LMFDB - Embedded newform 729.2.e.h.82.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(82,729)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("729.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$729 = 3^{6}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	729.e (of order $9$ , degree $6$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [6,3,0,9,-3,0,0,6,0,0,12,0,0,-21,0,9,9,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} - x^{3} + 1$ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			82.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	729.82
Dual form			729.2.e.h.649.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.152704 + 0.866025i) q^{2} +(1.15270 - 0.419550i) q^{4} +(-2.97178 - 2.49362i) q^{5} +(2.05303 + 0.747243i) q^{7} +(1.41875 + 2.45734i) q^{8} +(1.70574 - 2.95442i) q^{10} +(-0.124485 + 0.104455i) q^{11} +(0.418748 - 2.37484i) q^{13} +(-0.333626 + 1.89209i) q^{14} +(-0.0320889 + 0.0269258i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-1.79813 - 3.11446i) q^{19} +(-4.47178 - 1.62760i) q^{20} +(-0.109470 - 0.0918566i) q^{22} +(2.66637 - 0.970481i) q^{23} +(1.74510 + 9.89695i) q^{25} +2.12061 q^{26} +2.68004 q^{28} +(-1.16637 - 6.61484i) q^{29} +(4.87211 - 1.77330i) q^{31} +(4.31908 + 3.62414i) q^{32} +(2.47906 + 0.902302i) q^{34} +(-4.23783 - 7.34013i) q^{35} +(3.31908 - 5.74881i) q^{37} +(2.42262 - 2.03282i) q^{38} +(1.91147 - 10.8405i) q^{40} +(1.00727 - 5.71253i) q^{41} +(-4.76991 + 4.00243i) q^{43} +(-0.0996702 + 0.172634i) q^{44} +(1.24763 + 2.16095i) q^{46} +(6.95084 + 2.52990i) q^{47} +(-1.70574 - 1.43128i) q^{49} +(-8.30453 + 3.02260i) q^{50} +(-0.513671 - 2.91317i) q^{52} -1.40373 q^{53} +0.630415 q^{55} +(1.07650 + 6.10516i) q^{56} +(5.55051 - 2.02022i) q^{58} +(3.92262 + 3.29147i) q^{59} +(3.55303 + 1.29320i) q^{61} +(2.27972 + 3.94858i) q^{62} +(-2.52094 + 4.36640i) q^{64} +(-7.16637 + 6.01330i) q^{65} +(-1.01842 + 5.77574i) q^{67} +(0.639033 - 3.62414i) q^{68} +(5.70961 - 4.79093i) q^{70} +(-7.65910 + 13.2660i) q^{71} +(-4.34002 - 7.51714i) q^{73} +(5.48545 + 1.99654i) q^{74} +(-3.37939 - 2.83564i) q^{76} +(-0.333626 + 0.121430i) q^{77} +(-0.220285 - 1.24930i) q^{79} +0.162504 q^{80} +5.10101 q^{82} +(1.47178 + 8.34689i) q^{83} +(-10.9363 + 3.98048i) q^{85} +(-4.19459 - 3.51968i) q^{86} +(-0.433296 - 0.157707i) q^{88} +(3.86097 + 6.68739i) q^{89} +(2.63429 - 4.56272i) q^{91} +(2.66637 - 2.23735i) q^{92} +(-1.12954 + 6.40593i) q^{94} +(-2.42262 + 13.7394i) q^{95} +(-2.99273 + 2.51120i) q^{97} +(0.979055 - 1.69577i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q + 3 q^{2} + 9 q^{4} - 3 q^{5} + 6 q^{8} + 12 q^{11} - 21 q^{14} + 9 q^{16} + 9 q^{17} + 3 q^{19} - 12 q^{20} - 18 q^{22} - 3 q^{23} + 9 q^{25} + 24 q^{26} - 24 q^{28} + 12 q^{29} + 9 q^{32} + 18 q^{34}+ \cdots + 9 q^{98}+O(q^{100})$ 6 * q + 3 * q^2 + 9 * q^4 - 3 * q^5 + 6 * q^8 + 12 * q^11 - 21 * q^14 + 9 * q^16 + 9 * q^17 + 3 * q^19 - 12 * q^20 - 18 * q^22 - 3 * q^23 + 9 * q^25 + 24 * q^26 - 24 * q^28 + 12 * q^29 + 9 * q^32 + 18 * q^34 - 6 * q^35 + 3 * q^37 - 12 * q^38 - 9 * q^40 + 24 * q^41 - 15 * q^44 - 9 * q^46 + 30 * q^47 + 3 * q^50 + 18 * q^52 - 36 * q^53 + 18 * q^55 - 24 * q^56 + 36 * q^58 - 3 * q^59 + 9 * q^61 - 12 * q^62 - 12 * q^64 - 24 * q^65 - 18 * q^67 + 27 * q^68 - 9 * q^71 - 6 * q^73 - 3 * q^74 - 9 * q^76 - 21 * q^77 - 27 * q^79 + 6 * q^80 + 36 * q^82 - 6 * q^83 - 18 * q^85 - 21 * q^86 - 36 * q^88 + 6 * q^91 - 3 * q^92 + 36 * q^94 + 12 * q^95 + 9 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$ .

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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

)

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

$2$	0.152704	+	0.866025i	0.107978	+	0.612372i	0.989989	+	0.141144i	$0.0450781\pi$
$2$	0.152704	+	0.866025i	0.107978	+	0.612372i	−0.882011	+	0.471228i	$0.843811\pi$
$3$		0			0
$3$		0			0
$4$	1.15270	−	0.419550i	0.576352	−	0.209775i
$5$	−2.97178	−	2.49362i	−1.32902	−	1.11518i	−0.984305	−	0.176474i	$-0.943531\pi$
$5$	−2.97178	−	2.49362i	−1.32902	−	1.11518i	−0.344716	−	0.938707i	$-0.612025\pi$
$6$		0			0
$7$	2.05303	+	0.747243i	0.775974	+	0.282431i	0.699493	−	0.714640i	$-0.253409\pi$
$7$	2.05303	+	0.747243i	0.775974	+	0.282431i	0.0764810	+	0.997071i	$0.475632\pi$
$8$	1.41875	+	2.45734i	0.501603	+	0.868802i
$9$		0			0
$10$	1.70574	−	2.95442i	0.539401	−	0.934271i
$11$	−0.124485	+	0.104455i	−0.0375337	+	0.0314945i	−0.661362	−	0.750067i	$-0.730021\pi$
$11$	−0.124485	+	0.104455i	−0.0375337	+	0.0314945i	0.623828	+	0.781562i	$0.285577\pi$
$12$		0			0
$13$	0.418748	−	2.37484i	0.116140	−	0.658662i	−0.870040	−	0.492982i	$-0.835907\pi$
$13$	0.418748	−	2.37484i	0.116140	−	0.658662i	0.986180	−	0.165680i	$-0.0529819\pi$
$14$	−0.333626	+	1.89209i	−0.0891652	+	0.505681i
$15$		0			0
$16$	−0.0320889	+	0.0269258i	−0.00802222	+	0.00673144i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	−1.79813	−	3.11446i	−0.412520	−	0.714506i	0.582645	−	0.812727i	$-0.302018\pi$
$19$	−1.79813	−	3.11446i	−0.412520	−	0.714506i	−0.995165	+	0.0982214i	$0.968685\pi$
$20$	−4.47178	−	1.62760i	−0.999921	−	0.363941i
$21$		0			0
$22$	−0.109470	−	0.0918566i	−0.0233392	−	0.0195839i
$23$	2.66637	−	0.970481i	0.555977	−	0.202359i	−0.0487229	−	0.998812i	$-0.515515\pi$
$23$	2.66637	−	0.970481i	0.555977	−	0.202359i	0.604700	+	0.796453i	$0.293293\pi$
$24$		0			0
$25$	1.74510	+	9.89695i	0.349020	+	1.97939i
$26$	2.12061			0.415887
$27$		0			0
$28$	2.68004			0.506481
$29$	−1.16637	−	6.61484i	−0.216590	−	1.22834i	−0.878126	−	0.478430i	$-0.841206\pi$
$29$	−1.16637	−	6.61484i	−0.216590	−	1.22834i	0.661535	−	0.749914i	$-0.269905\pi$
$30$		0			0
$31$	4.87211	−	1.77330i	0.875057	−	0.318495i	0.134844	−	0.990867i	$-0.456947\pi$
$31$	4.87211	−	1.77330i	0.875057	−	0.318495i	0.740213	+	0.672372i	$0.234725\pi$
$32$	4.31908	+	3.62414i	0.763512	+	0.640663i
$33$		0			0
$34$	2.47906	+	0.902302i	0.425155	+	0.154744i
$35$	−4.23783	−	7.34013i	−0.716323	−	1.24071i
$36$		0			0
$37$	3.31908	−	5.74881i	0.545653	−	0.945099i	−0.452912	−	0.891555i	$-0.649615\pi$
$37$	3.31908	−	5.74881i	0.545653	−	0.945099i	0.998566	−	0.0535438i	$-0.0170517\pi$
$38$	2.42262	−	2.03282i	0.393001	−	0.329767i
$39$		0			0
$40$	1.91147	−	10.8405i	0.302231	−	1.71403i
$41$	1.00727	−	5.71253i	0.157310	−	0.892148i	−0.799334	−	0.600887i	$-0.794814\pi$
$41$	1.00727	−	5.71253i	0.157310	−	0.892148i	0.956644	−	0.291261i	$-0.0940748\pi$
$42$		0			0
$43$	−4.76991	+	4.00243i	−0.727405	+	0.610365i	−0.929423	−	0.369016i	$-0.879695\pi$
$43$	−4.76991	+	4.00243i	−0.727405	+	0.610365i	0.202018	+	0.979382i	$0.435250\pi$
$44$	−0.0996702	+	0.172634i	−0.0150259	+	0.0260255i
$45$		0			0
$46$	1.24763	+	2.16095i	0.183952	+	0.318615i
$47$	6.95084	+	2.52990i	1.01388	+	0.369024i	0.794923	−	0.606710i	$-0.207511\pi$
$47$	6.95084	+	2.52990i	1.01388	+	0.369024i	0.218961	+	0.975734i	$0.429733\pi$
$48$		0			0
$49$	−1.70574	−	1.43128i	−0.243677	−	0.204469i
$50$	−8.30453	+	3.02260i	−1.17444	+	0.427460i
$51$		0			0
$52$	−0.513671	−	2.91317i	−0.0712333	−	0.403984i
$53$	−1.40373			−0.192818			−0.0964088	−	0.995342i	$-0.530736\pi$
$53$	−1.40373			−0.192818			−0.0964088	+	0.995342i	$0.530736\pi$
$54$		0			0
$55$	0.630415			0.0850051
$56$	1.07650	+	6.10516i	0.143854	+	0.815836i
$57$		0			0
$58$	5.55051	−	2.02022i	0.728817	−	0.265268i
$59$	3.92262	+	3.29147i	0.510681	+	0.428513i	0.861369	−	0.507980i	$-0.169608\pi$
$59$	3.92262	+	3.29147i	0.510681	+	0.428513i	−0.350687	+	0.936493i	$0.614052\pi$
$60$		0			0
