$
$409$	1.46166	+	1.46166i	0.0722746	+	0.0722746i	−0.670045	+	0.742320i	$0.733725\pi$
$410$	0.735122	−	0.691997i	0.0363051	−	0.0341753i
$411$		0			0
$412$	1.56677	−	25.9000i	0.0771892	−	1.27600i
$413$	4.18707	+	10.1085i	0.206032	+	0.497406i
$414$		0			0
$415$		−	0.667921i		−	0.0327869i
$416$	11.8391	+	16.0901i	0.580459	+	0.788884i
$417$		0			0
$418$	17.5051	+	46.1576i	0.856205	+	2.25764i
$419$	−27.9116	+	11.5614i	−1.36357	+	0.564810i	−0.940038	−	0.341071i	$-0.889210\pi$
$419$	−27.9116	+	11.5614i	−1.36357	+	0.564810i	−0.423534	+	0.905880i	$0.639210\pi$
$420$		0			0
$421$	−2.85906	+	6.90238i	−0.139342	+	0.336401i	−0.978110	−	0.208087i	$-0.933276\pi$
$421$	−2.85906	+	6.90238i	−0.139342	+	0.336401i	0.838768	+	0.544489i	$0.183276\pi$
$422$	−15.0351	−	15.9721i	−0.731895	−	0.777507i
$423$		0			0
$424$	−10.3181	+	8.59898i	−0.501093	+	0.417603i
$425$	28.2455	+	28.2455i	1.37011	+	1.37011i
$426$		0			0
$427$	11.4991	−	27.7613i	0.556482	−	1.34347i
$428$	8.60960	−	2.97095i	0.416161	−	0.143606i
$429$		0			0
$430$	−0.975777	−	0.439164i	−0.0470562	−	0.0211784i
$431$			13.7945i			0.664456i	0.943199	+	0.332228i	$0.107800\pi$
$431$			13.7945i			0.664456i	−0.943199	+	0.332228i	$0.892200\pi$
$432$		0			0
$433$		−	12.2681i		−	0.589566i	−0.955564	−	0.294783i	$-0.904753\pi$
$433$		−	12.2681i		−	0.589566i	0.955564	−	0.294783i	$-0.0952474\pi$
$434$	0.215863	−	0.479626i	0.0103618	−	0.0230228i
$435$		0			0
$436$	−0.790285	−	0.384795i	−0.0378478	−	0.0184284i
$437$	4.47304	−	10.7989i	0.213974	−	0.516580i
$438$		0			0
$439$	0.996563	+	0.996563i	0.0475633	+	0.0475633i	0.730488	−	0.682925i	$-0.239292\pi$
$439$	0.996563	+	0.996563i	0.0475633	+	0.0475633i	−0.682925	+	0.730488i	$0.739292\pi$
$440$	0.529048	+	1.69781i	0.0252214	+	0.0809400i
$441$		0			0
$442$	29.1380	−	27.4286i	1.38595	−	1.30465i
$443$	−13.4819	+	32.5483i	−0.640546	+	1.54642i	0.185398	+	0.982663i	$0.440642\pi$
$443$	−13.4819	+	32.5483i	−0.640546	+	1.54642i	−0.825944	+	0.563752i	$0.809358\pi$
$444$		0			0
$445$	−1.16191	+	0.481277i	−0.0550796	+	0.0228147i
$446$	2.26610	−	0.859413i	0.107303	−	0.0406944i
$447$		0			0
$448$	−16.2299	−	2.97445i	−0.766792	−	0.140530i
$449$			19.2458i			0.908264i	0.890934	+	0.454132i	$0.150051\pi$
$449$			19.2458i			0.908264i	−0.890934	+	0.454132i	$0.849949\pi$
$450$		0			0
$451$	11.5666	+	27.9242i	0.544649	+	1.31490i
$452$	−10.3339	+	9.15493i	−0.486064	+	0.430612i
$453$		0			0
$454$	−18.4616	−	19.6122i	−0.866447	−	0.920445i
$455$	0.627614	+	0.627614i	0.0294230	+	0.0294230i
$456$		0			0
$457$	−3.82020	+	3.82020i	−0.178701	+	0.178701i	−0.790789	−	0.612088i	$-0.790330\pi$
$457$	−3.82020	+	3.82020i	−0.178701	+	0.178701i	0.612088	+	0.790789i	$0.290330\pi$
$458$	8.74146	+	0.264157i	0.408461	+	0.0123433i
$459$		0			0
$460$	0.184331	−	0.378576i	0.00859450	−	0.0176512i
$461$	−28.9476	+	11.9905i	−1.34823	+	0.558453i	−0.935798	−	0.352537i	$-0.885319\pi$
$461$	−28.9476	+	11.9905i	−1.34823	+	0.558453i	−0.412427	+	0.910990i	$0.635319\pi$
$462$		0			0
$463$	0.144143			0.00669887			0.00334944	−	0.999994i	$-0.498934\pi$
$463$	0.144143			0.00669887			0.00334944	+	0.999994i	$0.498934\pi$
$464$	25.0083	−	6.97136i	1.16098	−	0.323637i
$465$		0			0
$466$	−7.90941	+	17.5739i	−0.366396	+	0.814094i
$467$	−1.85206	−	4.47126i	−0.0857029	−	0.206905i	0.875218	−	0.483729i	$-0.160718\pi$
$467$	−1.85206	−	4.47126i	−0.0857029	−	0.206905i	−0.960921	+	0.276824i	$0.910718\pi$
$468$		0			0
$469$	8.57946	+	3.55373i	0.396163	+	0.164096i
$470$	−0.551499	−	0.0166657i	−0.0254388	−	0.000768731i
$471$		0			0
$472$	11.5263	−	9.60587i	0.530542	−	0.442146i
$473$	22.6523	−	22.6523i	1.04155	−	1.04155i
$474$		0			0
$475$	31.1602	+	12.9070i	1.42973	+	0.592212i
$476$	−1.99585	+	32.9931i	−0.0914798	+	1.51224i
$477$		0			0
$478$	−27.6126	+	10.4720i	−1.26297	+	0.478978i
$479$	32.1234			1.46776			0.733878	−	0.679282i	$-0.237709\pi$
$479$	32.1234			1.46776			0.733878	+	0.679282i	$0.237709\pi$
$480$		0			0
$481$	41.4574			1.89030
$482$	−23.8257	+	9.03586i	−1.08523	+	0.411572i
$483$		0			0
$484$	−31.1826	−	1.88633i	−1.41739	−	0.0857422i
$485$	−0.0820163	−	0.0339723i	−0.00372417	−	0.00154260i
$486$		0			0
$487$	−9.43579	+	9.43579i	−0.427577	+	0.427577i	−0.887802	−	0.460225i	$-0.847769\pi$
