LMFDB - Embedded newform 1638.2.p.i.991.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(919,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("1638.919");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.p (of order $3$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.3
Root			$-0.571299 + 1.29368i$ of defining polynomial
Character	$\chi$	$=$	1638.991
Dual form			1638.2.p.i.919.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.228205 + 0.395262i) q^{5} +(2.45374 - 0.989520i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.228205 + 0.395262i) q^{5} +(2.45374 - 0.989520i) q^{7} -1.00000 q^{8} +0.456409 q^{10} +3.83707 q^{11} +(-3.13422 - 1.78233i) q^{13} +(0.369922 - 2.61976i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.775934 + 1.34396i) q^{17} -2.88244 q^{19} +(0.228205 - 0.395262i) q^{20} +(1.91853 - 3.32300i) q^{22} +(1.62170 - 2.80886i) q^{23} +(2.39585 - 4.14973i) q^{25} +(-3.11065 + 1.82315i) q^{26} +(-2.08382 - 1.63024i) q^{28} +(2.20552 + 3.82007i) q^{29} +(4.80098 - 8.31553i) q^{31} +(0.500000 + 0.866025i) q^{32} +1.55187 q^{34} +(0.951075 + 0.744058i) q^{35} +(-0.140245 + 0.242912i) q^{37} +(-1.44122 + 2.49627i) q^{38} +(-0.228205 - 0.395262i) q^{40} +(3.57277 + 6.18822i) q^{41} +(1.21716 - 2.10818i) q^{43} +(-1.91853 - 3.32300i) q^{44} +(-1.62170 - 2.80886i) q^{46} +(3.93105 + 6.80879i) q^{47} +(5.04170 - 4.85605i) q^{49} +(-2.39585 - 4.14973i) q^{50} +(0.0235697 + 3.60547i) q^{52} +(-0.550397 + 0.953315i) q^{53} +(0.875637 + 1.51665i) q^{55} +(-2.45374 + 0.989520i) q^{56} +4.41103 q^{58} +(-4.68283 - 8.11090i) q^{59} -11.1037 q^{61} +(-4.80098 - 8.31553i) q^{62} +1.00000 q^{64} +(-0.0107575 - 1.64557i) q^{65} -1.78993 q^{67} +(0.775934 - 1.34396i) q^{68} +(1.11991 - 0.451626i) q^{70} +(5.06527 - 8.77331i) q^{71} +(1.40601 - 2.43529i) q^{73} +(0.140245 + 0.242912i) q^{74} +(1.44122 + 2.49627i) q^{76} +(9.41517 - 3.79685i) q^{77} +(2.70966 + 4.69326i) q^{79} -0.456409 q^{80} +7.14554 q^{82} -1.35738 q^{83} +(-0.354144 + 0.613395i) q^{85} +(-1.21716 - 2.10818i) q^{86} -3.83707 q^{88} +(-0.0898485 + 0.155622i) q^{89} +(-9.45421 - 1.27200i) q^{91} -3.24339 q^{92} +7.86211 q^{94} +(-0.657787 - 1.13932i) q^{95} +(4.73894 - 8.20808i) q^{97} +(-1.68461 - 6.79427i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8	$ 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} - 4 q^{10} - 12 q^{11} - 11 q^{13} + 3 q^{14} - 4 q^{16} - 4 q^{17} - 12 q^{19} - 2 q^{20} - 6 q^{22} + 10 q^{23} - 18 q^{25} - 10 q^{26} - 2 q^{29} + 6 q^{31} + 4 q^{32} - 8 q^{34} - 18 q^{35} - 28 q^{37} - 6 q^{38} + 2 q^{40} - 6 q^{43} + 6 q^{44} - 10 q^{46} - q^{47} - 7 q^{49} + 18 q^{50} + q^{52} - 7 q^{53} + q^{55} - 3 q^{56} - 4 q^{58} - 2 q^{59} - 48 q^{61} - 6 q^{62} + 8 q^{64} - 19 q^{65} + 30 q^{67} - 4 q^{68} - 18 q^{70} - 6 q^{71} + q^{73} + 28 q^{74} + 6 q^{76} + 22 q^{77} - 12 q^{79} + 4 q^{80} + 32 q^{83} - 13 q^{85} + 6 q^{86} + 12 q^{88} - 25 q^{89} + 34 q^{91} - 20 q^{92} - 2 q^{94} + 8 q^{95} - q^{97} - 2 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 - 4 * q^10 - 12 * q^11 - 11 * q^13 + 3 * q^14 - 4 * q^16 - 4 * q^17 - 12 * q^19 - 2 * q^20 - 6 * q^22 + 10 * q^23 - 18 * q^25 - 10 * q^26 - 2 * q^29 + 6 * q^31 + 4 * q^32 - 8 * q^34 - 18 * q^35 - 28 * q^37 - 6 * q^38 + 2 * q^40 - 6 * q^43 + 6 * q^44 - 10 * q^46 - q^47 - 7 * q^49 + 18 * q^50 + q^52 - 7 * q^53 + q^55 - 3 * q^56 - 4 * q^58 - 2 * q^59 - 48 * q^61 - 6 * q^62 + 8 * q^64 - 19 * q^65 + 30 * q^67 - 4 * q^68 - 18 * q^70 - 6 * q^71 + q^73 + 28 * q^74 + 6 * q^76 + 22 * q^77 - 12 * q^79 + 4 * q^80 + 32 * q^83 - 13 * q^85 + 6 * q^86 + 12 * q^88 - 25 * q^89 + 34 * q^91 - 20 * q^92 - 2 * q^94 + 8 * q^95 - q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.228205	+	0.395262i	0.102056	+	0.176767i	0.912532	−	0.409006i	$-0.134125\pi$