$61$	3.55303	+	1.29320i	0.454919	+	0.165577i	0.559309	−	0.828959i	$-0.311067\pi$
$61$	3.55303	+	1.29320i	0.454919	+	0.165577i	−0.104389	+	0.994536i	$0.533289\pi$
$62$	2.27972	+	3.94858i	0.289524	+	0.501470i
$63$		0			0
$64$	−2.52094	+	4.36640i	−0.315118	+	0.545801i
$65$	−7.16637	+	6.01330i	−0.888879	+	0.745858i
$66$		0			0
$67$	−1.01842	+	5.77574i	−0.124420	+	0.705619i	0.857231	+	0.514932i	$0.172183\pi$
$67$	−1.01842	+	5.77574i	−0.124420	+	0.705619i	−0.981651	+	0.190687i	$0.938928\pi$
$68$	0.639033	−	3.62414i	0.0774941	−	0.439491i
$69$		0			0
$70$	5.70961	−	4.79093i	0.682429	−	0.572626i
$71$	−7.65910	+	13.2660i	−0.908968	+	1.57438i	−0.0934675	+	0.995622i	$0.529795\pi$
$71$	−7.65910	+	13.2660i	−0.908968	+	1.57438i	−0.815500	+	0.578756i	$0.803538\pi$
$72$		0			0
$73$	−4.34002	−	7.51714i	−0.507961	−	0.879815i	−0.999958	−	0.00921733i	$-0.997066\pi$
$73$	−4.34002	−	7.51714i	−0.507961	−	0.879815i	0.491996	−	0.870597i	$-0.336267\pi$
$74$	5.48545	+	1.99654i	0.637671	+	0.232093i
$75$		0			0
$76$	−3.37939	−	2.83564i	−0.387642	−	0.325270i
$77$	−0.333626	+	0.121430i	−0.0380202	+	0.0138382i
$78$		0			0
$79$	−0.220285	−	1.24930i	−0.0247840	−	0.140557i	0.969905	−	0.243484i	$-0.0782903\pi$
$79$	−0.220285	−	1.24930i	−0.0247840	−	0.140557i	−0.994689	+	0.102927i	$0.967179\pi$
$80$	0.162504			0.0181685
$81$		0			0
$82$	5.10101			0.563313
$83$	1.47178	+	8.34689i	0.161549	+	0.916190i	0.952552	+	0.304377i	$0.0984483\pi$
$83$	1.47178	+	8.34689i	0.161549	+	0.916190i	−0.791003	+	0.611813i	$0.790441\pi$
$84$		0			0
$85$	−10.9363	+	3.98048i	−1.18621	+	0.431744i
$86$	−4.19459	−	3.51968i	−0.452315	−	0.379537i
$87$		0			0
$88$	−0.433296	−	0.157707i	−0.0461895	−	0.0168116i
$89$	3.86097	+	6.68739i	0.409262	+	0.708862i	0.994807	−	0.101778i	$-0.0324530\pi$
$89$	3.86097	+	6.68739i	0.409262	+	0.708862i	−0.585546	+	0.810640i	$0.699120\pi$
$90$		0			0
$91$	2.63429	−	4.56272i	0.276148	−	0.478303i
$92$	2.66637	−	2.23735i	0.277989	−	0.233260i
$93$		0			0
$94$	−1.12954	+	6.40593i	−0.116503	+	0.660721i
$95$	−2.42262	+	13.7394i	−0.248555	+	1.40963i
$96$		0			0
$97$	−2.99273	+	2.51120i	−0.303865	+	0.254973i	−0.781951	−	0.623340i	$-0.785775\pi$
$97$	−2.99273	+	2.51120i	−0.303865	+	0.254973i	0.478086	+	0.878313i	$0.341331\pi$
$98$	0.979055	−	1.69577i	0.0988995	−	0.171299i
$99$		0			0
$100$	6.16385	+	10.6761i	0.616385	+	1.06761i
$101$	−7.62449	−	2.77509i	−0.758665	−	0.276131i	−0.0664176	−	0.997792i	$-0.521157\pi$
$101$	−7.62449	−	2.77509i	−0.758665	−	0.276131i	−0.692247	+	0.721661i	$0.743379\pi$
$102$		0			0
$103$	14.2836	+	11.9854i	1.40740	+	1.18095i	0.957698	+	0.287775i	$0.0929155\pi$
$103$	14.2836	+	11.9854i	1.40740	+	1.18095i	0.449705	+	0.893177i	$0.351529\pi$
$104$	6.42989	−	2.34029i	0.630503	−	0.229484i
$105$		0			0
$106$	−0.214355	−	1.21567i	−0.0208200	−	0.118076i
$107$	−7.59627			−0.734359			−0.367179	−	0.930150i	$-0.619676\pi$
$107$	−7.59627			−0.734359			−0.367179	+	0.930150i	$0.619676\pi$
$108$		0			0
$109$	−15.6382			−1.49786			−0.748932	−	0.662647i	$-0.769433\pi$
$109$	−15.6382			−1.49786			−0.748932	+	0.662647i	$0.769433\pi$
$110$	0.0962667	+	0.545955i	0.00917867	+	0.0520548i
$111$		0			0
$112$	−0.0859997	+	0.0313013i	−0.00812620	+	0.00295770i
$113$	1.77197	+	1.48686i	0.166693	+	0.139872i	0.722318	−	0.691561i	$-0.243077\pi$
$113$	1.77197	+	1.48686i	0.166693	+	0.139872i	−0.555625	+	0.831433i	$0.687521\pi$
$114$		0			0
$115$	−10.3439	−	3.76487i	−0.964573	−	0.351076i
$116$	−4.11974	−	7.13559i	−0.382508	−	0.662523i
$117$		0			0
$118$	−2.25150	+	3.89971i	−0.207267	+	0.358997i
$119$	5.02094	−	4.21307i	0.460269	−	0.386212i
$120$		0			0
$121$	−1.90554	+	10.8069i	−0.173231	+	0.982444i
$122$	−0.577382	+	3.27449i	−0.0522737	+	0.296459i
$123$		0			0
$124$	4.87211	−	4.08819i	0.437529	−	0.367130i
$125$	9.79473	−	16.9650i	0.876067	−	1.51739i
$126$		0			0
$127$	−0.0209445	−	0.0362770i	−0.00185853	−	0.00321906i	0.865095	−	0.501609i	$-0.167258\pi$
$127$	−0.0209445	−	0.0362770i	−0.00185853	−	0.00321906i	−0.866953	+	0.498390i	$0.833925\pi$
$128$	6.42989	+	2.34029i	0.568328	+	0.206854i
$129$		0			0
$130$	−6.30200	−	5.28801i	−0.552722	−	0.463789i
$131$	17.2417	−	6.27546i	1.50641	−	0.548290i	0.548702	−	0.836018i	$-0.315122\pi$
$131$	17.2417	−	6.27546i	1.50641	−	0.548290i	0.957712	+	0.287728i	$0.0929000\pi$
$132$		0			0
$133$	−1.36437	−	7.73773i	−0.118306	−	0.670946i
$134$	−5.15745			−0.445536
$135$		0			0
$136$	8.51249			0.729940
$137$	−2.48545	−	14.0957i	−0.212347	−	1.20428i	−0.885452	−	0.464731i	$-0.846151\pi$
$137$	−2.48545	−	14.0957i	−0.212347	−	1.20428i	0.673106	−	0.739546i	$-0.264960\pi$
$138$		0			0
$139$	−9.86231	+	3.58959i	−0.836510	+	0.304465i	−0.724528	−	0.689245i	$-0.757942\pi$
$139$	−9.86231	+	3.58959i	−0.836510	+	0.304465i	−0.111982	+	0.993710i	$0.535720\pi$
$140$	−7.96451	−	6.68302i	−0.673124	−	0.564818i
$141$		0			0
$142$	−12.6582	−	4.60722i	−1.06225	−	0.386629i
$143$	0.195937	+	0.339373i	0.0163851	+	0.0283798i
$144$		0			0
$145$	−13.0287	+	22.5663i	−1.08197	+	1.87403i
$146$	5.84730	−	4.90646i	0.483926	−	0.406062i
$147$		0			0
$148$	1.41400	−	8.01919i	0.116230	−	0.659174i
$149$	0.220752	−	1.25195i	0.0180847	−	0.102563i	−0.974429	−	0.224694i	$-0.927862\pi$
$149$	0.220752	−	1.25195i	0.0180847	−	0.102563i	0.992514	+	0.122131i	$0.0389728\pi$
$150$		0			0
$151$	6.01889	−	5.05044i	0.489810	−	0.410999i	−0.364148	−	0.931341i	$-0.618640\pi$
$151$	6.01889	−	5.05044i	0.489810	−	0.410999i	0.853958	+	0.520342i	$0.174195\pi$
$152$	5.10220	−	8.83726i	0.413843	−	0.716797i
$153$		0			0
$154$	−0.156107	−	0.270386i	−0.0125795	−	0.0217883i
$155$	−18.9008	−	6.87933i	−1.51815	−	0.552561i
$156$		0			0
$157$	−9.46245	−	7.93994i	−0.755186	−	0.633676i	0.181683	−	0.983357i	$-0.441845\pi$
$157$	−9.46245	−	7.93994i	−0.755186	−	0.633676i	−0.936869	+	0.349681i	$0.886290\pi$
$158$	1.04829	−	0.381545i	0.0833971	−	0.0303541i
$159$		0			0
$160$	−3.79813	−	21.5403i	−0.300269	−	1.70291i
$161$	6.19934			0.488576
$162$		0			0
$163$	−13.7469			−1.07674			−0.538371	−	0.842708i	$-0.680960\pi$
$163$	−13.7469			−1.07674			−0.538371	+	0.842708i	$0.680960\pi$
$164$	−1.23560	−	7.00746i	−0.0964845	−	0.547191i
$165$		0			0
$166$	−7.00387	+	2.54920i	−0.543606	+	0.197856i
$167$	2.84730	+	2.38917i	0.220330	+	0.184879i	0.746271	−	0.665642i	$-0.231842\pi$
$167$	2.84730	+	2.38917i	0.220330	+	0.184879i	−0.525941	+	0.850521i	$0.676287\pi$
$168$		0			0
$169$	6.75150	+	2.45734i	0.519346	+	0.189026i
$170$	−5.11721	−	8.86327i	−0.392472	−	0.679782i
$171$		0			0
$172$	−3.81908	+	6.61484i	−0.291202	+	0.504377i
$173$	1.19459	−	1.00238i	0.0908232	−	0.0762097i	−0.596246	−	0.802802i	$-0.703342\pi$
$173$	1.19459	−	1.00238i	0.0908232	−	0.0762097i	0.687069	+	0.726592i	$0.258897\pi$
$174$		0			0
$175$	−3.81268	+	21.6228i	−0.288212	+	1.63453i
$176$	0.00118205	−	0.00670372i	8.91001e−5	−	0.000505312i
$177$		0			0
$178$	−5.20187	+	4.36488i	−0.389896	+	0.327162i
$179$	−6.09627	+	10.5590i	−0.455656	+	0.789220i	−0.998726	−	0.0504679i	$-0.983929\pi$
$179$	−6.09627	+	10.5590i	−0.455656	+	0.789220i	0.543069	+	0.839688i	$0.317262\pi$
$180$		0			0
$181$	8.43629	+	14.6121i	0.627064	+	1.08611i	0.988138	+	0.153570i	$0.0490771\pi$
$181$	8.43629	+	14.6121i	0.627064	+	1.08611i	−0.361073	+	0.932537i	$0.617590\pi$
$182$	4.35369	+	1.58461i	0.322717	+	0.117459i
$183$		0			0
$184$	6.16772	+	5.17533i	0.454690	+	0.381530i
$185$	−24.1989	+	8.80769i	−1.77914	+	0.647554i
$186$		0			0
$187$	0.0846555	+	0.480105i	0.00619062	+	0.0351088i
$188$	9.07367			0.661766
$189$		0			0
$190$	−12.2686			−0.890056