$487$	−9.43579	+	9.43579i	−0.427577	+	0.427577i	0.460225	+	0.887802i	$0.347769\pi$
$488$	−41.0378	−	3.72943i	−1.85769	−	0.168823i
$489$		0			0
$490$	0.473018	+	0.0142941i	0.0213688	+	0.000645741i
$491$	−27.9412	−	11.5736i	−1.26097	−	0.522311i	−0.350762	−	0.936464i	$-0.614078\pi$
$491$	−27.9412	−	11.5736i	−1.26097	−	0.522311i	−0.910207	+	0.414154i	$0.864078\pi$
$492$		0			0
$493$	−19.9022	−	48.0481i	−0.896349	−	2.16398i
$494$	13.8671	−	30.8113i	0.623911	−	1.38627i
$495$		0			0
$496$	−0.716015	−	0.0869461i	−0.0321500	−	0.00390399i
$497$	−23.8044			−1.06777
$498$		0			0
$499$	−22.7996	+	9.44389i	−1.02065	+	0.422767i	−0.829329	−	0.558761i	$-0.811277\pi$
$499$	−22.7996	+	9.44389i	−1.02065	+	0.422767i	−0.191320	+	0.981528i	$0.561277\pi$
$500$	2.18802	+	1.06536i	0.0978512	+	0.0476444i
$501$		0			0
$502$	11.0428	+	0.333702i	0.492865	+	0.0148938i
$503$	10.5553	−	10.5553i	0.470637	−	0.470637i	−0.431483	−	0.902121i	$-0.642010\pi$
$503$	10.5553	−	10.5553i	0.470637	−	0.470637i	0.902121	+	0.431483i	$0.142010\pi$
$504$		0			0
$505$	−0.859797	−	0.859797i	−0.0382605	−	0.0382605i
$506$	8.64042	+	9.17890i	0.384113	+	0.408052i
$507$		0			0
$508$	−16.5149	−	18.6416i	−0.732731	−	0.827089i
$509$	12.2451	+	29.5623i	0.542754	+	1.31032i	0.922772	+	0.385345i	$0.125918\pi$
$509$	12.2451	+	29.5623i	0.542754	+	1.31032i	−0.380018	+	0.924979i	$0.624082\pi$
$510$		0			0
$511$			16.3041i			0.721250i
$512$	2.72701	+	22.4625i	0.120518	+	0.992711i
$513$		0			0
$514$	23.3809	−	8.86714i	1.03129	−	0.391113i
$515$	−1.46064	+	0.605017i	−0.0643635	+	0.0266602i
$516$		0			0
$517$	6.32128	−	15.2609i	0.278010	−	0.671174i
$518$	−24.9340	+	23.4712i	−1.09554	+	1.03127i
$519$		0			0
$520$	0.565655	−	1.07775i	0.0248056	−	0.0472624i
$521$	8.34477	+	8.34477i	0.365591	+	0.365591i	0.865866	−	0.500275i	$-0.166768\pi$
$521$	8.34477	+	8.34477i	0.365591	+	0.365591i	−0.500275	+	0.865866i	$0.666768\pi$
$522$		0			0
$523$	3.09553	−	7.47328i	0.135358	−	0.326784i	−0.841637	−	0.540043i	$-0.818408\pi$
$523$	3.09553	−	7.47328i	0.135358	−	0.326784i	0.976996	+	0.213259i	$0.0684079\pi$
$524$	−11.2227	+	23.0489i	−0.490265	+	1.00690i
$525$		0			0
$526$	13.3240	−	29.6045i	0.580952	−	1.29082i
$527$			1.44487i			0.0629393i
$528$		0			0
$529$			20.0152i			0.870226i
$530$	0.746290	+	0.335880i	0.0324168	+	0.0145897i
$531$		0			0
$532$	9.10372	+	26.3819i	0.394696	+	1.14380i
$533$	7.91672	−	19.1126i	0.342911	−	0.827861i
$534$		0			0
$535$	−0.392403	−	0.392403i	−0.0169651	−	0.0169651i
$536$	1.15256	−	12.6825i	0.0497829	−	0.547799i
$537$		0			0
$538$	20.6951	+	21.9848i	0.892227	+	0.947832i
$539$	−5.42173	+	13.0892i	−0.233530	+	0.563792i
$540$		0			0
$541$	−36.3196	+	15.0441i	−1.56150	+	0.646795i	−0.985350	−	0.170547i	$-0.945447\pi$
$541$	−36.3196	+	15.0441i	−1.56150	+	0.646795i	−0.576153	+	0.817342i	$0.695447\pi$
$542$	−0.835107	−	2.20201i	−0.0358709	−	0.0945844i
$543$		0			0
$544$	44.0104	−	10.8471i	1.88693	−	0.465066i
$545$			0.0535572i			0.00229414i
$546$		0			0
$547$	−13.4841	−	32.5535i	−0.576538	−	1.39189i	−0.895901	−	0.444253i	$-0.853469\pi$
$547$	−13.4841	−	32.5535i	−0.576538	−	1.39189i	0.319363	−	0.947632i	$-0.396531\pi$
$548$	−18.5033	−	1.11932i	−0.790422	−	0.0478150i
$549$		0			0
$550$	−26.4857	+	24.9319i	−1.12936	+	1.06310i
$551$	−31.0503	−	31.0503i	−1.32279	−	1.32279i
$552$		0			0
$553$	11.5874	−	11.5874i	0.492745	−	0.492745i
$554$	−0.629661	+	20.8367i	−0.0267517	+	0.885264i
$555$		0			0
$556$	−2.05187	−	5.94617i	−0.0870186	−	0.252174i
$557$	5.30271	−	2.19645i	0.224683	−	0.0930667i	−0.267502	−	0.963557i	$-0.586198\pi$
$557$	5.30271	−	2.19645i	0.224683	−	0.0930667i	0.492185	+	0.870491i	$0.336198\pi$
$558$		0			0
$559$	−21.9263			−0.927385
$560$	0.269965	+	0.968444i	0.0114081	+	0.0409242i
$561$		0			0
$562$	−14.4160	−	6.48813i	−0.608101	−	0.273685i
$563$	16.8002	+	40.5592i	0.708043	+	1.70937i	0.704833	+	0.709373i	$0.251022\pi$
$563$	16.8002	+	40.5592i	0.708043	+	1.70937i	0.00321001	+	0.999995i	$0.498978\pi$
$564$		0			0
$565$	0.777166	+	0.321913i	0.0326956	+	0.0135430i
$566$	−0.0745461	+	2.46687i	−0.00313341	+	0.103690i
$567$		0			0
$568$	9.71147	+	31.1659i	0.407484	+	1.30769i
$569$	−3.25683	+	3.25683i	−0.136534	+	0.136534i	−0.772070	−	0.635537i	$-0.780779\pi$
