LMFDB - Embedded newform 729.2.e.c.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

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")

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

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.c.649.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

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	$-0.954922\pi$
$2$	−0.152704	−	0.866025i	−0.107978	−	0.612372i	0.882011	−	0.471228i	$-0.156189\pi$
$3$		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	$0.0564692\pi$
$5$	2.97178	+	2.49362i	1.32902	+	1.11518i	0.344716	+	0.938707i	$0.387975\pi$
$6$		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	−0.623828	−	0.781562i	$-0.714423\pi$
$11$	0.124485	−	0.104455i	0.0375337	−	0.0314945i	0.661362	+	0.750067i	$0.269979\pi$
$12$		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	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		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	−0.604700	−	0.796453i	$-0.706707\pi$
$23$	−2.66637	+	0.970481i	−0.555977	+	0.202359i	0.0487229	+	0.998812i	$0.484485\pi$
$24$		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	$0.158794\pi$
$29$	1.16637	+	6.61484i	0.216590	+	1.22834i	−0.661535	+	0.749914i	$0.730095\pi$
$30$		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	$0.205186\pi$
$41$	−1.00727	+	5.71253i	−0.157310	+	0.892148i	−0.956644	+	0.291261i	$0.905925\pi$
$42$		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	−0.218961	−	0.975734i	$-0.570267\pi$
$47$	−6.95084	−	2.52990i	−1.01388	−	0.369024i	−0.794923	+	0.606710i	$0.792489\pi$
$48$		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	$-0.469264\pi$
$53$	1.40373			0.192818			0.0964088	+	0.995342i	$0.469264\pi$
$54$		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	0.350687	−	0.936493i	$-0.385948\pi$
$59$	−3.92262	−	3.29147i	−0.510681	−	0.428513i	−0.861369	+	0.507980i	$0.830392\pi$
$60$		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	$-0.470205\pi$
$71$	7.65910	−	13.2660i	0.908968	−	1.57438i	0.815500	−	0.578756i	$-0.196462\pi$
$72$		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	$-0.901552\pi$
$83$	−1.47178	−	8.34689i	−0.161549	−	0.916190i	0.791003	−	0.611813i	$-0.209559\pi$
$84$		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	0.585546	−	0.810640i	$-0.300880\pi$
$89$	−3.86097	−	6.68739i	−0.409262	−	0.708862i	−0.994807	+	0.101778i	$0.967547\pi$
$90$		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	0.692247	−	0.721661i	$-0.256621\pi$
$101$	7.62449	+	2.77509i	0.758665	+	0.276131i	0.0664176	+	0.997792i	$0.478843\pi$
$102$		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	$-0.380324\pi$
$107$	7.59627			0.734359			0.367179	+	0.930150i	$0.380324\pi$
$108$		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	0.555625	−	0.831433i	$-0.312479\pi$
$113$	−1.77197	−	1.48686i	−0.166693	−	0.139872i	−0.722318	+	0.691561i	$0.756923\pi$
$114$		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	−0.957712	−	0.287728i	$-0.907100\pi$
$131$	−17.2417	+	6.27546i	−1.50641	+	0.548290i	−0.548702	+	0.836018i	$0.684878\pi$
$132$		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	$0.153849\pi$
$137$	2.48545	+	14.0957i	0.212347	+	1.20428i	−0.673106	+	0.739546i	$0.735040\pi$
$138$		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	−0.992514	−	0.122131i	$-0.961027\pi$
$149$	−0.220752	+	1.25195i	−0.0180847	+	0.102563i	0.974429	+	0.224694i	$0.0721383\pi$
$150$		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	0.525941	−	0.850521i	$-0.323713\pi$
$167$	−2.84730	−	2.38917i	−0.220330	−	0.184879i	−0.746271	+	0.665642i	$0.768158\pi$
$168$		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	−0.687069	−	0.726592i	$-0.741103\pi$
$173$	−1.19459	+	1.00238i	−0.0908232	+	0.0762097i	0.596246	+	0.802802i	$0.296658\pi$
$174$		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	−0.543069	−	0.839688i	$-0.682738\pi$
$179$	6.09627	−	10.5590i	0.455656	−	0.789220i	0.998726	+	0.0504679i	$0.0160713\pi$
$180$		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	$-0.837688\pi$
$191$	−3.03462	−	17.2102i	−0.219577	−	1.24528i	0.653208	−	0.757179i	$-0.273423\pi$