$191$	3.03462	+	17.2102i	0.219577	+	1.24528i	0.872785	+	0.488105i	$0.162312\pi$
$191$	3.03462	+	17.2102i	0.219577	+	1.24528i	−0.653208	+	0.757179i	$0.726577\pi$
$192$		0			0
$193$	1.87211	−	0.681393i	0.134758	−	0.0490477i	−0.273761	−	0.961798i	$-0.588268\pi$
$193$	1.87211	−	0.681393i	0.134758	−	0.0490477i	0.408519	+	0.912750i	$0.366046\pi$
$194$	−2.63176	−	2.20831i	−0.188949	−	0.158547i
$195$		0			0
$196$	−2.56670	−	0.934204i	−0.183336	−	0.0667288i
$197$	10.5963	+	18.3533i	0.754953	+	1.30762i	0.945398	+	0.325919i	$0.105674\pi$
$197$	10.5963	+	18.3533i	0.754953	+	1.30762i	−0.190445	+	0.981698i	$0.560993\pi$
$198$		0			0
$199$	1.54189	−	2.67063i	0.109302	−	0.189316i	−0.806186	−	0.591662i	$-0.798472\pi$
$199$	1.54189	−	2.67063i	0.109302	−	0.189316i	0.915488	+	0.402346i	$0.131805\pi$
$200$	−21.8444	+	18.3296i	−1.54463	+	1.29610i
$201$		0			0
$202$	1.23901	−	7.02676i	0.0871763	−	0.494401i
$203$	2.54829	−	14.4520i	0.178855	−	1.01433i
$204$		0			0
$205$	−17.2383	+	14.4646i	−1.20397	+	1.01025i
$206$	−8.19846	+	14.2002i	−0.571214	+	0.989372i
$207$		0			0
$208$	0.0505072	+	0.0874810i	0.00350204	+	0.00606572i
$209$	0.549163	+	0.199879i	0.0379864	+	0.0138259i
$210$		0			0
$211$	0.771974	+	0.647763i	0.0531449	+	0.0445939i	0.668973	−	0.743287i	$-0.266734\pi$
$211$	0.771974	+	0.647763i	0.0531449	+	0.0445939i	−0.615828	+	0.787880i	$0.711179\pi$
$212$	−1.61809	+	0.588936i	−0.111131	+	0.0404483i
$213$		0			0
$214$	−1.15998	−	6.57856i	−0.0792944	−	0.449701i
$215$	24.1557			1.64740
$216$		0			0
$217$	11.3277			0.768974
$218$	−2.38800	−	13.5430i	−0.161736	−	0.917250i
$219$		0			0
$220$	0.726682	−	0.264490i	0.0489929	−	0.0178319i
$221$	−5.54189	−	4.65020i	−0.372788	−	0.312806i
$222$		0			0
$223$	−17.1814	−	6.25351i	−1.15055	−	0.418766i	−0.304838	−	0.952404i	$-0.598602\pi$
$223$	−17.1814	−	6.25351i	−1.15055	−	0.418766i	−0.845713	+	0.533638i	$0.820825\pi$
$224$	6.15910	+	10.6679i	0.411522	+	0.712777i
$225$		0			0
$226$	−1.01707	+	1.76162i	−0.0676548	+	0.117181i
$227$	2.02616	−	1.70015i	0.134481	−	0.112843i	−0.573066	−	0.819509i	$-0.694246\pi$
$227$	2.02616	−	1.70015i	0.134481	−	0.112843i	0.707547	+	0.706666i	$0.249802\pi$
$228$		0			0
$229$	−0.601319	+	3.41025i	−0.0397363	+	0.225356i	−0.998209	−	0.0598300i	$-0.980944\pi$
$229$	−0.601319	+	3.41025i	−0.0397363	+	0.225356i	0.958472	+	0.285186i	$0.0920553\pi$
$230$	1.68092	−	9.53298i	0.110837	−	0.628586i
$231$		0			0
$232$	14.6001	−	12.2510i	0.958546	−	0.804316i
$233$	3.06283	−	5.30498i	0.200653	−	0.347541i	−0.748086	−	0.663602i	$-0.769027\pi$
$233$	3.06283	−	5.30498i	0.200653	−	0.347541i	0.948739	+	0.316061i	$0.102360\pi$
$234$		0			0
$235$	−14.3478	−	24.8511i	−0.935945	−	1.62110i
$236$	5.90255	+	2.14835i	0.384223	+	0.139846i
$237$		0			0
$238$	4.41534	+	3.70491i	0.286204	+	0.240154i
$239$	−27.2053	+	9.90193i	−1.75977	+	0.640503i	−0.999954	−	0.00963943i	$-0.996932\pi$
$239$	−27.2053	+	9.90193i	−1.75977	+	0.640503i	−0.759813	+	0.650142i	$0.774709\pi$
$240$		0			0
$241$	3.87686	+	21.9868i	0.249730	+	1.41629i	0.809245	+	0.587471i	$0.199876\pi$
$241$	3.87686	+	21.9868i	0.249730	+	1.41629i	−0.559515	+	0.828820i	$0.689012\pi$
$242$	−9.65002			−0.620326
$243$		0			0
$244$	4.63816			0.296927
$245$	1.50000	+	8.50692i	0.0958315	+	0.543487i
$246$		0			0
$247$	−8.14930	+	2.96610i	−0.518528	+	0.188729i
$248$	11.2699	+	9.45658i	0.715640	+	0.600494i
$249$		0			0
$250$	16.1878	+	5.89187i	1.02381	+	0.372635i
$251$	−11.3610	−	19.6778i	−0.717098	−	1.24205i	−0.962145	−	0.272539i	$-0.912137\pi$
$251$	−11.3610	−	19.6778i	−0.717098	−	1.24205i	0.245047	−	0.969511i	$-0.421197\pi$
$252$		0			0
$253$	−0.230552	+	0.399328i	−0.0144947	+	0.0251055i
$254$	0.0282185	−	0.0236781i	0.00177059	−	0.00148570i
$255$		0			0
$256$	−2.79591	+	15.8564i	−0.174744	+	0.991025i
$257$	3.40167	−	19.2919i	0.212191	−	1.20339i	−0.673525	−	0.739164i	$-0.735221\pi$
$257$	3.40167	−	19.2919i	0.212191	−	1.20339i	0.885716	−	0.464228i	$-0.153668\pi$
$258$		0			0
$259$	11.1099	−	9.32234i	0.690338	−	0.579262i
$260$	−5.73783	+	9.93821i	−0.355845	+	0.616341i
$261$		0			0
$262$	8.06758	+	13.9735i	0.498417	+	0.863283i
$263$	16.7271	+	6.08818i	1.03144	+	0.375414i	0.801629	−	0.597822i	$-0.203967\pi$
$263$	16.7271	+	6.08818i	1.03144	+	0.375414i	0.229811	+	0.973235i	$0.426189\pi$
$264$		0			0
$265$	4.17159	+	3.50038i	0.256259	+	0.215027i
$266$	6.49273	−	2.36316i	0.398095	−	0.144895i
$267$		0			0
$268$	1.24928	+	7.08499i	0.0763116	+	0.432785i
$269$	−22.7888			−1.38946			−0.694729	−	0.719272i	$-0.744476\pi$
$269$	−22.7888			−1.38946			−0.694729	+	0.719272i	$0.744476\pi$
$270$		0			0
$271$	−3.44562			−0.209307			−0.104653	−	0.994509i	$-0.533373\pi$
$271$	−3.44562			−0.209307			−0.104653	+	0.994509i	$0.533373\pi$
$272$	0.0218219	+	0.123758i	0.00132315	+	0.00750393i
$273$		0			0
$274$	11.8277	−	4.30493i	0.714537	−	0.260070i
$275$	−1.25103	−	1.04974i	−0.0754399	−	0.0633016i
$276$		0			0
$277$	2.45589	+	0.893871i	0.147560	+	0.0537075i	0.414744	−	0.909938i	$-0.363871\pi$
$277$	2.45589	+	0.893871i	0.147560	+	0.0537075i	−0.267184	+	0.963645i	$0.586093\pi$
$278$	−4.61468	−	7.99287i	−0.276770	−	0.479380i
$279$		0			0
$280$	12.0248	−	20.8276i	0.718620	−	1.24469i
$281$	10.4834	−	8.79661i	0.625387	−	0.524762i	−0.274105	−	0.961700i	$-0.588382\pi$
$281$	10.4834	−	8.79661i	0.625387	−	0.524762i	0.899492	+	0.436938i	$0.143937\pi$
$282$		0			0
$283$	3.97313	−	22.5327i	0.236178	−	1.33943i	−0.603941	−	0.797029i	$-0.706404\pi$
$283$	3.97313	−	22.5327i	0.236178	−	1.33943i	0.840119	−	0.542402i	$-0.182485\pi$
$284$	−3.26295	+	18.5051i	−0.193620	+	1.09807i
$285$		0			0
$286$	−0.263985	+	0.221510i	−0.0156098	+	0.0130981i
$287$	6.33662	−	10.9753i	0.374039	−	0.647854i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−21.5326	−	7.83721i	−1.26444	−	0.460217i
$291$		0			0
$292$	−8.15657	−	6.84418i	−0.477327	−	0.400525i
$293$	22.8170	−	8.30472i	1.33298	−	0.485167i	0.425388	−	0.905011i	$-0.360138\pi$
$293$	22.8170	−	8.30472i	1.33298	−	0.485167i	0.907596	+	0.419844i	$0.137915\pi$
$294$		0			0
$295$	−3.44949	−	19.5630i	−0.200837	−	1.13900i
$296$	18.8357			1.09481
$297$		0			0
$298$	1.11793			0.0647597
$299$	−1.18820	−	6.73859i	−0.0687152	−	0.389703i
$300$		0			0
$301$	−12.7836	+	4.65284i	−0.736834	+	0.268186i
$302$	5.29292	+	4.44129i	0.304573	+	0.255567i
$303$		0			0
$304$	0.141559	+	0.0515234i	0.00811898	+	0.00295507i
$305$	−7.33409	−	12.7030i	−0.419949	−	0.727373i
$306$		0			0
$307$	8.07444	−	13.9853i	0.460833	−	0.798186i	−0.538170	−	0.842836i	$-0.680884\pi$
$307$	8.07444	−	13.9853i	0.460833	−	0.798186i	0.999003	+	0.0446505i	$0.0142174\pi$
$308$	−0.333626	+	0.279945i	−0.0190101	+	0.0159514i
$309$		0			0
$310$	3.07145	−	17.4191i	0.174447	−	0.989337i
$311$	−3.24897	+	18.4258i	−0.184232	+	1.04483i	0.742706	+	0.669618i	$0.233542\pi$
$311$	−3.24897	+	18.4258i	−0.184232	+	1.04483i	−0.926938	+	0.375215i	$0.877569\pi$
$312$		0			0
$313$	2.12449	−	1.78265i	0.120083	−	0.100762i	−0.580769	−	0.814069i	$-0.697248\pi$
$313$	2.12449	−	1.78265i	0.120083	−	0.100762i	0.700852	+	0.713307i	$0.252803\pi$
$314$	5.43124	−	9.40718i	0.306502	−	0.530878i
$315$		0			0
$316$	−0.778066	−	1.34765i	−0.0437696	−	0.0758112i
$317$	16.4281	+	5.97935i	0.922696	+	0.335834i	0.759311	−	0.650728i	$-0.225536\pi$
$317$	16.4281	+	5.97935i	0.922696	+	0.335834i	0.163386	+	0.986562i	$0.447759\pi$
$318$		0			0
$319$	0.836152	+	0.701615i	0.0468155	+	0.0392829i
$320$	18.3799	−	6.68972i	1.02746	−	0.373967i
$321$		0			0
$322$	0.946662	+	5.36879i	0.0527554	+	0.299191i
$323$	−10.7888			−0.600305