$569$	−3.25683	+	3.25683i	−0.136534	+	0.136534i	0.635537	+	0.772070i	$0.280779\pi$
$570$		0			0
$571$	−25.6347	−	10.6182i	−1.07278	−	0.444359i	−0.224807	−	0.974403i	$-0.572175\pi$
$571$	−25.6347	−	10.6182i	−1.07278	−	0.444359i	−0.847970	+	0.530044i	$0.822175\pi$
$572$	24.1639	+	27.2756i	1.01034	+	1.14045i
$573$		0			0
$574$	6.05928	+	15.9771i	0.252909	+	0.666872i
$575$	8.61262			0.359171
$576$		0			0
$577$	−14.9524			−0.622478			−0.311239	−	0.950332i	$-0.600744\pi$
$577$	−14.9524			−0.622478			−0.311239	+	0.950332i	$0.600744\pi$
$578$	−23.6729	−	62.4206i	−0.984661	−	2.59635i
$579$		0			0
$580$	−1.04897	−	1.18405i	−0.0435559	−	0.0491649i
$581$	10.4442	+	4.32613i	0.433299	+	0.179478i
$582$		0			0
$583$	−17.3248	+	17.3248i	−0.717520	+	0.717520i
$584$	21.3461	−	6.65156i	0.883307	−	0.275243i
$585$		0			0
$586$	0.916592	−	30.3317i	0.0378641	−	1.25299i
$587$	−3.16860	−	1.31248i	−0.130782	−	0.0541718i	0.316333	−	0.948648i	$-0.397548\pi$
$587$	−3.16860	−	1.31248i	−0.130782	−	0.0541718i	−0.447115	+	0.894477i	$0.647548\pi$
$588$		0			0
$589$	0.466860	+	1.12710i	0.0192366	+	0.0464413i
$590$	−0.833676	−	0.375209i	−0.0343219	−	0.0154471i
$591$		0			0
$592$	40.9020	+	23.0692i	1.68106	+	0.948140i
$593$	−3.48166			−0.142974			−0.0714872	−	0.997442i	$-0.522775\pi$
$593$	−3.48166			−0.142974			−0.0714872	+	0.997442i	$0.522775\pi$
$594$		0			0
$595$	1.86066	−	0.770711i	0.0762796	−	0.0315961i
$596$	9.61377	+	27.8600i	0.393795	+	1.14119i
$597$		0			0
$598$	0.260612	−	8.62414i	0.0106572	−	0.352667i
$599$	20.5605	−	20.5605i	0.840079	−	0.840079i	−0.148790	−	0.988869i	$-0.547538\pi$
$599$	20.5605	−	20.5605i	0.840079	−	0.840079i	0.988869	+	0.148790i	$0.0475377\pi$
$600$		0			0
$601$	6.82607	+	6.82607i	0.278441	+	0.278441i	0.832487	−	0.554045i	$-0.186917\pi$
$601$	6.82607	+	6.82607i	0.278441	+	0.278441i	−0.554045	+	0.832487i	$0.686917\pi$
$602$	13.1873	−	12.4137i	0.537474	−	0.505943i
$603$		0			0
$604$	−24.5970	−	1.48795i	−1.00084	−	0.0605437i
$605$	0.728417	+	1.75855i	0.0296144	+	0.0714954i
$606$		0			0
$607$		−	13.6931i		−	0.555787i	−0.960612	−	0.277894i	$-0.910364\pi$
$607$		−	13.6931i		−	0.555787i	0.960612	−	0.277894i	$-0.0896362\pi$
$608$	30.8265	−	22.6820i	1.25018	−	0.919878i
$609$		0			0
$610$	0.890322	+	2.34760i	0.0360481	+	0.0950516i
$611$	−10.4453	+	4.32658i	−0.422571	+	0.175035i
$612$		0			0
$613$	−5.13394	+	12.3944i	−0.207358	+	0.500606i	−0.993006	−	0.118068i	$-0.962330\pi$
$613$	−5.13394	+	12.3944i	−0.207358	+	0.500606i	0.785648	+	0.618674i	$0.212330\pi$
$614$	−15.7957	−	16.7801i	−0.637463	−	0.677191i
$615$		0			0
$616$	−29.9752	−	2.72408i	−1.20773	−	0.109757i
$617$	19.4552	+	19.4552i	0.783236	+	0.783236i	0.980375	−	0.197140i	$-0.0631652\pi$
$617$	19.4552	+	19.4552i	0.783236	+	0.783236i	−0.197140	+	0.980375i	$0.563165\pi$
$618$		0			0
$619$	−7.30269	+	17.6303i	−0.293520	+	0.708620i	0.706480	+	0.707733i	$0.250282\pi$
$619$	−7.30269	+	17.6303i	−0.293520	+	0.708620i	−1.00000		0.000886580i	$0.999718\pi$
$620$	0.0143357	+	0.0415438i	0.000575735	+	0.00166844i
$621$		0			0
$622$	−8.25602	−	3.71575i	−0.331036	−	0.148988i
$623$		−	21.2858i		−	0.852799i
$624$		0			0
$625$			24.7775i			0.991099i
$626$	6.01551	−	13.3658i	0.240428	−	0.534206i
$627$		0			0
$628$	2.74365	−	5.63486i	0.109484	−	0.224855i
$629$	35.9987	−	86.9085i	1.43536	−	3.46527i
$630$		0			0
$631$	17.8228	+	17.8228i	0.709515	+	0.709515i	0.966433	−	0.256918i	$-0.0827071\pi$
$631$	17.8228	+	17.8228i	0.709515	+	0.709515i	−0.256918	+	0.966433i	$0.582707\pi$
$632$	−19.8980	−	10.4434i	−0.791501	−	0.415418i
$633$		0			0
$634$	−14.2625	+	13.4258i	−0.566435	+	0.533205i
$635$	−0.580710	+	1.40196i	−0.0230448	+	0.0556350i
$636$		0			0
$637$	8.95887	−	3.71089i	0.354963	−	0.147031i
$638$	44.2804	−	16.7932i	1.75308	−	0.664850i
$639$		0			0
$640$	1.15780	−	0.748547i	0.0457659	−	0.0295889i
$641$		−	18.3169i		−	0.723474i	−0.932280	−	0.361737i	$-0.882184\pi$
$641$		−	18.3169i		−	0.723474i	0.932280	−	0.361737i	$-0.117816\pi$
$642$		0			0
$643$	−8.48914	−	20.4946i	−0.334779	−	0.808228i	−0.998200	−	0.0599810i	$-0.980896\pi$
$643$	−8.48914	−	20.4946i	−0.334779	−	0.808228i	0.663421	−	0.748247i	$-0.269104\pi$
$644$	4.72584	+	5.33442i	0.186224	+	0.210205i