$192$		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	$-0.894326\pi$
$197$	−10.5963	−	18.3533i	−0.754953	−	1.30762i	0.190445	−	0.981698i	$-0.439007\pi$
$198$		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	−0.707547	−	0.706666i	$-0.750198\pi$
$227$	−2.02616	+	1.70015i	−0.134481	+	0.112843i	0.573066	+	0.819509i	$0.305754\pi$
$228$		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	−0.948739	−	0.316061i	$-0.897640\pi$
$233$	−3.06283	+	5.30498i	−0.200653	+	0.347541i	0.748086	+	0.663602i	$0.230973\pi$
$234$		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	0.759813	−	0.650142i	$-0.225291\pi$
$239$	27.2053	−	9.90193i	1.75977	−	0.640503i	0.999954	+	0.00963943i	$0.00306837\pi$
$240$		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	$0.0878633\pi$
$251$	11.3610	+	19.6778i	0.717098	+	1.24205i	−0.245047	+	0.969511i	$0.578803\pi$
$252$		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	$0.264779\pi$
$257$	−3.40167	+	19.2919i	−0.212191	+	1.20339i	−0.885716	+	0.464228i	$0.846332\pi$
$258$		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	−0.229811	−	0.973235i	$-0.573811\pi$
$263$	−16.7271	−	6.08818i	−1.03144	−	0.375414i	−0.801629	+	0.597822i	$0.796033\pi$
$264$		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	$-0.255524\pi$
$269$	22.7888			1.38946			0.694729	+	0.719272i	$0.255524\pi$
$270$		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	−0.899492	−	0.436938i	$-0.856063\pi$
$281$	−10.4834	+	8.79661i	−0.625387	+	0.524762i	0.274105	+	0.961700i	$0.411618\pi$
$282$		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	−0.907596	−	0.419844i	$-0.862085\pi$
$293$	−22.8170	+	8.30472i	−1.33298	+	0.485167i	−0.425388	+	0.905011i	$0.639862\pi$
$294$		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	$-0.766458\pi$
$311$	3.24897	−	18.4258i	0.184232	−	1.04483i	0.926938	−	0.375215i	$-0.122431\pi$
$312$		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	−0.163386	−	0.986562i	$-0.552241\pi$
$317$	−16.4281	−	5.97935i	−0.922696	−	0.335834i	−0.759311	+	0.650728i	$0.774464\pi$
$318$		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	−0.690633	−	0.723205i	$-0.742668\pi$
$347$	−14.0608	+	5.11770i	−0.754822	+	0.274733i	−0.0641886	+	0.997938i	$0.520446\pi$
$348$		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	$-0.917851\pi$
$353$	−2.73560	−	15.5144i	−0.145602	−	0.825747i	0.821281	−	0.570524i	$-0.193260\pi$
$354$		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	0.521373	−	0.853329i	$-0.325420\pi$
$359$	−9.06283	−	15.6973i	−0.478318	−	0.828471i	−0.999691	+	0.0248577i	$0.992087\pi$
$360$		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	0.998131	−	0.0611076i	$-0.0194633\pi$
$383$	21.7481	+	18.2488i	1.11128	+	0.932471i	0.113144	+	0.993579i	$0.463908\pi$
$384$		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	−0.406457	−	0.913670i	$-0.633236\pi$
$389$	8.33796	−	6.99638i	0.422752	−	0.354731i	0.829209	+	0.558939i	$0.188791\pi$
$390$		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	−0.375441	−	0.926846i	$-0.622509\pi$
$401$	−1.34730	+	0.490376i	−0.0672808	+	0.0244882i	0.308161	+	0.951334i	$0.400287\pi$
$402$		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	$0.152784\pi$
$419$	−2.13785	+	12.1244i	−0.104441	+	0.592314i	−0.991442	+	0.130547i	$0.958327\pi$
$420$		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	$-0.848324\pi$
$431$	−36.8958			−1.77721			−0.888604	+	0.458675i	$0.848324\pi$
$432$		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	−0.168728	−	0.985663i	$-0.553966\pi$
$443$	16.2626	−	13.6460i	0.772661	−	0.648340i	0.941389	+	0.337323i	$0.109521\pi$
$444$		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	$-0.546097\pi$
$449$	16.6297	−	28.8035i	0.784804	−	1.35932i	0.929116	−	0.369788i	$-0.120570\pi$
$450$		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	$-0.942079\pi$
$461$	−2.60236	−	14.7587i	−0.121204	−	0.687382i	0.862286	−	0.506421i	$-0.169032\pi$
$462$		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	0.871873	−	0.489731i	$-0.162905\pi$
$467$	0.255367	+	0.442308i	0.0118170	+	0.0204676i	−0.860056	+	0.510199i	$0.829572\pi$