$324$		0			0
$325$	24.2344			1.34428
$326$	−2.09920	−	11.9052i	−0.116264	−	0.659367i
$327$		0			0
$328$	15.4667	−	5.62943i	0.854007	−	0.310833i
$329$	12.3799	+	10.3879i	0.682523	+	0.572705i
$330$		0			0
$331$	30.5018	+	11.1018i	1.67653	+	0.610207i	0.992828	−	0.119553i	$-0.0381460\pi$
$331$	30.5018	+	11.1018i	1.67653	+	0.610207i	0.683703	+	0.729760i	$0.260368\pi$
$332$	5.19846	+	9.00400i	0.285303	+	0.494159i
$333$		0			0
$334$	−1.63429	+	2.83067i	−0.0894241	+	0.154887i
$335$	17.4290	−	14.6247i	0.952249	−	0.799032i
$336$		0			0
$337$	1.43882	−	8.15993i	0.0783773	−	0.444500i	−0.920213	−	0.391418i	$-0.871985\pi$
$337$	1.43882	−	8.15993i	0.0783773	−	0.444500i	0.998590	−	0.0530814i	$-0.0169043\pi$
$338$	−1.09714	+	6.22221i	−0.0596768	+	0.338444i
$339$		0			0
$340$	−10.9363	+	9.17664i	−0.593104	+	0.497673i
$341$	−0.421274	+	0.729669i	−0.0228133	+	0.0395138i
$342$		0			0
$343$	−10.0792	−	17.4577i	−0.544225	−	0.942626i
$344$	−16.6027	−	6.04288i	−0.895156	−	0.325810i
$345$		0			0
$346$	1.05051	+	0.881480i	0.0564756	+	0.0473887i
$347$	14.0608	−	5.11770i	0.754822	−	0.274733i	0.0641886	−	0.997938i	$-0.479554\pi$
$347$	14.0608	−	5.11770i	0.754822	−	0.274733i	0.690633	+	0.723205i	$0.257332\pi$
$348$		0			0
$349$	5.84255	+	33.1347i	0.312744	+	1.77366i	0.584598	+	0.811323i	$0.301252\pi$
$349$	5.84255	+	33.1347i	0.312744	+	1.77366i	−0.271853	+	0.962339i	$0.587637\pi$
$350$	−19.3081			−1.03206
$351$		0			0
$352$	−0.916222			−0.0488348
$353$	2.73560	+	15.5144i	0.145602	+	0.825747i	0.966882	+	0.255223i	$0.0821489\pi$
$353$	2.73560	+	15.5144i	0.145602	+	0.825747i	−0.821281	+	0.570524i	$0.806740\pi$
$354$		0			0
$355$	55.8414	−	20.3246i	2.96375	−	1.07872i
$356$	7.25624	+	6.08871i	0.384580	+	0.322701i
$357$		0			0
$358$	−10.0753	−	3.66712i	−0.532497	−	0.193813i
$359$	9.06283	+	15.6973i	0.478318	+	0.828471i	0.999691	−	0.0248577i	$-0.00791328\pi$
$359$	9.06283	+	15.6973i	0.478318	+	0.828471i	−0.521373	+	0.853329i	$0.674580\pi$
$360$		0			0
$361$	3.03343	−	5.25406i	0.159654	−	0.276529i
$362$	−11.3662	+	9.53736i	−0.597393	+	0.501272i
$363$		0			0
$364$	1.12226	−	6.36467i	0.0588226	−	0.333600i
$365$	−5.84730	+	33.1617i	−0.306061	+	1.73576i
$366$		0			0
$367$	−14.6643	+	12.3048i	−0.765471	+	0.642306i	−0.939545	−	0.342426i	$-0.888751\pi$
$367$	−14.6643	+	12.3048i	−0.765471	+	0.642306i	0.174074	+	0.984733i	$0.444307\pi$
$368$	−0.0594300	+	0.102936i	−0.00309800	+	0.00536590i
$369$		0			0
$370$	−11.3229	−	19.6119i	−0.588652	−	1.01958i
$371$	−2.88191	−	1.04893i	−0.149621	−	0.0544577i
$372$		0			0
$373$	−11.6821	−	9.80245i	−0.604876	−	0.507552i	0.288132	−	0.957591i	$-0.406966\pi$
$373$	−11.6821	−	9.80245i	−0.604876	−	0.507552i	−0.893009	+	0.450039i	$0.851410\pi$
$374$	−0.402856	+	0.146628i	−0.0208312	+	0.00758193i
$375$		0			0
$376$	3.64466	+	20.6699i	0.187959	+	1.06597i
$377$	−16.1976			−0.834218
$378$		0			0
$379$	9.84760			0.505837			0.252919	−	0.967488i	$-0.418610\pi$
$379$	9.84760			0.505837			0.252919	+	0.967488i	$0.418610\pi$
$380$	2.97178	+	16.8538i	0.152449	+	0.864582i
$381$		0			0
$382$	−14.4410	+	5.25611i	−0.738868	+	0.268926i
$383$	−21.7481	−	18.2488i	−1.11128	−	0.932471i	−0.113144	−	0.993579i	$-0.536092\pi$
$383$	−21.7481	−	18.2488i	−1.11128	−	0.932471i	−0.998131	+	0.0611076i	$0.980537\pi$
$384$		0			0
$385$	1.29426	+	0.471073i	0.0659617	+	0.0240081i
$386$	0.875982	+	1.51724i	0.0445863	+	0.0772257i
$387$		0			0
$388$	−2.39615	+	4.15026i	−0.121646	+	0.210698i
$389$	−8.33796	+	6.99638i	−0.422752	+	0.354731i	−0.829209	−	0.558939i	$-0.811209\pi$
$389$	−8.33796	+	6.99638i	−0.422752	+	0.354731i	0.406457	+	0.913670i	$0.366764\pi$
$390$		0			0
$391$	1.47818	−	8.38316i	0.0747547	−	0.423955i
$392$	1.09714	−	6.22221i	0.0554141	−	0.314269i
$393$		0			0
$394$	−14.2763	+	11.9792i	−0.719230	+	0.603506i
$395$	−2.46064	+	4.26195i	−0.123808	+	0.214442i
$396$		0			0
$397$	9.05350	+	15.6811i	0.454382	+	0.787013i	0.998652	−	0.0518969i	$-0.0165267\pi$
$397$	9.05350	+	15.6811i	0.454382	+	0.787013i	−0.544270	+	0.838910i	$0.683193\pi$
$398$	2.54829	+	0.927500i	0.127734	+	0.0464914i
$399$		0			0
$400$	−0.322481	−	0.270594i	−0.0161241	−	0.0135297i
$401$	1.34730	−	0.490376i	0.0672808	−	0.0244882i	−0.308161	−	0.951334i	$-0.599713\pi$
$401$	1.34730	−	0.490376i	0.0672808	−	0.0244882i	0.375441	+	0.926846i	$0.377491\pi$
$402$		0			0
$403$	−2.17112	−	12.3130i	−0.108151	−	0.613356i
$404$	−9.95306			−0.495183
$405$		0			0
$406$	12.9050			0.640463
$407$	0.187319	+	1.06234i	0.00928505	+	0.0526581i
$408$		0			0
$409$	−8.08512	+	2.94274i	−0.399784	+	0.145509i	−0.534084	−	0.845431i	$-0.679343\pi$
$409$	−8.08512	+	2.94274i	−0.399784	+	0.145509i	0.134301	+	0.990941i	$0.457121\pi$
$410$	−15.1591	−	12.7200i	−0.748655	−	0.628196i
$411$		0			0
$412$	21.4932	+	7.82288i	1.05889	+	0.385406i
$413$	5.59374	+	9.68864i	0.275250	+	0.476747i
$414$		0			0
$415$	16.4402	−	28.4752i	0.807016	−	1.39779i
$416$	10.4153	−	8.73951i	0.510654	−	0.428490i
$417$		0			0
$418$	−0.0892411	+	0.506111i	−0.00436492	+	0.0247547i
$419$	2.13785	−	12.1244i	0.104441	−	0.592314i	−0.887001	−	0.461767i	$-0.847216\pi$
$419$	2.13785	−	12.1244i	0.104441	−	0.592314i	0.991442	−	0.130547i	$-0.0416732\pi$
$420$		0			0
$421$	8.51573	−	7.14555i	0.415031	−	0.348253i	−0.411238	−	0.911528i	$-0.634903\pi$
$421$	8.51573	−	7.14555i	0.415031	−	0.348253i	0.826269	+	0.563275i	$0.190459\pi$
$422$	−0.443096	+	0.767465i	−0.0215696	+	0.0373596i
$423$		0			0
$424$	−1.99154	−	3.44946i	−0.0967179	−	0.167520i
$425$	28.3307	+	10.3115i	1.37424	+	0.500183i
$426$		0			0
$427$	6.32816	+	5.30996i	0.306241	+	0.256967i
$428$	−8.75624	+	3.18701i	−0.423249	+	0.154050i
$429$		0			0
$430$	3.68866	+	20.9194i	0.177883	+	1.00883i
$431$	36.8958			1.77721			0.888604	−	0.458675i	$-0.151676\pi$
$431$	36.8958			1.77721			0.888604	+	0.458675i	$0.151676\pi$
$432$		0			0
$433$	−37.9982			−1.82608			−0.913040	−	0.407871i	$-0.866271\pi$
$433$	−37.9982			−1.82608			−0.913040	+	0.407871i	$0.866271\pi$
$434$	1.72978	+	9.81007i	0.0830321	+	0.470899i
$435$		0			0
$436$	−18.0262	+	6.56099i	−0.863296	+	0.314214i
$437$	−7.81702	−	6.55926i	−0.373939	−	0.313772i
$438$		0			0
$439$	−0.189845	−	0.0690979i	−0.00906081	−	0.00329786i	0.337486	−	0.941331i	$-0.390424\pi$
$439$	−0.189845	−	0.0690979i	−0.00906081	−	0.00329786i	−0.346547	+	0.938033i	$0.612646\pi$
$440$	0.894400	+	1.54915i	0.0426388	+	0.0738526i
$441$		0			0
$442$	3.18092	−	5.50952i	0.151301	−	0.262061i
$443$	−16.2626	+	13.6460i	−0.772661	+	0.648340i	−0.941389	−	0.337323i	$-0.890479\pi$
$443$	−16.2626	+	13.6460i	−0.772661	+	0.648340i	0.168728	+	0.985663i	$0.446034\pi$
$444$		0			0
$445$	5.20187	−	29.5013i	0.246592	−	1.39849i
$446$	2.79204	−	15.8345i	0.132207	−	0.749783i
$447$		0			0
$448$	−8.43835	+	7.08062i	−0.398674	+	0.334528i
$449$	−16.6297	+	28.8035i	−0.784804	+	1.35932i	0.144312	+	0.989532i	$0.453903\pi$
$449$	−16.6297	+	28.8035i	−0.784804	+	1.35932i	−0.929116	+	0.369788i	$0.879430\pi$
$450$		0			0
$451$	0.471315	+	0.816341i	0.0221933	+	0.0384400i
$452$	2.66637	+	0.970481i	0.125416	+	0.0456476i
$453$		0			0
$454$	1.78177	+	1.49509i	0.0836228	+	0.0701679i
$455$	−19.2062	+	6.99049i	−0.900401	+	0.327719i
$456$		0			0
$457$	−0.00592979	−	0.0336295i	−0.000277384	−	0.00157312i	0.984669	−	0.174435i	$-0.0558098\pi$
$457$	−0.00592979	−	0.0336295i	−0.000277384	−	0.00157312i	−0.984946	+	0.172862i	$0.944699\pi$
$458$	−3.04519			−0.142292
$459$		0			0
$460$	−13.5030			−0.629580
$461$	2.60236	+	14.7587i	0.121204	+	0.687382i	0.983490	+	0.180961i	$0.0579207\pi$