$645$		0			0
$646$	−52.5494	−	55.8244i	−2.06753	−	2.19638i
$647$	24.9793	+	24.9793i	0.982037	+	0.982037i	0.999841	−	0.0178043i	$-0.00566759\pi$
$647$	24.9793	+	24.9793i	0.982037	+	0.982037i	−0.0178043	+	0.999841i	$0.505668\pi$
$648$		0			0
$649$	19.3534	−	19.3534i	0.759689	−	0.759689i
$650$	24.8850	+	0.751996i	0.976069	+	0.0294957i
$651$		0			0
$652$	17.7506	+	8.64288i	0.695166	+	0.338481i
$653$	6.70064	−	2.77550i	0.262216	−	0.108614i	−0.247702	−	0.968836i	$-0.579675\pi$
$653$	6.70064	−	2.77550i	0.262216	−	0.108614i	0.509919	+	0.860223i	$0.329675\pi$
$654$		0			0
$655$	1.56201			0.0610329
$656$	18.4460	−	14.4513i	0.720195	−	0.564227i
$657$		0			0
$658$	3.83267	−	8.51579i	0.149413	−	0.331980i
$659$	−3.51969	−	8.49729i	−0.137108	−	0.331008i	0.840381	−	0.541997i	$-0.182332\pi$
$659$	−3.51969	−	8.49729i	−0.137108	−	0.331008i	−0.977488	+	0.210989i	$0.932332\pi$
$660$		0			0
$661$	6.03361	+	2.49920i	0.234680	+	0.0972078i	0.496925	−	0.867794i	$-0.334463\pi$
$661$	6.03361	+	2.49920i	0.234680	+	0.0972078i	−0.262244	+	0.965002i	$0.584463\pi$
$662$	−27.8334	−	0.841096i	−1.08178	−	0.0326901i
$663$		0			0
$664$	1.40306	−	15.4390i	0.0544495	−	0.599149i
$665$	1.20242	−	1.20242i	0.0466279	−	0.0466279i
$666$		0			0
$667$	−10.3597	−	4.29113i	−0.401129	−	0.166153i
$668$	6.10165	+	0.369107i	0.236080	+	0.0142812i
$669$		0			0
$670$	−0.725511	+	0.275148i	−0.0280289	+	0.0106299i
$671$	−75.1670			−2.90179
$672$		0			0
$673$	−36.2759			−1.39833			−0.699167	−	0.714958i	$-0.746446\pi$
$673$	−36.2759			−1.39833			−0.699167	+	0.714958i	$0.746446\pi$
$674$	−6.53898	+	2.47989i	−0.251872	+	0.0955218i
$675$		0			0
$676$	−0.0639437	+	1.05704i	−0.00245937	+	0.0406555i
$677$	−19.3813	−	8.02798i	−0.744882	−	0.308540i	−0.0222308	−	0.999753i	$-0.507077\pi$
$677$	−19.3813	−	8.02798i	−0.744882	−	0.308540i	−0.722652	+	0.691212i	$0.757077\pi$
$678$		0			0
$679$	1.06244	−	1.06244i	0.0407728	−	0.0407728i
$680$	−1.76814	−	2.12164i	−0.0678052	−	0.0813612i
$681$		0			0
$682$	−1.31510	−	0.0397410i	−0.0503579	−	0.00152176i
$683$	−8.60884	−	3.56590i	−0.329408	−	0.136445i	0.211849	−	0.977302i	$-0.432051\pi$
$683$	−8.60884	−	3.56590i	−0.329408	−	0.136445i	−0.541257	+	0.840857i	$0.682051\pi$
$684$		0			0
$685$	0.432232	+	1.04350i	0.0165147	+	0.0398701i
$686$	−11.6671	+	25.9231i	−0.445452	+	0.989749i
$687$		0			0
$688$	−21.6326	−	12.2010i	−0.824734	−	0.465161i
$689$	16.7696			0.638871
$690$		0			0
$691$	4.94706	−	2.04914i	0.188195	−	0.0779529i	−0.286596	−	0.958052i	$-0.592524\pi$
$691$	4.94706	−	2.04914i	0.188195	−	0.0779529i	0.474791	+	0.880099i	$0.342524\pi$
$692$	−2.98236	+	6.12510i	−0.113372	+	0.232842i
$693$		0			0
$694$	26.3968	+	0.797684i	1.00201	+	0.0302797i
$695$	−0.271011	+	0.271011i	−0.0102800	+	0.0102800i
$696$		0			0
$697$	−33.1921	−	33.1921i	−1.25724	−	1.25724i
$698$	−18.2767	−	19.4158i	−0.691785	−	0.734898i
$699$		0			0
$700$	−15.3925	+	13.6364i	−0.581780	+	0.515408i
$701$	0.265844	+	0.641804i	0.0100408	+	0.0242406i	0.928820	−	0.370530i	$-0.120824\pi$
$701$	0.265844	+	0.641804i	0.0100408	+	0.0242406i	−0.918780	+	0.394771i	$0.870824\pi$
$702$		0			0
$703$		−	79.4267i		−	2.99563i
$704$	8.66244	+	40.3563i	0.326478	+	1.52098i
$705$		0			0
$706$	−25.8322	+	9.79681i	−0.972209	+	0.368708i
$707$	19.0135	−	7.87564i	0.715076	−	0.296194i
$708$		0			0
$709$	−7.96079	+	19.2190i	−0.298974	+	0.721786i	0.700989	+	0.713172i	$0.252742\pi$
$709$	−7.96079	+	19.2190i	−0.298974	+	0.721786i	−0.999963	+	0.00861450i	$0.997258\pi$
$710$	1.44828	−	1.36332i	0.0543531	−	0.0511645i
$711$		0			0
$712$	−27.8684	+	8.68396i	−1.04441	+	0.325445i
$713$	0.220284	+	0.220284i	0.00824970	+	0.00824970i
$714$		0			0
$715$	0.849668	−	2.05128i	0.0317758	−	0.0767135i
$716$	−23.2369	−	11.3142i	−0.868405	−	0.422832i
$717$		0			0
$718$	15.5392	−	34.5265i	0.579917	−	1.28852i
$719$			0.421640i			0.0157245i	0.999969	+	0.00786226i	$0.00250266\pi$
$719$			0.421640i			0.0157245i	−0.999969	+	0.00786226i	$0.997497\pi$
$720$		0			0
$721$		−	26.7586i		−	0.996542i
$722$	−34.5274	−	15.5396i	−1.28497	−	0.578324i
$723$		0			0
$724$	36.9867	−	12.7631i	1.37460	−	0.474338i
$725$	12.3820	−	29.8929i	0.459858	−	1.11019i
$726$		0			0
$727$	13.5301	+	13.5301i	0.501804	+	0.501804i	0.911998	−	0.410194i	$-0.134539\pi$