$468$		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	0.651697	−	0.758479i	$-0.274057\pi$
$479$	14.5189	+	5.28444i	0.663385	+	0.241452i	0.0116878	+	0.999932i	$0.496280\pi$
$480$		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	0.679318	−	0.733844i	$-0.262276\pi$
$491$	1.65270	+	1.38678i	0.0745855	+	0.0625846i	−0.604733	+	0.796428i	$0.706720\pi$
$492$		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	$0.386707\pi$
$503$	−14.2981	+	24.7651i	−0.637522	+	1.10422i	−0.985975	+	0.166894i	$0.946626\pi$
$504$		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	−0.306545	−	0.951856i	$-0.599173\pi$
$509$	1.58987	−	0.578665i	0.0704698	−	0.0256489i	0.377015	+	0.926207i	$0.376951\pi$
$510$		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	0.999943	−	0.0106337i	$-0.00338487\pi$
$521$	11.2019	+	19.4022i	0.490763	+	0.850026i	−0.509181	+	0.860660i	$0.670052\pi$
$522$		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	−0.724053	−	0.689744i	$-0.757723\pi$
$557$	5.55350	−	9.61894i	0.235309	−	0.407568i	0.959363	+	0.282176i	$0.0910563\pi$
$558$		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	−0.644117	−	0.764927i	$-0.722775\pi$
$563$	−15.3246	+	5.57770i	−0.645855	+	0.235072i	−0.00173729	+	0.999998i	$0.500553\pi$
$564$		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	$0.216780\pi$
$569$	6.25418	+	35.4692i	0.262189	+	1.48695i	−0.514733	+	0.857351i	$0.672109\pi$
$570$		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	0.968397	−	0.249412i	$-0.0802374\pi$
$587$	37.5514	+	13.6676i	1.54991	+	0.564123i	0.581516	+	0.813535i	$0.302460\pi$
$588$		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	$-0.705467\pi$
$593$	−29.2995			−1.20319			−0.601594	+	0.798802i	$0.705467\pi$
$594$		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	0.786657	−	0.617390i	$-0.211810\pi$
$599$	7.71554	+	6.47410i	0.315248	+	0.264525i	−0.471409	+	0.881915i	$0.656254\pi$
$600$		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	−0.160301	−	0.987068i	$-0.551246\pi$
$617$	8.72803	−	3.17674i	0.351377	−	0.127891i	0.511678	+	0.859177i	$0.329024\pi$
$618$		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	0.287142	−	0.957888i	$-0.407295\pi$
$641$	−2.74985	−	1.00086i	−0.108612	−	0.0395317i	−0.395755	+	0.918356i	$0.629517\pi$
$642$		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	$-0.432406\pi$
$647$	10.7219			0.421523			0.210761	+	0.977538i	$0.432406\pi$
$648$		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	0.995144	−	0.0984334i	$-0.0313831\pi$
$653$	27.3685	+	22.9649i	1.07101	+	0.898685i	0.0758669	+	0.997118i	$0.475828\pi$
$654$		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	−0.0531299	−	0.998588i	$-0.516920\pi$
$659$	23.6446	−	19.8401i	0.921061	−	0.772862i	0.974191	+	0.225726i	$0.0724753\pi$
$660$		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	$-0.871384\pi$
$677$	−4.94150	−	28.0247i	−0.189917	−	1.07708i	0.729555	−	0.683922i	$-0.239727\pi$
$678$		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	0.721174	−	0.692754i	$-0.243603\pi$
$683$	−6.25537	−	10.8346i	−0.239355	−	0.414575i	−0.960529	+	0.278179i	$0.910269\pi$
$684$		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	$-0.0674008\pi$
$701$	51.7701			1.95533			0.977665	+	0.210167i	$0.0674008\pi$
$702$		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	−0.840615	−	0.541633i	$-0.817806\pi$
$719$	1.30747	−	2.26460i	0.0487603	−	0.0844553i	0.889375	+	0.457178i	$0.151140\pi$
$720$		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	−0.993537	−	0.113509i	$-0.963791\pi$
$743$	−0.575017	+	3.26109i	−0.0210953	+	0.119638i	0.972442	+	0.233146i	$0.0749021\pi$
$744$		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	0.741970	−	0.670433i	$-0.233892\pi$
$761$	5.80865	+	4.87404i	0.210563	+	0.176684i	−0.531406	+	0.847117i	$0.678336\pi$
$762$		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	−0.864362	−	0.502870i	$-0.832277\pi$
$773$	0.0922341	−	0.159754i	0.00331743	−	0.00574596i	0.867679	+	0.497124i	$0.165611\pi$
$774$		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	−

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more