$461$	2.60236	+	14.7587i	0.121204	+	0.687382i	−0.862286	+	0.506421i	$0.830968\pi$
$462$		0			0
$463$	28.6065	−	10.4119i	1.32946	−	0.483883i	0.422981	−	0.906138i	$-0.360984\pi$
$463$	28.6065	−	10.4119i	1.32946	−	0.483883i	0.906477	+	0.422255i	$0.138761\pi$
$464$	0.215537	+	0.180857i	0.0100061	+	0.00839609i
$465$		0			0
$466$	5.06196	+	1.84240i	0.234491	+	0.0853476i
$467$	−0.255367	−	0.442308i	−0.0118170	−	0.0204676i	0.860056	−	0.510199i	$-0.170428\pi$
$467$	−0.255367	−	0.442308i	−0.0118170	−	0.0204676i	−0.871873	+	0.489731i	$0.837095\pi$
$468$		0			0
$469$	−6.40673	+	11.0968i	−0.295835	+	0.512401i
$470$	19.3307	−	16.2204i	0.891658	−	0.748190i
$471$		0			0
$472$	−2.52306	+	14.3090i	−0.116133	+	0.658624i
$473$	0.175708	−	0.996487i	0.00807904	−	0.0458185i
$474$		0			0
$475$	27.6857	−	23.2311i	1.27031	−	1.06592i
$476$	4.02007	−	6.96296i	0.184259	−	0.319147i
$477$		0			0
$478$	−12.7297	−	22.0484i	−0.582242	−	1.00847i
$479$	−14.5189	−	5.28444i	−0.663385	−	0.241452i	−0.0116878	−	0.999932i	$-0.503720\pi$
$479$	−14.5189	−	5.28444i	−0.663385	−	0.241452i	−0.651697	+	0.758479i	$0.725943\pi$
$480$		0			0
$481$	−12.2626	−	10.2896i	−0.559128	−	0.469164i
$482$	−18.4491	+	6.71492i	−0.840333	+	0.305856i
$483$		0			0
$484$	2.33750	+	13.2566i	0.106250	+	0.602573i
$485$	15.1557			0.688185
$486$		0			0
$487$	29.5107			1.33726			0.668629	−	0.743596i	$-0.266881\pi$
$487$	29.5107			1.33726			0.668629	+	0.743596i	$0.266881\pi$
$488$	1.86303	+	10.5657i	0.0843352	+	0.478289i
$489$		0			0
$490$	−7.13816	+	2.59808i	−0.322469	+	0.117369i
$491$	−1.65270	−	1.38678i	−0.0745855	−	0.0625846i	0.604733	−	0.796428i	$-0.293280\pi$
$491$	−1.65270	−	1.38678i	−0.0745855	−	0.0625846i	−0.679318	+	0.733844i	$0.737724\pi$
$492$		0			0
$493$	−18.9354	−	6.89193i	−0.852808	−	0.310397i
$494$	−3.81315	−	6.60457i	−0.171562	−	0.297153i
$495$		0			0
$496$	−0.108593	+	0.188089i	−0.00487597	+	0.00844543i
$497$	−25.6373	+	21.5122i	−1.14999	+	0.964955i
$498$		0			0
$499$	1.30154	−	7.38138i	0.0582648	−	0.330436i	−0.941717	−	0.336405i	$-0.890789\pi$
$499$	1.30154	−	7.38138i	0.0582648	−	0.330436i	0.999982	+	0.00596898i	$0.00190000\pi$
$500$	4.17277	−	23.6650i	0.186612	−	1.05833i
$501$		0			0
$502$	15.3066	−	12.8438i	0.683167	−	0.573245i
$503$	14.2981	−	24.7651i	0.637522	−	1.10422i	−0.348453	−	0.937326i	$-0.613293\pi$
$503$	14.2981	−	24.7651i	0.637522	−	1.10422i	0.985975	−	0.166894i	$-0.0533739\pi$
$504$		0			0
$505$	15.7383	+	27.2595i	0.700345	+	1.21303i
$506$	−0.381034	−	0.138685i	−0.0169390	−	0.00616530i
$507$		0			0
$508$	−0.0393628	−	0.0330293i	−0.00174644	−	0.00146544i
$509$	−1.58987	+	0.578665i	−0.0704698	+	0.0256489i	−0.377015	−	0.926207i	$-0.623049\pi$
$509$	−1.58987	+	0.578665i	−0.0704698	+	0.0256489i	0.306545	+	0.951856i	$0.400827\pi$
$510$		0			0
$511$	−3.29308	−	18.6760i	−0.145677	−	0.826177i
$512$	−0.473897			−0.0209435
$513$		0			0
$514$	17.2267			0.759836
$515$	−12.5608	−	71.2357i	−0.553494	−	3.13902i
$516$		0			0
$517$	−1.12954	+	0.411118i	−0.0496770	+	0.0180810i
$518$	9.76991	+	8.19793i	0.429265	+	0.360196i
$519$		0			0
$520$	−24.9440	−	9.07888i	−1.09387	−	0.398135i
$521$	−11.2019	−	19.4022i	−0.490763	−	0.850026i	0.509181	−	0.860660i	$-0.329948\pi$
$521$	−11.2019	−	19.4022i	−0.490763	−	0.850026i	−0.999943	+	0.0106337i	$0.996615\pi$
$522$		0			0
$523$	−1.21436	+	2.10332i	−0.0531000	+	0.0919720i	−0.891354	−	0.453309i	$-0.850244\pi$
$523$	−1.21436	+	2.10332i	−0.0531000	+	0.0919720i	0.838254	+	0.545281i	$0.183577\pi$
$524$	17.2417	−	14.4675i	0.753207	−	0.632016i
$525$		0			0
$526$	−2.71823	+	15.4158i	−0.118520	+	0.672162i
$527$	2.70099	−	15.3181i	0.117657	−	0.667266i
$528$		0			0
$529$	−11.4513	+	9.60878i	−0.497883	+	0.417773i
$530$	−2.39440	+	4.14722i	−0.104006	+	0.180144i
$531$		0			0
$532$	−4.81908	−	8.34689i	−0.208934	−	0.361883i
$533$	−13.1446	−	4.78423i	−0.569354	−	0.207228i
$534$		0			0
$535$	22.5744	+	18.9422i	0.975978	+	0.818943i
$536$	−15.6379	+	5.69171i	−0.675452	+	0.245845i
$537$		0			0
$538$	−3.47993	−	19.7357i	−0.150031	−	0.850866i
$539$	0.361844			0.0155857
$540$		0			0
$541$	38.9394			1.67414			0.837069	−	0.547098i	$-0.184267\pi$
$541$	38.9394			1.67414			0.837069	+	0.547098i	$0.184267\pi$
$542$	−0.526159	−	2.98400i	−0.0226005	−	0.128174i
$543$		0			0
$544$	15.8944	−	5.78509i	0.681467	−	0.248034i
$545$	46.4732	+	38.9956i	1.99069	+	1.67039i
$546$		0			0
$547$	13.7875	+	5.01822i	0.589509	+	0.214564i	0.619513	−	0.784986i	$-0.287330\pi$
$547$	13.7875	+	5.01822i	0.589509	+	0.214564i	−0.0300044	+	0.999550i	$0.509552\pi$
$548$	−8.77884	−	15.2054i	−0.375013	−	0.649542i
$549$		0			0
$550$	0.718063	−	1.24372i	0.0306183	−	0.0530325i
$551$	−18.5043	+	15.5270i	−0.788311	+	0.661472i
$552$		0			0
$553$	0.481277	−	2.72946i	0.0204660	−	0.116068i
$554$	−0.399091	+	2.26336i	−0.0169558	+	0.0961609i
$555$		0			0
$556$	−9.86231	+	8.27546i	−0.418255	+	0.350958i
$557$	−5.55350	+	9.61894i	−0.235309	+	0.407568i	−0.959363	−	0.282176i	$-0.908944\pi$
$557$	−5.55350	+	9.61894i	−0.235309	+	0.407568i	0.724053	+	0.689744i	$0.242277\pi$
$558$		0			0
$559$	7.50774	+	13.0038i	0.317544	+	0.550002i
$560$	0.333626	+	0.121430i	0.0140983	+	0.00513135i
$561$		0			0
$562$	9.21894	+	7.73561i	0.388878	+	0.326307i
$563$	15.3246	−	5.57770i	0.645855	−	0.235072i	0.00173729	−	0.999998i	$-0.499447\pi$
$563$	15.3246	−	5.57770i	0.645855	−	0.235072i	0.644117	+	0.764927i	$0.277225\pi$
$564$		0			0
$565$	−1.55825	−	8.83726i	−0.0655560	−	0.371786i
$566$	20.1206			0.845733
$567$		0			0
$568$	−43.4653			−1.82376
$569$	−6.25418	−	35.4692i	−0.262189	−	1.48695i	−0.776922	−	0.629597i	$-0.783220\pi$
$569$	−6.25418	−	35.4692i	−0.262189	−	1.48695i	0.514733	−	0.857351i	$-0.327891\pi$
$570$		0			0
$571$	−36.7968	+	13.3930i	−1.53990	+	0.560478i	−0.966021	−	0.258462i	$-0.916784\pi$
$571$	−36.7968	+	13.3930i	−1.53990	+	0.560478i	−0.573879	+	0.818940i	$0.694562\pi$
$572$	0.368241	+	0.308991i	0.0153969	+	0.0129196i
$573$		0			0
$574$	10.4726	+	3.81170i	0.437116	+	0.159097i
$575$	14.2579	+	24.6954i	0.594595	+	1.02987i
$576$		0			0
$577$	−5.90286	+	10.2240i	−0.245739	+	0.425633i	−0.962339	−	0.271852i	$-0.912364\pi$
$577$	−5.90286	+	10.2240i	−0.245739	+	0.425633i	0.716600	+	0.697484i	$0.245697\pi$
$578$	−5.38919	+	4.52206i	−0.224161	+	0.188093i
$579$		0			0
$580$	−5.55051	+	31.4785i	−0.230472	+	1.30707i
$581$	−3.21554	+	18.2362i	−0.133403	+	0.756566i
$582$		0			0
$583$	0.174744	−	0.146628i	0.00723716	−	0.00607269i
$584$	12.3148	−	21.3299i	0.509590	−	0.882636i
$585$		0			0
$586$	10.6763	+	18.4920i	0.441035	+	0.763896i
$587$	−37.5514	−	13.6676i	−1.54991	−	0.564123i	−0.581516	−	0.813535i	$-0.697540\pi$
$587$	−37.5514	−	13.6676i	−1.54991	−	0.564123i	−0.968397	+	0.249412i	$0.919763\pi$
$588$		0			0
$589$	−14.2836	−	11.9854i	−0.588545	−	0.493848i
$590$	16.4153	−	5.97470i	0.675809	−	0.245974i
$591$		0			0
$592$	0.0482857	+	0.273842i	0.00198453	+	0.0112548i
$593$	29.2995			1.20319			0.601594	−	0.798802i	$-0.294533\pi$
$593$	29.2995			1.20319			0.601594	+	0.798802i	$0.294533\pi$
$594$		0			0
$595$	−25.4270			−1.04240
$596$	−0.270792	−	1.53574i	−0.0110921	−	0.0629063i
$597$		0			0
$598$	5.65435	−	2.05802i	0.231224	−	0.0841585i
$599$	−7.71554	−	6.47410i	−0.315248	−	0.264525i	0.471409	−	0.881915i	$-0.343746\pi$
$599$	−7.71554	−	6.47410i	−0.315248	−	0.264525i	−0.786657	+	0.617390i	$0.788190\pi$
$600$		0			0
$601$	28.5847	+	10.4040i	1.16599	+	0.424387i	0.851235	−	0.524784i	$-0.175854\pi$
$601$	28.5847	+	10.4040i	1.16599	+	0.424387i	0.314759	+	0.949172i	$0.398076\pi$
$602$	−5.98158	−	10.3604i	−0.243791	−	0.422259i