$727$	13.5301	+	13.5301i	0.501804	+	0.501804i	−0.410194	+	0.911998i	$0.634539\pi$
$728$	13.1889	+	15.8257i	0.488813	+	0.586539i
$729$		0			0
$730$	−0.933762	−	0.991955i	−0.0345601	−	0.0367139i
$731$	−19.0393	+	45.9648i	−0.704193	+	1.70007i
$732$		0			0
$733$	−15.1560	+	6.27780i	−0.559798	+	0.231876i	−0.644597	−	0.764522i	$-0.722975\pi$
$733$	−15.1560	+	6.27780i	−0.559798	+	0.231876i	0.0847995	+	0.996398i	$0.472975\pi$
$734$	−15.0325	−	39.6377i	−0.554860	−	1.46305i
$735$		0			0
$736$	5.05608	−	8.36358i	0.186369	−	0.308285i
$737$		−	23.2299i		−	0.855683i
$738$		0			0
$739$	12.1357	+	29.2981i	0.446418	+	1.07775i	0.973654	+	0.228030i	$0.0732283\pi$
$739$	12.1357	+	29.2981i	0.446418	+	1.07775i	−0.527236	+	0.849719i	$0.676772\pi$
$740$	0.172770	−	2.85603i	0.00635114	−	0.104990i
$741$		0			0
$742$	−10.0858	+	9.49416i	−0.370263	+	0.348542i
$743$	19.5022	+	19.5022i	0.715466	+	0.715466i	0.967673	−	0.252207i	$-0.0811563\pi$
$743$	19.5022	+	19.5022i	0.715466	+	0.715466i	−0.252207	+	0.967673i	$0.581156\pi$
$744$		0			0
$745$	1.26979	−	1.26979i	0.0465214	−	0.0465214i
$746$	0.215734	−	7.13905i	0.00789859	−	0.261379i
$747$		0			0
$748$	78.1608	−	26.9713i	2.85784	−	0.986167i
$749$	8.67758	−	3.59437i	0.317072	−	0.131335i
$750$		0			0
$751$	−12.9491			−0.472520			−0.236260	−	0.971690i	$-0.575922\pi$
$751$	−12.9491			−0.472520			−0.236260	+	0.971690i	$0.575922\pi$
$752$	−12.7129	−	1.54373i	−0.463592	−	0.0562941i
$753$		0			0
$754$	−29.5582	−	13.3032i	−1.07645	−	0.484472i
$755$	0.574580	+	1.38716i	0.0209111	+	0.0504839i
$756$		0			0
$757$	−21.4252	−	8.87462i	−0.778713	−	0.322553i	−0.0423168	−	0.999104i	$-0.513474\pi$
$757$	−21.4252	−	8.87462i	−0.778713	−	0.322553i	−0.736396	+	0.676551i	$0.763474\pi$
$758$	0.833679	−	27.5880i	0.0302806	−	1.00204i
$759$		0			0
$760$	−2.06482	−	1.08372i	−0.0748988	−	0.0393105i
$761$	4.44075	−	4.44075i	0.160977	−	0.160977i	−0.622022	−	0.782999i	$-0.713689\pi$
$761$	4.44075	−	4.44075i	0.160977	−	0.160977i	0.782999	+	0.622022i	$0.213689\pi$
$762$		0			0
$763$	−0.837468	−	0.346890i	−0.0303184	−	0.0125583i
$764$	−8.48453	+	7.51657i	−0.306959	+	0.271940i
$765$		0			0
$766$	15.1427	+	39.9283i	0.547128	+	1.44267i
$767$	−18.7332			−0.676418
$768$		0			0
$769$	−52.6752			−1.89952			−0.949759	−	0.312982i	$-0.898672\pi$
$769$	−52.6752			−1.89952			−0.949759	+	0.312982i	$0.898672\pi$
$770$	0.650317	+	1.71476i	0.0234358	+	0.0617955i
$771$		0			0
$772$	2.28428	−	2.02368i	0.0822129	−	0.0728337i
$773$	2.67650	+	1.10864i	0.0962670	+	0.0398751i	0.430297	−	0.902687i	$-0.358409\pi$
$773$	2.67650	+	1.10864i	0.0962670	+	0.0398751i	−0.334030	+	0.942562i	$0.608409\pi$
$774$		0			0
$775$	−0.635630	+	0.635630i	−0.0228325	+	0.0228325i
$776$	−1.82444	−	0.957557i	−0.0654937	−	0.0343743i
$777$		0			0
$778$	0.333798	−	11.0460i	0.0119672	−	0.396019i
$779$	−36.6172	−	15.1673i	−1.31195	−	0.543426i
$780$		0			0
$781$	22.7876	+	55.0142i	0.815406	+	1.96856i
$782$	−17.8527	−	8.03492i	−0.638413	−	0.287328i
$783$		0			0
$784$	10.9038	+	1.32405i	0.389421	+	0.0472875i
$785$	−0.381871			−0.0136296
$786$		0			0
$787$	0.481468	−	0.199430i	0.0171625	−	0.00710893i	−0.374086	−	0.927394i	$-0.622043\pi$
$787$	0.481468	−	0.199430i	0.0171625	−	0.00710893i	0.391248	+	0.920285i	$0.372043\pi$
$788$	36.6637	−	12.6517i	1.30609	−	0.450697i
$789$		0			0
$790$	−0.0413580	+	1.36861i	−0.00147145	+	0.0486931i
$791$	−10.0674	+	10.0674i	−0.357957	+	0.357957i
$792$		0			0
$793$	36.3791	+	36.3791i	1.29186	+	1.29186i
$794$	10.7001	−	10.0724i	0.379734	−	0.357457i
$795$		0			0
$796$	−0.928483	+	15.3486i	−0.0329092	+	0.544017i
$797$	3.02312	+	7.29846i	0.107084	+	0.258525i	0.968334	−	0.249657i	$-0.0803179\pi$
$797$	3.02312	+	7.29846i	0.107084	+	0.258525i	−0.861250	+	0.508182i	$0.830318\pi$
$798$		0			0
$799$			25.6537i			0.907562i
$800$	24.1331	+	14.5893i	0.853234	+	0.515810i
$801$		0			0
$802$	8.59885	+	22.6734i	0.303636	+	0.800627i
$803$	37.6802	−	15.6077i	1.32971	−	0.550782i
$804$		0			0
$805$	0.166174	−	0.401178i	0.00585685	−	0.0141397i
$806$	0.617246	+	0.655714i	0.0217416	+	0.0230965i
$807$		0			0
$808$	−18.0681	−	21.6803i	−0.635633	−	0.762712i
$809$	−19.9360	−	19.9360i	−0.700912	−	0.700912i	0.263694	−	0.964606i	$-0.415059\pi$
$809$	−19.9360	−	19.9360i	−0.700912	−	0.700912i	−0.964606	+	0.263694i	$0.915059\pi$
$810$		0			0
$811$	−15.1406	+	36.5527i	−0.531660	+	1.28354i	0.398764	+	0.917054i	$0.369439\pi$
$811$	−15.1406	+	36.5527i	−0.531660	+	1.28354i	−0.930423	+	0.366487i	$0.880561\pi$
$812$	25.3090	−	8.73348i	0.888172	−	0.306485i
$813$		0			0
$814$	78.1132	+	35.1561i	2.73787	+	1.23222i
$815$		−	1.20295i		−	0.0421373i
$816$		0			0
$817$			42.0078i			1.46967i
$818$	1.19978	−	2.66578i	0.0419492	−	0.0932068i
$819$		0			0
$820$	−1.28369	−	0.625037i	−0.0448284	−	0.0218272i
$821$	−11.7121	+	28.2755i	−0.408755	+	0.986821i	0.576711	+	0.816948i	$0.304336\pi$
$821$	−11.7121	+	28.2755i	−0.408755	+	0.986821i	−0.985466	+	0.169873i	$0.945664\pi$
$822$		0			0
$823$	19.5237	+	19.5237i	0.680552	+	0.680552i	0.960125	−	0.279572i	$-0.0901927\pi$
$823$	19.5237	+	19.5237i	0.680552	+	0.680552i	−0.279572	+	0.960125i	$0.590193\pi$
$824$	−35.0336	+	10.9167i	−1.22045	+	0.380301i
$825$		0			0
$826$	11.2668	−	10.6059i	0.392024	−	0.369026i
$827$	−4.84438	+	11.6954i	−0.168455	+	0.406687i	−0.985452	−	0.169955i	$-0.945638\pi$
$827$	−4.84438	+	11.6954i	−0.168455	+	0.406687i	0.816996	+	0.576643i	$0.195638\pi$
$828$		0			0
$829$	−42.9741	+	17.8004i	−1.49255	+	0.618235i	−0.971870	−	0.235516i	$-0.924322\pi$
$829$	−42.9741	+	17.8004i	−1.49255	+	0.618235i	−0.520681	+	0.853751i	$0.674322\pi$
$830$	−0.883200	+	0.334952i	−0.0306563	+	0.0116263i
$831$		0			0
$832$	15.3391	−	23.7239i	0.531787	−	0.822480i
$833$		−	22.0030i		−	0.762359i
$834$		0			0
$835$	−0.142533	−	0.344105i	−0.00493256	−	0.0119082i
$836$	52.2562	−	46.2946i	1.80732	−	1.60113i
$837$		0			0
$838$	29.2850	+	31.1101i	1.01163	+	1.07468i
$839$	34.0889	+	34.0889i	1.17688	+	1.17688i	0.980535	+	0.196344i	$0.0629068\pi$
$839$	34.0889	+	34.0889i	1.17688	+	1.17688i	0.196344	+	0.980535i	$0.437093\pi$
$840$		0			0
$841$	−9.28141	+	9.28141i	−0.320049	+	0.320049i
$842$	10.5609	+	0.319138i	0.363952	+	0.0109982i
$843$		0			0
$844$	−13.5802	+	27.8908i	−0.467451	+	0.960041i
$845$	0.0596123	−	0.0246922i	0.00205073	−	0.000849438i
$846$		0			0
$847$	−32.2163			−1.10696
$848$	16.5449	+	9.33155i	0.568155	+	0.320447i
$849$		0			0
$850$	23.1848	−	51.5141i	0.795231	−	1.76692i
$851$	−7.76170	−	18.7384i	−0.266068	−	0.642344i
$852$		0			0
$853$	32.8374	+	13.6017i	1.12433	+	0.465713i	0.865850	−	0.500304i	$-0.166778\pi$
$853$	32.8374	+	13.6017i	1.12433	+	0.465713i	0.258480	+	0.966017i	$0.416778\pi$
$854$	−42.4758	−	1.28357i	−1.45349	−	0.0439230i
$855$		0			0
$856$	−8.24611	−	9.89471i	−0.281846	−	0.338194i
$857$	32.2409	−	32.2409i	1.10133	−	1.10133i	0.107078	−	0.994251i	$-0.465850\pi$
$857$	32.2409	−	32.2409i	1.10133	−	1.10133i	0.994251	−	0.107078i	$-0.0341495\pi$
$858$		0			0
$859$	0.456468	+	0.189075i	0.0155745	+	0.00645116i	0.390457	−	0.920621i	$-0.372317\pi$
$859$	0.456468	+	0.189075i	0.0155745	+	0.00645116i	−0.374883	+	0.927072i	$0.622317\pi$
$860$	−0.0913758	+	1.51052i	−0.00311589	+	0.0515082i
$861$		0			0
$862$	18.2406	−	6.91770i	0.621277	−	0.235618i
$863$	−6.78208			−0.230865			−0.115432	−	0.993315i	$-0.536825\pi$
$863$	−6.78208			−0.230865			−0.115432	+	0.993315i	$0.536825\pi$
$864$		0			0
$865$	0.415095			0.0141136
$866$	−16.2222	+	6.15225i	−0.551254	+	0.209062i
$867$		0			0
$868$	−0.742469	−	0.0449142i	−0.0252010	−	0.00152449i
$869$	−37.8719	−	15.6871i	−1.28472	−	0.532147i
$870$		0			0
$871$	−11.2427	+	11.2427i	−0.380945	+	0.380945i
$872$	−0.112505	+	1.23797i	−0.00380989	+	0.0419231i
$873$		0			0
$874$	−16.5227	−	0.499296i	−0.558887	−	0.0168889i
$875$	2.31865	+	0.960416i	0.0783847	+	0.0324680i
$876$		0			0
$877$	−12.2357	−	29.5396i	−0.413170	−	0.997482i	−0.984281	−	0.176609i	$-0.943487\pi$
$877$	−12.2357	−	29.5396i	−0.413170	−	0.997482i	0.571111	−	0.820873i	$-0.306513\pi$
$878$	0.818008	−	1.81753i	0.0276064	−	0.0613386i
$879$		0			0
$880$	1.97973	−	1.55099i	0.0667367	−	0.0522840i
$881$	−26.2391			−0.884019			−0.442009	−	0.897010i	$-0.645734\pi$
$881$	−26.2391			−0.884019			−0.442009	+	0.897010i	$0.645734\pi$
$882$		0			0
$883$	4.38436	−	1.81606i	0.147545	−	0.0611153i	−0.307689	−	0.951487i	$-0.599556\pi$
$883$	4.38436	−	1.81606i	0.147545	−	0.0611153i	0.455234	+	0.890372i	$0.349556\pi$