$603$		0			0
$604$	4.81908	−	8.34689i	0.196085	−	0.339630i
$605$	32.6111	−	27.3640i	1.32583	−	1.11250i
$606$		0			0
$607$	−4.00681	+	22.7237i	−0.162631	+	0.922328i	0.788842	+	0.614596i	$0.210681\pi$
$607$	−4.00681	+	22.7237i	−0.162631	+	0.922328i	−0.951473	+	0.307732i	$0.900430\pi$
$608$	3.52094	−	19.9683i	0.142793	−	0.809820i
$609$		0			0
$610$	9.88120	−	8.29131i	0.400078	−	0.335705i
$611$	8.91875	−	15.4477i	0.360814	−	0.624948i
$612$		0			0
$613$	−0.382789	−	0.663010i	−0.0154607	−	0.0267787i	0.858192	−	0.513330i	$-0.171588\pi$
$613$	−0.382789	−	0.663010i	−0.0154607	−	0.0267787i	−0.873652	+	0.486551i	$0.838255\pi$
$614$	13.3447	+	4.85706i	0.538547	+	0.196015i
$615$		0			0
$616$	−0.771726	−	0.647555i	−0.0310937	−	0.0260907i
$617$	−8.72803	+	3.17674i	−0.351377	+	0.127891i	−0.511678	−	0.859177i	$-0.670976\pi$
$617$	−8.72803	+	3.17674i	−0.351377	+	0.127891i	0.160301	+	0.987068i	$0.448754\pi$
$618$		0			0
$619$	−6.09199	−	34.5494i	−0.244858	−	1.38866i	−0.820823	−	0.571182i	$-0.806485\pi$
$619$	−6.09199	−	34.5494i	−0.244858	−	1.38866i	0.575966	−	0.817474i	$-0.304626\pi$
$620$	−24.6732			−0.990901
$621$		0			0
$622$	−16.4534			−0.659720
$623$	2.92959	+	16.6145i	0.117371	+	0.665647i
$624$		0			0
$625$	−24.1942	+	8.80596i	−0.967767	+	0.352238i
$626$	1.86824	+	1.56764i	0.0746699	+	0.0626555i
$627$		0			0
$628$	−14.2386	−	5.18243i	−0.568182	−	0.206801i
$629$	−9.95723	−	17.2464i	−0.397021	−	0.687660i
$630$		0			0
$631$	−17.8810	+	30.9709i	−0.711833	+	1.23293i	0.252336	+	0.967640i	$0.418801\pi$
$631$	−17.8810	+	30.9709i	−0.711833	+	1.23293i	−0.964168	+	0.265291i	$0.914532\pi$
$632$	2.75743	−	2.31376i	0.109685	−	0.0920362i
$633$		0			0
$634$	−2.66964	+	15.1403i	−0.106025	+	0.601296i
$635$	−0.0282185	+	0.160035i	−0.00111982	+	0.00635080i
$636$		0			0
$637$	−4.11334	+	3.45150i	−0.162976	+	0.136754i
$638$	−0.479933	+	0.831268i	−0.0190007	+	0.0329102i
$639$		0			0
$640$	−13.2724	−	22.9885i	−0.524639	−	0.908702i
$641$	2.74985	+	1.00086i	0.108612	+	0.0395317i	0.395755	−	0.918356i	$-0.370483\pi$
$641$	2.74985	+	1.00086i	0.108612	+	0.0395317i	−0.287142	+	0.957888i	$0.592705\pi$
$642$		0			0
$643$	−15.5137	−	13.0175i	−0.611799	−	0.513361i	0.283414	−	0.958998i	$-0.408533\pi$
$643$	−15.5137	−	13.0175i	−0.611799	−	0.513361i	−0.895214	+	0.445637i	$0.852977\pi$
$644$	7.14600	−	2.60093i	0.281592	−	0.102491i
$645$		0			0
$646$	−1.64749	−	9.34337i	−0.0648196	−	0.367610i
$647$	−10.7219			−0.421523			−0.210761	−	0.977538i	$-0.567594\pi$
$647$	−10.7219			−0.421523			−0.210761	+	0.977538i	$0.567594\pi$
$648$		0			0
$649$	−0.832119			−0.0326635
$650$	3.70068	+	20.9876i	0.145153	+	0.823202i
$651$		0			0
$652$	−15.8461	+	5.76751i	−0.620582	+	0.225873i
$653$	−27.3685	−	22.9649i	−1.07101	−	0.898685i	−0.0758669	−	0.997118i	$-0.524172\pi$
$653$	−27.3685	−	22.9649i	−1.07101	−	0.898685i	−0.995144	+	0.0984334i	$0.968617\pi$
$654$		0			0
$655$	−66.8872	−	24.3449i	−2.61350	−	0.951236i
$656$	0.121492	+	0.210430i	0.00474347	+	0.00821593i
$657$		0			0
$658$	−7.10576	+	12.3075i	−0.277011	+	0.479798i
$659$	−23.6446	+	19.8401i	−0.921061	+	0.772862i	−0.974191	−	0.225726i	$-0.927525\pi$
$659$	−23.6446	+	19.8401i	−0.921061	+	0.772862i	0.0531299	+	0.998588i	$0.483080\pi$
$660$		0			0
$661$	−1.71007	+	9.69831i	−0.0665142	+	0.377221i	0.933321	+	0.359044i	$0.116897\pi$
$661$	−1.71007	+	9.69831i	−0.0665142	+	0.377221i	−0.999835	+	0.0181766i	$0.994214\pi$
$662$	−4.95666	+	28.1106i	−0.192646	+	1.09255i
$663$		0			0
$664$	−18.4231	+	15.4588i	−0.714954	+	0.599918i
$665$	−15.2404	+	26.3971i	−0.590996	+	1.02363i
$666$		0			0
$667$	−9.52956	−	16.5057i	−0.368986	−	0.639103i
$668$	4.28446	+	1.55942i	0.165771	+	0.0603357i
$669$		0			0
$670$	15.3268	+	12.8607i	0.592127	+	0.496853i
$671$	−0.577382	+	0.210150i	−0.0222896	+	0.00811274i
$672$		0			0
$673$	−3.42040	−	19.3980i	−0.131847	−	0.747739i	−0.977004	−	0.213222i	$-0.931604\pi$
$673$	−3.42040	−	19.3980i	−0.131847	−	0.747739i	0.845157	−	0.534518i	$-0.179507\pi$
$674$	7.28642			0.280662
$675$		0			0
$676$	8.81345			0.338979
$677$	4.94150	+	28.0247i	0.189917	+	1.07708i	0.919473	+	0.393153i	$0.128616\pi$
$677$	4.94150	+	28.0247i	0.189917	+	1.07708i	−0.729555	+	0.683922i	$0.760273\pi$
$678$		0			0
$679$	−8.02064	+	2.91927i	−0.307804	+	0.112031i
$680$	−25.2973	−	21.2269i	−0.970105	−	0.814015i
$681$		0			0
$682$	−0.696242	−	0.253411i	−0.0266605	−	0.00970362i
$683$	6.25537	+	10.8346i	0.239355	+	0.414575i	0.960529	−	0.278179i	$-0.0897307\pi$
$683$	6.25537	+	10.8346i	0.239355	+	0.414575i	−0.721174	+	0.692754i	$0.756397\pi$
$684$		0			0
$685$	−27.7631	+	48.0871i	−1.06077	+	1.83731i
$686$	13.5797	−	11.3947i	0.518474	−	0.435051i
$687$		0			0
$688$	0.0452926	−	0.256867i	0.00172677	−	0.00979297i
$689$	−0.587811	+	3.33364i	−0.0223938	+	0.127002i
$690$		0			0
$691$	32.6530	−	27.3991i	1.24218	−	1.04231i	0.244828	−	0.969566i	$-0.421268\pi$
$691$	32.6530	−	27.3991i	1.24218	−	1.04231i	0.997351	−	0.0727455i	$-0.0231761\pi$
$692$	0.956462	−	1.65664i	0.0363592	−	0.0629760i
$693$		0			0
$694$	6.57919	+	11.3955i	0.249743	+	0.432567i
$695$	38.2597	+	13.9254i	1.45127	+	0.528220i
$696$		0			0
$697$	−13.3307	−	11.1858i	−0.504936	−	0.423691i
$698$	−27.8033	+	10.1196i	−1.05237	+	0.383032i
$699$		0			0
$700$	4.67695	+	26.5243i	0.176772	+	1.00252i
$701$	−51.7701			−1.95533			−0.977665	−	0.210167i	$-0.932599\pi$
$701$	−51.7701			−1.95533			−0.977665	+	0.210167i	$0.932599\pi$
$702$		0			0
$703$	−23.8726			−0.900371
$704$	−0.142275	−	0.806879i	−0.00536217	−	0.0304104i
$705$		0			0
$706$	−13.0181	+	4.73821i	−0.489943	+	0.178325i
$707$	−13.5797	−	11.3947i	−0.510716	−	0.428541i
$708$		0			0
$709$	−14.2442	−	5.18447i	−0.534953	−	0.194707i	0.0603955	−	0.998175i	$-0.480764\pi$
$709$	−14.2442	−	5.18447i	−0.534953	−	0.194707i	−0.595349	+	0.803468i	$0.702986\pi$
$710$	26.1288	+	45.2564i	0.980597	+	1.69844i
$711$		0			0
$712$	−10.9555	+	18.9754i	−0.410574	+	0.711135i
$713$	11.2699	−	9.45658i	0.422062	−	0.354152i
$714$		0			0
$715$	0.263985	−	1.49713i	0.00987248	−	0.0559896i
$716$	−2.59714	+	14.7291i	−0.0970598	+	0.550454i
$717$		0			0
$718$	−12.2103	+	10.2457i	−0.455685	+	0.382365i
$719$	−1.30747	+	2.26460i	−0.0487603	+	0.0844553i	−0.889375	−	0.457178i	$-0.848860\pi$
$719$	−1.30747	+	2.26460i	−0.0487603	+	0.0844553i	0.840615	+	0.541633i	$0.182194\pi$
$720$		0			0
$721$	20.3687	+	35.2796i	0.758570	+	1.31388i
$722$	5.01337	+	1.82472i	0.186578	+	0.0679089i
$723$		0			0
$724$	15.8550	+	13.3040i	0.589248	+	0.494438i
$725$	63.4313	−	23.0871i	2.35578	−	0.857433i
$726$		0			0
$727$	−0.711829	−	4.03698i	−0.0264003	−	0.149723i	0.968758	−	0.248007i	$-0.0797757\pi$
$727$	−0.711829	−	4.03698i	−0.0264003	−	0.149723i	−0.995158	+	0.0982840i	$0.968665\pi$
$728$	14.9495			0.554067
$729$		0			0
$730$	−29.6117			−1.09598
$731$	3.24376	+	18.3963i	0.119975	+	0.680410i
$732$		0			0
$733$	35.9038	−	13.0679i	1.32614	−	0.482674i	0.420717	−	0.907192i	$-0.361779\pi$
$733$	35.9038	−	13.0679i	1.32614	−	0.482674i	0.905420	+	0.424518i	$0.139556\pi$
$734$	−12.8956	−	10.8207i	−0.475985	−	0.399399i
$735$		0			0
$736$	15.0334	+	5.47172i	0.554140	+	0.201690i
$737$	−0.476529	−	0.825373i	−0.0175532	−	0.0304030i
$738$		0			0
$739$	12.1047	−	20.9660i	0.445279	−	0.771247i	−0.552792	−	0.833319i	$-0.686438\pi$
$739$	12.1047	−	20.9660i	0.445279	−	0.771247i	0.998072	+	0.0620725i	$0.0197710\pi$
$740$	−24.1989	+	20.3053i	−0.889570	+	0.746438i
$741$		0			0
$742$	0.468322	−	2.65598i	0.0171926	−	0.0975042i
$743$	0.575017	−	3.26109i	0.0210953	−	0.119638i	−0.972442	−	0.233146i	$-0.925098\pi$