$884$	−50.8815	−	24.7746i	−1.71133	−	0.833259i
$885$		0			0
$886$	49.8000	+	1.50490i	1.67306	+	0.0505581i
$887$	−30.1519	+	30.1519i	−1.01240	+	1.01240i	−0.0124795	+	0.999922i	$0.503972\pi$
$887$	−30.1519	+	30.1519i	−1.01240	+	1.01240i	−0.999922	+	0.0124795i	$0.996028\pi$
$888$		0			0
$889$	−18.1610	−	18.1610i	−0.609101	−	0.609101i
$890$	1.21908	+	1.29505i	0.0408635	+	0.0434102i
$891$		0			0
$892$	−2.27283	−	2.56551i	−0.0760999	−	0.0858997i
$893$	8.28913	+	20.0117i	0.277385	+	0.669667i
$894$		0			0
$895$			1.57475i			0.0526382i
$896$	4.20589	+	22.9527i	0.140509	+	0.766796i
$897$		0			0
$898$	25.4489	−	9.65145i	0.849242	−	0.322073i
$899$	1.08126	−	0.447873i	0.0360621	−	0.0149374i
$900$		0			0
$901$	14.5615	−	35.1546i	0.485115	−	1.17117i
$902$	31.1241	−	29.2982i	1.03632	−	0.975524i
$903$		0			0
$904$	17.2880	+	9.07356i	0.574989	+	0.301782i
$905$	−1.68576	−	1.68576i	−0.0560365	−	0.0560365i
$906$		0			0
$907$	5.58141	−	13.4747i	0.185328	−	0.447420i	−0.803722	−	0.595005i	$-0.797150\pi$
$907$	5.58141	−	13.4747i	0.185328	−	0.447420i	0.989049	+	0.147585i	$0.0471500\pi$
$908$	−16.6752	+	34.2473i	−0.553387	+	1.13654i
$909$		0			0
$910$	0.515164	−	1.14464i	0.0170775	−	0.0379445i
$911$		−	21.1579i		−	0.700992i	−0.936564	−	0.350496i	$-0.886013\pi$
$911$		−	21.1579i		−	0.700992i	0.936564	−	0.350496i	$-0.113987\pi$
$912$		0			0
$913$		−	28.2789i		−	0.935894i
$914$	6.96727	+	3.13573i	0.230457	+	0.103721i
$915$		0			0
$916$	−4.03440	−	11.6914i	−0.133300	−	0.386295i
$917$	−10.1172	+	24.4250i	−0.334099	+	0.806586i
$918$		0			0
$919$	−29.9775	−	29.9775i	−0.988867	−	0.988867i	0.0110721	−	0.999939i	$-0.496476\pi$
$919$	−29.9775	−	29.9775i	−0.988867	−	0.988867i	−0.999939	+	0.0110721i	$0.996476\pi$
$920$	−0.593036	−	0.0538939i	−0.0195518	−	0.00177683i
$921$		0			0
$922$	30.3720	+	32.2648i	1.00025	+	1.06258i
$923$	15.5969	−	37.6543i	0.513379	−	1.23941i
$924$		0			0
$925$	54.0697	−	22.3964i	1.77780	−	0.736389i
$926$	−0.0722852	−	0.190602i	−0.00237544	−	0.00626356i
$927$		0			0
$928$	−21.7596	−	29.5728i	−0.714293	−	0.970774i
$929$		−	14.0169i		−	0.459879i	−0.973205	−	0.229939i	$-0.926147\pi$
$929$		−	14.0169i		−	0.459879i	0.973205	−	0.229939i	$-0.0738528\pi$
$930$		0			0
$931$	−7.10954	−	17.1639i	−0.233006	−	0.562526i
$932$	27.2046	+	1.64569i	0.891117	+	0.0539064i
$933$		0			0
$934$	−4.98363	+	4.69127i	−0.163069	+	0.153503i
$935$	−3.56237	−	3.56237i	−0.116502	−	0.116502i
$936$		0			0
$937$	−25.7289	+	25.7289i	−0.840527	+	0.840527i	−0.988927	−	0.148400i	$-0.952588\pi$
$937$	−25.7289	+	25.7289i	−0.840527	+	0.840527i	0.148400	+	0.988927i	$0.452588\pi$
$938$	0.396680	−	13.1269i	0.0129520	−	0.428608i
$939$		0			0
$940$	0.254531	+	0.737612i	0.00830188	+	0.0240583i
$941$	−9.43096	+	3.90643i	−0.307441	+	0.127346i	−0.531069	−	0.847328i	$-0.678210\pi$
$941$	−9.43096	+	3.90643i	−0.307441	+	0.127346i	0.223629	+	0.974674i	$0.428210\pi$
$942$		0			0
$943$	−10.1209			−0.329583
$944$	−18.4822	−	10.4242i	−0.601546	−	0.339280i
$945$		0			0
$946$	−41.3131	−	18.5936i	−1.34321	−	0.604531i
$947$	−22.2008	−	53.5975i	−0.721430	−	1.74169i	−0.669237	−	0.743049i	$-0.733379\pi$
$947$	−22.2008	−	53.5975i	−0.721430	−	1.74169i	−0.0521935	−	0.998637i	$-0.516621\pi$
$948$		0			0
$949$	−25.7901	−	10.6826i	−0.837183	−	0.346772i
$950$	1.44072	−	47.6761i	0.0467431	−	1.54682i
$951$		0			0
$952$	44.6282	−	13.9064i	1.44641	−	0.450709i
$953$	29.8819	−	29.8819i	0.967968	−	0.967968i	−0.0315343	−	0.999503i	$-0.510039\pi$
$953$	29.8819	−	29.8819i	0.967968	−	0.967968i	0.999503	+	0.0315343i	$0.0100393\pi$
$954$		0			0
$955$	0.638085	+	0.264303i	0.0206479	+	0.00855266i
$956$	27.6945	+	31.2609i	0.895705	+	1.01105i
$957$		0			0
$958$	−16.1094	−	42.4772i	−0.520470	−	1.37238i
$959$	−19.1167			−0.617310
$960$		0			0
$961$	30.9675			0.998951
$962$	−20.7903	−	54.8198i	−0.670305	−	1.76746i
$963$		0			0
$964$	23.8965	+	26.9738i	0.769654	+	0.868767i
$965$	−0.171791	−	0.0711580i	−0.00553013	−	0.00229066i
$966$		0			0
$967$	3.08765	−	3.08765i	0.0992920	−	0.0992920i	−0.655716	−	0.755008i	$-0.727633\pi$
$967$	3.08765	−	3.08765i	0.0992920	−	0.0992920i	0.755008	+	0.655716i	$0.227633\pi$
$968$	13.1433	+	42.1791i	0.422440	+	1.35569i
$969$		0			0
$970$	−0.00379211	+	0.125488i	−0.000121757	+	0.00402917i
$971$	10.8014	+	4.47409i	0.346634	+	0.143580i	0.549206	−	0.835687i	$-0.314930\pi$
$971$	10.8014	+	4.47409i	0.346634	+	0.143580i	−0.202572	+	0.979267i	$0.564930\pi$
$972$		0			0
$973$	−2.48243	−	5.99311i	−0.0795830	−	0.192130i
$974$	17.2090	+	7.74518i	0.551411	+	0.248171i
$975$		0			0
$976$	15.6483	+	56.1351i	0.500890	+	1.79684i
$977$	48.2773			1.54453			0.772264	−	0.635302i	$-0.219124\pi$
$977$	48.2773			1.54453			0.772264	+	0.635302i	$0.219124\pi$
$978$		0			0
$979$	−49.1935	+	20.3766i	−1.57223	+	0.651240i
$980$	−0.218310	−	0.632646i	−0.00697365	−	0.0202091i
$981$		0			0
$982$	−1.29189	+	42.7510i	−0.0412258	+	1.36424i
$983$	−17.1123	+	17.1123i	−0.545798	+	0.545798i	−0.925223	−	0.379424i	$-0.876122\pi$
$983$	−17.1123	+	17.1123i	−0.545798	+	0.545798i	0.379424	+	0.925223i	$0.376122\pi$
$984$		0			0
$985$	−1.67104	−	1.67104i	−0.0532436	−	0.0532436i
$986$	−53.5540	+	50.4123i	−1.70551	+	1.60545i
$987$		0			0
$988$	−47.6963	−	2.88530i	−1.51742	−	0.0917935i
$989$	4.10507	+	9.91052i	0.130534	+	0.315136i
$990$		0			0
$991$			18.8851i			0.599905i	0.953954	+	0.299952i	$0.0969708\pi$
$991$			18.8851i			0.599905i	−0.953954	+	0.299952i	$0.903029\pi$
$992$	0.244101	+	0.990399i	0.00775020	+	0.0314452i
$993$		0			0
$994$	11.9375	+	31.4769i	0.378636	+	0.998387i
$995$	0.865590	−	0.358539i	0.0274411	−	0.0113665i
$996$		0			0
$997$	17.9768	−	43.3998i	0.569330	−	1.37448i	−0.332791	−	0.943001i	$-0.607990\pi$
$997$	17.9768	−	43.3998i	0.569330	−	1.37448i	0.902121	−	0.431483i	$-0.142010\pi$
$998$	23.9214	+	25.4122i	0.757219	+	0.804410i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.a.107.12	✓	128
3.2	odd	2	inner	864.2.w.a.107.21	yes	128
32.3	odd	8	inner	864.2.w.a.323.21	yes	128
96.35	even	8	inner	864.2.w.a.323.12	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.a.107.12	✓	128	1.1	even	1	trivial
864.2.w.a.107.21	yes	128	3.2	odd	2	inner
864.2.w.a.323.12	yes	128	96.35	even	8	inner
864.2.w.a.323.21	yes	128	32.3	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.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.501484 - 1.32231i) q^{2} +(-1.49703 + 1.32624i) q^{4} +(0.112585 + 0.0466342i) q^{5} +(-1.45843 + 1.45843i) q^{7} +(2.50444 + 1.31445i) q^{8} +O(q^{10})\)	\(q+(-0.501484 - 1.32231i) q^{2} +(-1.49703 + 1.32624i) q^{4} +(0.112585 + 0.0466342i) q^{5} +(-1.45843 + 1.45843i) q^{7} +(2.50444 + 1.31445i) q^{8} +(0.00520548 - 0.172259i) q^{10} +(4.76670 + 1.97443i) q^{11} +(-1.35139 - 3.26255i) q^{13} +(2.65988 + 1.19712i) q^{14} +(0.482180 - 3.97083i) q^{16} -8.01284 q^{17} +(-6.25059 + 2.58908i) q^{19} +(-0.230391 + 0.0795019i) q^{20} +(0.220393 - 7.29322i) q^{22} +(-1.22164 + 1.22164i) q^{23} +(-3.52503 - 3.52503i) q^{25} +(-3.63642 + 3.42308i) q^{26} +(0.249082 - 4.11753i) q^{28} +(2.48379 + 5.99639i) q^{29} -0.180319i q^{31} +(-5.49249 + 1.35372i) q^{32} +(4.01831 + 10.5955i) q^{34} +(-0.232210 + 0.0961845i) q^{35} +(-4.49262 + 10.8462i) q^{37} +(6.55815 + 6.96686i) q^{38} +(0.220664 + 0.264780i) q^{40} +(4.14237 + 4.14237i) q^{41} +(2.37609 - 5.73640i) q^{43} +(-9.75444 + 3.36601i) q^{44} +(2.22802 + 1.00276i) q^{46} -3.20157i q^{47} +2.74597i q^{49} +(-2.89345 + 6.42895i) q^{50} +(6.35000 + 3.09186i) q^{52} +(-1.81727 + 4.38729i) q^{53} +(0.444583 + 0.444583i) q^{55} +(-5.56958 + 1.73551i) q^{56} +(6.68353 - 6.29144i) q^{58} +(2.03007 - 4.90102i) q^{59} +(-13.4598 + 5.57525i) q^{61} +(-0.238438 + 0.0904270i) q^{62} +(4.54444 + 6.58393i) q^{64} -0.430336i q^{65} +(-1.72299 - 4.15968i) q^{67} +(11.9954 - 10.6269i) q^{68} +(0.243636 + 0.258819i) q^{70} +(8.16098 + 8.16098i) q^{71} +(5.58960 - 5.58960i) q^{73} +(16.5950 + 0.501483i) q^{74} +(5.92357 - 12.1657i) q^{76} +(-9.83146 + 4.07232i) q^{77} -7.94510 q^{79} +(0.239463 - 0.424570i) q^{80} +(3.40018 - 7.55484i) q^{82} +(-2.09749 - 5.06378i) q^{83} +(-0.902125 - 0.373672i) q^{85} +(-8.77689 - 0.265228i) q^{86} +(9.34262 + 11.2104i) q^{88} +(-7.29752 + 7.29752i) q^{89} +(6.72911 + 2.78729i) q^{91} +(0.208641 - 3.44900i) q^{92} +(-4.23348 + 1.60554i) q^{94} -0.824463 q^{95} -0.728484 q^{97} +(3.63103 - 1.37706i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

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