$743$	0.575017	−	3.26109i	0.0210953	−	0.119638i	0.993537	+	0.113509i	$0.0362090\pi$
$744$		0			0
$745$	−3.77790	+	3.17004i	−0.138412	+	0.116141i
$746$	6.70527	−	11.6139i	0.245497	−	0.425214i
$747$		0			0
$748$	0.299011	+	0.517902i	0.0109329	+	0.0189364i
$749$	−15.5954	−	5.67626i	−0.569843	−	0.207406i
$750$		0			0
$751$	10.5032	+	8.81327i	0.383269	+	0.321601i	0.813984	−	0.580887i	$-0.197294\pi$
$751$	10.5032	+	8.81327i	0.383269	+	0.321601i	−0.430715	+	0.902488i	$0.641739\pi$
$752$	−0.291164	+	0.105975i	−0.0106177	+	0.00386451i
$753$		0			0
$754$	−2.47343	−	14.0275i	−0.0900770	−	0.510852i
$755$	−30.4807			−1.10931
$756$		0			0
$757$	12.3833			0.450079			0.225040	−	0.974350i	$-0.427749\pi$
$757$	12.3833			0.450079			0.225040	+	0.974350i	$0.427749\pi$
$758$	1.50376	+	8.52827i	0.0546192	+	0.309761i
$759$		0			0
$760$	−37.1994	+	13.5395i	−1.34936	+	0.491128i
$761$	−5.80865	−	4.87404i	−0.210563	−	0.176684i	0.531406	−	0.847117i	$-0.321664\pi$
$761$	−5.80865	−	4.87404i	−0.210563	−	0.176684i	−0.741970	+	0.670433i	$0.766108\pi$
$762$		0			0
$763$	−32.1057	−	11.6855i	−1.16230	−	0.423044i
$764$	10.7185	+	18.5650i	0.387783	+	0.671660i
$765$		0			0
$766$	12.4829	−	21.6211i	0.451026	−	0.781201i
$767$	9.45929	−	7.93729i	0.341555	−	0.286599i
$768$		0			0
$769$	0.558659	−	3.16831i	0.0201457	−	0.114252i	−0.973077	−	0.230482i	$-0.925970\pi$
$769$	0.558659	−	3.16831i	0.0201457	−	0.114252i	0.993222	+	0.116230i	$0.0370809\pi$
$770$	−0.210323	+	1.19280i	−0.00757950	+	0.0429855i
$771$		0			0
$772$	1.87211	−	1.57089i	0.0673788	−	0.0565375i
$773$	−0.0922341	+	0.159754i	−0.00331743	+	0.00574596i	−0.867679	−	0.497124i	$-0.834389\pi$
$773$	−0.0922341	+	0.159754i	−0.00331743	+	0.00574596i	0.864362	+	0.502870i	$0.167723\pi$
$774$		0			0
$775$	26.0526	+	45.1245i	0.935838	+	1.62092i
$776$	−10.4168	−	3.79140i	−0.373941	−	0.136103i
$777$		0			0
$778$	−7.33228	−	6.15251i	−0.262875	−	0.220578i
$779$	−19.6027	+	7.13479i	−0.702338	+	0.255630i
$780$		0			0
$781$	−0.432257	−	2.45145i	−0.0154674	−	0.0877197i
$782$	7.48576			0.267690
$783$		0			0
$784$	0.0932736			0.00333120
$785$	8.32114	+	47.1915i	0.296994	+	1.68434i
$786$		0			0
$787$	0.449188	−	0.163491i	0.0160118	−	0.00582783i	−0.334002	−	0.942572i	$-0.608399\pi$
$787$	0.449188	−	0.163491i	0.0160118	−	0.00582783i	0.350014	+	0.936745i	$0.386177\pi$
$788$	19.9145	+	16.7102i	0.709424	+	0.595277i
$789$		0			0
$790$	−4.06670	−	1.48016i	−0.144687	−	0.0526617i
$791$	2.52687	+	4.37667i	0.0898453	+	0.155617i
$792$		0			0
$793$	4.55896	−	7.89636i	0.161894	−	0.280408i
$794$	−12.1977	+	10.2351i	−0.432882	+	0.363231i
$795$		0			0
$796$	0.656879	−	3.72534i	0.0232824	−	0.132041i
$797$	−2.51770	+	14.2786i	−0.0891816	+	0.505774i	0.907194	+	0.420712i	$0.138220\pi$
$797$	−2.51770	+	14.2786i	−0.0891816	+	0.505774i	−0.996376	+	0.0850617i	$0.972891\pi$
$798$		0			0
$799$	16.9991	−	14.2640i	0.601386	−	0.504623i
$800$	−28.3307	+	49.0702i	−1.00164	+	1.73489i
$801$		0			0
$802$	0.630415	+	1.09191i	0.0222607	+	0.0385567i
$803$	1.32547	+	0.482433i	0.0467750	+	0.0170247i
$804$		0			0
$805$	−18.4231	−	15.4588i	−0.649328	−	0.544851i
$806$	10.3319	−	3.76049i	0.363925	−	0.132458i
$807$		0			0
$808$	−3.99788	−	22.6731i	−0.140645	−	0.797638i
$809$	14.8743			0.522954			0.261477	−	0.965210i	$-0.415790\pi$
$809$	14.8743			0.522954			0.261477	+	0.965210i	$0.415790\pi$
$810$		0			0
$811$	21.5963			0.758347			0.379174	−	0.925325i	$-0.376208\pi$
$811$	21.5963			0.758347			0.379174	+	0.925325i	$0.376208\pi$
$812$	−3.12594	−	17.7281i	−0.109699	−	0.622133i
$813$		0			0
$814$	−0.891407	+	0.324446i	−0.0312438	+	0.0113718i
$815$	40.8528	+	34.2796i	1.43101	+	1.20076i
$816$		0			0
$817$	21.0424	+	7.65879i	0.736179	+	0.267947i
$818$	−3.78312	−	6.55255i	−0.132274	−	0.229105i
$819$		0			0
$820$	−13.8020	+	23.9058i	−0.481987	+	0.834826i
$821$	2.51367	−	2.10922i	0.0877277	−	0.0736123i	−0.597869	−	0.801594i	$-0.703986\pi$
$821$	2.51367	−	2.10922i	0.0877277	−	0.0736123i	0.685597	+	0.727981i	$0.259541\pi$
$822$		0			0
$823$	2.38444	−	13.5228i	0.0831163	−	0.471376i	−0.914631	−	0.404290i	$-0.867519\pi$
$823$	2.38444	−	13.5228i	0.0831163	−	0.471376i	0.997747	−	0.0670860i	$-0.0213702\pi$
$824$	−9.18732	+	52.1039i	−0.320055	+	1.81512i
$825$		0			0
$826$	−7.53643	+	6.32381i	−0.262226	+	0.220034i
$827$	10.1163	−	17.5220i	0.351779	−	0.609300i	−0.634782	−	0.772691i	$-0.718910\pi$
$827$	10.1163	−	17.5220i	0.351779	−	0.609300i	0.986561	+	0.163392i	$0.0522434\pi$
$828$		0			0
$829$	−12.7638	−	22.1076i	−0.443306	−	0.767828i	0.554627	−	0.832099i	$-0.312861\pi$
$829$	−12.7638	−	22.1076i	−0.443306	−	0.767828i	−0.997932	+	0.0642710i	$0.979528\pi$
$830$	27.1707	+	9.88933i	0.943109	+	0.343264i
$831$		0			0
$832$	9.31386	+	7.81526i	0.322900	+	0.270945i
$833$	−6.27719	+	2.28471i	−0.217492	+	0.0791605i
$834$		0			0
$835$	−2.50387	−	14.2002i	−0.0866500	−	0.491417i
$836$	0.716881			0.0247939
$837$		0			0
$838$	10.8265			0.373994
$839$	−3.01801	−	17.1160i	−0.104193	−	0.590909i	−0.991539	−	0.129805i	$-0.958565\pi$
$839$	−3.01801	−	17.1160i	−0.104193	−	0.590909i	0.887346	−	0.461104i	$-0.152546\pi$
$840$		0			0
$841$	−15.1446	+	5.51217i	−0.522226	+	0.190075i
$842$	7.48861	+	6.28369i	0.258074	+	0.216550i
$843$		0			0
$844$	1.16163	+	0.422797i	0.0399848	+	0.0145533i
$845$	−13.9363	−	24.1384i	−0.479423	−	0.830385i
$846$		0			0
$847$	−11.9875	+	20.7630i	−0.411896	+	0.713424i
$848$	0.0450442	−	0.0377966i	0.00154683	−	0.00129794i
$849$		0			0
$850$	−4.60385	+	26.1097i	−0.157911	+	0.895555i
$851$	3.27079	−	18.5496i	0.112121	−	0.635872i
$852$		0			0
$853$	10.1905	−	8.55082i	0.348915	−	0.292775i	−0.451439	−	0.892302i	$-0.649089\pi$
$853$	10.1905	−	8.55082i	0.348915	−	0.292775i	0.800354	+	0.599527i	$0.204645\pi$
$854$	−3.63223	+	6.29120i	−0.124292	+	0.215280i
$855$		0			0
$856$	−10.7772	−	18.6666i	−0.368357	−	0.638013i
$857$	−18.7199	−	6.81348i	−0.639459	−	0.232744i	0.00188429	−	0.999998i	$-0.499400\pi$
$857$	−18.7199	−	6.81348i	−0.639459	−	0.232744i	−0.641343	+	0.767254i	$0.721622\pi$
$858$		0			0
$859$	20.1811	+	16.9340i	0.688572	+	0.577780i	0.918497	−	0.395428i	$-0.129404\pi$
$859$	20.1811	+	16.9340i	0.688572	+	0.577780i	−0.229925	+	0.973208i	$0.573848\pi$
$860$	27.8444	−	10.1345i	0.949485	−	0.345584i
$861$		0			0
$862$	5.63412	+	31.9527i	0.191899	+	1.08831i
$863$	−38.2995			−1.30373			−0.651866	−	0.758334i	$-0.726013\pi$
$863$	−38.2995			−1.30373			−0.651866	+	0.758334i	$0.726013\pi$
$864$		0			0
$865$	−6.04963			−0.205694
$866$	−5.80247	−	32.9074i	−0.197176	−	1.11824i
$867$		0			0
$868$	13.0575	−	4.75253i	0.443200	−	0.161311i
$869$	0.157918	+	0.132509i	0.00535701	+	0.00449506i
$870$		0			0
$871$	13.2900	+	4.83716i	0.450314	+	0.163901i
$872$	−22.1866	−	38.4283i	−0.751333	−	1.30135i
$873$		0			0
$874$	4.48680	−	7.77136i	0.151768	−	0.262870i
$875$	32.7859	−	27.5106i	1.10836	−	0.930028i
$876$		0			0
$877$	−4.69846	+	26.6463i	−0.158656	+	0.899782i	0.796711	+	0.604360i	$0.206571\pi$
$877$	−4.69846	+	26.6463i	−0.158656	+	0.899782i	−0.955367	+	0.295422i	$0.904540\pi$
$878$	0.0308505	−	0.174962i	0.00104116	−	0.00590468i
$879$		0			0
$880$	−0.0202293	+	0.0169744i	−0.000681930	+	0.000572207i
$881$	15.2888	−	26.4810i	0.515093	−	0.892167i	−0.484754	−	0.874651i	$-0.661091\pi$
$881$	15.2888	−	26.4810i	0.515093	−	0.892167i	0.999847	−	0.0175162i	$-0.00557586\pi$
$882$		0			0
$883$	−22.0526	−	38.1963i	−0.742130	−	1.28541i	−0.951524	−	0.307575i	$-0.900482\pi$
$883$	−22.0526	−	38.1963i	−0.742130	−	1.28541i	0.209394	−	0.977831i	$-0.432851\pi$
$884$	−8.33915	−	3.03520i	−0.280476	−	0.102085i
$885$		0			0
$886$	−14.3011	−	12.0001i	−0.480456	−	0.403150i
$887$	−7.40895	+	2.69664i	−0.248768	+	0.0905442i	−0.463395	−	0.886152i	$-0.653369\pi$
$887$	−7.40895	+	2.69664i	−0.248768	+	0.0905442i	0.214627	+	0.976696i	$0.431147\pi$
$888$		0			0
$889$	−0.0158921	−	0.0901285i	−0.000533004	−	0.00302281i
$890$	26.3432			0.883025
$891$		0			0
$892$	−22.4287			−0.750969
$893$	−4.61927	−	26.1972i	−0.154578	−	0.876655i
$894$		0			0
$895$	44.4470	−	16.1774i	1.48570	−	0.540751i
$896$	11.4520	+	9.60938i	0.382585	+	0.321027i
$897$		0			0
$898$	−27.4840	−	10.0033i	−0.917152	−	0.333816i
$899$	−17.4128	−	30.1599i	−0.580750	−	1.00589i
$900$		0			0
$901$	−2.10560	+	3.64701i	−0.0701477	+	0.121499i
$902$	−0.635001	+	0.532829i	−0.0211432	+	0.0177413i
$903$		0			0
$904$	−1.13975	+	6.46383i	−0.0379075	+	0.214984i
$905$	11.3662	−	64.4608i	0.377825	−	2.14275i
$906$		0			0
$907$	−9.88713	+	8.29628i	−0.328297	+	0.275474i	−0.792005	−	0.610514i	$-0.790963\pi$
$907$	−9.88713	+	8.29628i	−0.328297	+	0.275474i	0.463709	+	0.885988i	$0.346518\pi$
$908$	1.62226	−	2.80984i	0.0538367	−	0.0932479i
$909$		0			0
$910$	−8.98680	−	15.5656i	−0.297909	−	0.515994i
$911$	19.9081	+	7.24595i	0.659584	+	0.240069i	0.650057	−	0.759886i	$-0.274745\pi$
$911$	19.9081	+	7.24595i	0.659584	+	0.240069i	0.00952715	+	0.999955i	$0.496967\pi$
$912$		0			0
$913$	−1.05509	−	0.885328i	−0.0349185	−	0.0293001i
$914$	0.0282185	−	0.0102707i	0.000933385	−	0.000339724i
$915$		0			0
$916$	0.737627	+	4.18329i	0.0243719	+	0.138220i
$917$	40.0871			1.32379
$918$		0			0
$919$	31.4688			1.03806			0.519031	−	0.854756i	$-0.326293\pi$
$919$	31.4688			1.03806			0.519031	+	0.854756i	$0.326293\pi$
$920$	−5.42380	−	30.7599i	−0.178817	−	1.01412i
$921$		0			0
$922$	−12.3840	+	4.50742i	−0.407846	+	0.148444i
$923$	28.2973	+	23.7442i	0.931416	+	0.781550i
$924$		0			0
$925$	62.6878	+	22.8165i	2.06116	+	0.750202i
$926$	13.3853	+	23.1840i	0.439869	+	0.761875i
$927$		0			0
$928$	18.9354	−	32.7971i	0.621585	−	1.07662i
$929$	1.78240	−	1.49561i	0.0584788	−	0.0490695i	−0.613080	−	0.790021i	$-0.710070\pi$
$929$	1.78240	−	1.49561i	0.0584788	−	0.0490695i	0.671559	+	0.740951i	$0.265625\pi$
$930$		0			0
$931$	−1.39053	+	7.88609i	−0.0455728	+	0.258456i
$932$	1.30483	−	7.40008i	0.0427413	−	0.242398i
$933$		0			0
$934$	0.344055	−	0.288696i	0.0112578	−	0.00944643i
$935$	0.945622	−	1.63787i	0.0309252	−	0.0535639i
$936$		0			0
$937$	5.49912	+	9.52476i	0.179649	+	0.311160i	0.941760	−	0.336285i	$-0.109171\pi$
$937$	5.49912	+	9.52476i	0.179649	+	0.311160i	−0.762112	+	0.647446i	$0.775837\pi$
$938$	−10.5884	−	3.85387i	−0.345724	−	0.125833i
$939$		0			0
$940$	−26.9650	−	22.6263i	−0.879500	−	0.737989i
$941$	−22.6501	+	8.24395i	−0.738371	+	0.268745i	−0.683704	−	0.729759i	$-0.739632\pi$
$941$	−22.6501	+	8.24395i	−0.738371	+	0.268745i	−0.0546673	+	0.998505i	$0.517410\pi$
$942$		0			0
$943$	−2.85814	−	16.2093i	−0.0930737	−	0.527847i
$944$	−0.214498			−0.00698131
$945$		0			0
$946$	0.889814			0.0289304
$947$	2.06980	+	11.7384i	0.0672596	+	0.381448i	0.999793	+	0.0203634i	$0.00648231\pi$
$947$	2.06980	+	11.7384i	0.0672596	+	0.381448i	−0.932533	+	0.361085i	$0.882407\pi$
$948$		0			0
$949$	−19.6694	+	7.15906i	−0.638495	+	0.232393i
$950$	24.3464	+	20.4291i	0.789902	+	0.662807i
$951$		0			0
$952$	17.4764	+	6.36090i	0.566414	+	0.206158i
$953$	−18.4145	−	31.8948i	−0.596503	−	1.03317i	−0.993333	−	0.115281i	$-0.963223\pi$
$953$	−18.4145	−	31.8948i	−0.596503	−	1.03317i	0.396830	−	0.917892i	$-0.370110\pi$
$954$		0			0
$955$	33.8974	−	58.7120i	1.09689	−	1.89988i
$956$	−27.2053	+	22.8280i	−0.879883	+	0.738310i
$957$		0			0
$958$	2.35937	−	13.3807i	0.0762279	−	0.432310i
$959$	5.43020	−	30.7962i	0.175350	−	0.994460i
$960$		0			0
$961$	−3.15451	+	2.64695i	−0.101759	+	0.0853856i
$962$	7.03849	−	12.1910i	0.226930	−	0.393054i
$963$		0			0
$964$	13.6934	+	23.7177i	0.441035	+	0.763895i
$965$	−7.26264	−	2.64339i	−0.233793	−	0.0850936i
$966$		0			0
$967$	41.0296	+	34.4279i	1.31942	+	1.10713i	0.986427	+	0.164200i	$0.0525042\pi$
$967$	41.0296	+	34.4279i	1.31942	+	1.10713i	0.332996	+	0.942928i	$0.391940\pi$
$968$	−29.2597	+	10.6497i	−0.940443	+	0.342293i
$969$		0			0
$970$	2.31433	+	13.1252i	0.0743087	+	0.421425i
$971$	−53.2327			−1.70832			−0.854159	−	0.520012i	$-0.825927\pi$
$971$	−53.2327			−1.70832			−0.854159	+	0.520012i	$0.825927\pi$
$972$		0			0
$973$	−22.9299			−0.735100
$974$	4.50640	+	25.5570i	0.144394	+	0.818901i
$975$		0			0
$976$	−0.148833	+	0.0541709i	−0.00476404	+	0.00173397i
$977$	−10.3086	−	8.64998i	−0.329803	−	0.276737i	0.462817	−	0.886454i	$-0.346839\pi$
$977$	−10.3086	−	8.64998i	−0.329803	−	0.276737i	−0.792620	+	0.609717i	$0.791283\pi$
$978$		0			0
$979$	−1.17917	−	0.429182i	−0.0376864	−	0.0137167i
$980$	5.29813	+	9.17664i	0.169243	+	0.293137i
$981$		0			0
$982$	0.948615	−	1.64305i	0.0302715	−	0.0524318i
$983$	7.84524	−	6.58294i	0.250224	−	0.209963i	−0.509045	−	0.860740i	$-0.670001\pi$
$983$	7.84524	−	6.58294i	0.250224	−	0.209963i	0.759269	+	0.650777i	$0.225557\pi$
$984$		0			0
$985$	14.2763	−	80.9650i	0.454881	−	2.57976i
$986$	3.07708	−	17.4510i	0.0979941	−	0.555752i
$987$		0			0
$988$	−8.14930	+	6.83807i	−0.259264	+	0.217548i
$989$	−8.83409	+	15.3011i	−0.280908	+	0.486547i
$990$		0			0
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	0.849705	−	0.527258i	$-0.176780\pi$
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	−0.881471	+	0.472237i	$0.843446\pi$
$992$	27.4697	+	9.99816i	0.872165	+	0.317442i
$993$		0			0
$994$	−22.5450	−	18.9175i	−0.715085	−	0.600028i
$995$	−11.2417	+	4.09164i	−0.356386	+	0.129714i
$996$		0			0
$997$	6.68573	+	37.9166i	0.211739	+	1.20083i	0.886476	+	0.462774i	$0.153146\pi$
$997$	6.68573	+	37.9166i	0.211739	+	1.20083i	−0.674737	+	0.738058i	$0.735743\pi$
$998$	6.59121			0.208641
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.h.82.1		6
3.2	odd	2		729.2.e.c.82.1		6
9.2	odd	6		729.2.e.b.325.1		6
9.4	even	3		729.2.e.a.568.1		6
9.5	odd	6		729.2.e.i.568.1		6
9.7	even	3		729.2.e.g.325.1		6
27.2	odd	18		729.2.e.c.649.1		6
27.4	even	9		243.2.c.f.163.1		6
27.5	odd	18		243.2.a.f.1.1	yes	3
27.7	even	9		729.2.e.g.406.1		6
27.11	odd	18		729.2.e.i.163.1		6
27.13	even	9		243.2.c.f.82.1		6
27.14	odd	18		243.2.c.e.82.3		6
27.16	even	9		729.2.e.a.163.1		6
27.20	odd	18		729.2.e.b.406.1		6
27.22	even	9		243.2.a.e.1.3	✓	3
27.23	odd	18		243.2.c.e.163.3		6
27.25	even	9	inner	729.2.e.h.649.1		6
108.59	even	18		3888.2.a.bk.1.3		3
108.103	odd	18		3888.2.a.bd.1.1		3
135.49	even	18		6075.2.a.bv.1.1		3
135.59	odd	18		6075.2.a.bq.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.a.e.1.3	✓	3	27.22	even	9
243.2.a.f.1.1	yes	3	27.5	odd	18
243.2.c.e.82.3		6	27.14	odd	18
243.2.c.e.163.3		6	27.23	odd	18
243.2.c.f.82.1		6	27.13	even	9
243.2.c.f.163.1		6	27.4	even	9
729.2.e.a.163.1		6	27.16	even	9
729.2.e.a.568.1		6	9.4	even	3
729.2.e.b.325.1		6	9.2	odd	6
729.2.e.b.406.1		6	27.20	odd	18
729.2.e.c.82.1		6	3.2	odd	2
729.2.e.c.649.1		6	27.2	odd	18
729.2.e.g.325.1		6	9.7	even	3
729.2.e.g.406.1		6	27.7	even	9
729.2.e.h.82.1		6	1.1	even	1	trivial
729.2.e.h.649.1		6	27.25	even	9	inner
729.2.e.i.163.1		6	27.11	odd	18
729.2.e.i.568.1		6	9.5	odd	6
3888.2.a.bd.1.1		3	108.103	odd	18
3888.2.a.bk.1.3		3	108.59	even	18
6075.2.a.bq.1.3		3	135.59	odd	18
6075.2.a.bv.1.1		3	135.49	even	18

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	729.2.e.h.82.1

Level	$729$
Weight	$2$
Character	729.82
Analytic conductor	$5.821$
Analytic rank	$0$
Dimension	$6$
Inner twists	$2$