$5$	0.228205	+	0.395262i	0.102056	+	0.176767i	−0.810475	+	0.585773i	$0.800791\pi$
$6$		0			0
$7$	2.45374	−	0.989520i	0.927427	−	0.374003i
$7$	2.45374	−	0.989520i	0.927427	−	0.374003i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.456409			0.144329
$11$	3.83707			1.15692			0.578460	−	0.815711i	$-0.303654\pi$
$11$	3.83707			1.15692			0.578460	+	0.815711i	$0.303654\pi$
$12$		0			0
$13$	−3.13422	−	1.78233i	−0.869275	−	0.494328i
$13$	−3.13422	−	1.78233i	−0.869275	−	0.494328i
$14$	0.369922	−	2.61976i	0.0988658	−	0.700161i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.775934	+	1.34396i	0.188192	+	0.325958i	0.944647	−	0.328087i	$-0.106404\pi$
$17$	0.775934	+	1.34396i	0.188192	+	0.325958i	−0.756456	+	0.654045i	$0.773071\pi$
$18$		0			0
$19$	−2.88244			−0.661278			−0.330639	−	0.943757i	$-0.607264\pi$
$19$	−2.88244			−0.661278			−0.330639	+	0.943757i	$0.607264\pi$
$20$	0.228205	−	0.395262i	0.0510281	−	0.0883833i
$21$		0			0
$22$	1.91853	−	3.32300i	0.409033	−	0.708465i
$23$	1.62170	−	2.80886i	0.338147	−	0.585688i	−0.645937	−	0.763391i	$-0.723533\pi$
$23$	1.62170	−	2.80886i	0.338147	−	0.585688i	0.984084	+	0.177703i	$0.0568665\pi$
$24$		0			0
$25$	2.39585	−	4.14973i	0.479169	−	0.829945i
$26$	−3.11065	+	1.82315i	−0.610048	+	0.357549i
$27$		0			0
$28$	−2.08382	−	1.63024i	−0.393805	−	0.308087i
$29$	2.20552	+	3.82007i	0.409554	+	0.709369i	0.994840	−	0.101459i	$-0.0323509\pi$
$29$	2.20552	+	3.82007i	0.409554	+	0.709369i	−0.585286	+	0.810827i	$0.699018\pi$
$30$		0			0
$31$	4.80098	−	8.31553i	0.862281	−	1.49351i	−0.00744135	−	0.999972i	$-0.502369\pi$
$31$	4.80098	−	8.31553i	0.862281	−	1.49351i	0.869722	−	0.493542i	$-0.164298\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	1.55187			0.266143
$35$	0.951075	+	0.744058i	0.160761	+	0.125769i
$36$		0			0
$37$	−0.140245	+	0.242912i	−0.0230562	+	0.0399345i	−0.877323	−	0.479900i	$-0.840673\pi$
$37$	−0.140245	+	0.242912i	−0.0230562	+	0.0399345i	0.854267	+	0.519834i	$0.174006\pi$
$38$	−1.44122	+	2.49627i	−0.233797	+	0.404948i
$39$		0			0
$40$	−0.228205	−	0.395262i	−0.0360823	−	0.0624964i
$41$	3.57277	+	6.18822i	0.557973	+	0.966438i	0.997666	+	0.0682894i	$0.0217541\pi$
$41$	3.57277	+	6.18822i	0.557973	+	0.966438i	−0.439692	+	0.898148i	$0.644913\pi$
$42$		0			0
$43$	1.21716	−	2.10818i	0.185615	−	0.321494i	−0.758169	−	0.652058i	$-0.773906\pi$
$43$	1.21716	−	2.10818i	0.185615	−	0.321494i	0.943783	+	0.330564i	$0.107239\pi$
$44$	−1.91853	−	3.32300i	−0.289230	−	0.500961i
$45$		0			0
$46$	−1.62170	−	2.80886i	−0.239106	−	0.414144i
$47$	3.93105	+	6.80879i	0.573403	+	0.993163i	0.996213	+	0.0869451i	$0.0277105\pi$
$47$	3.93105	+	6.80879i	0.573403	+	0.993163i	−0.422810	+	0.906218i	$0.638956\pi$
$48$		0			0
$49$	5.04170	−	4.85605i	0.720243	−	0.693722i
$50$	−2.39585	−	4.14973i	−0.338824	−	0.586860i
$51$		0			0
$52$	0.0235697	+	3.60547i	0.00326854	+	0.499989i
$53$	−0.550397	+	0.953315i	−0.0756028	+	0.130948i	−0.901348	−	0.433095i	$-0.857421\pi$
$53$	−0.550397	+	0.953315i	−0.0756028	+	0.130948i	0.825745	+	0.564043i	$0.190755\pi$
$54$		0			0
$55$	0.875637	+	1.51665i	0.118071	+	0.204505i
$56$	−2.45374	+	0.989520i	−0.327895	+	0.132230i
$57$		0			0
$58$	4.41103			0.579197
$59$	−4.68283	−	8.11090i	−0.609652	−	1.05595i	−0.991298	−	0.131640i	$-0.957976\pi$
$59$	−4.68283	−	8.11090i	−0.609652	−	1.05595i	0.381645	−	0.924309i	$-0.375358\pi$
$60$		0			0
$61$	−11.1037			−1.42169			−0.710844	−	0.703350i	$-0.751687\pi$
$61$	−11.1037			−1.42169			−0.710844	+	0.703350i	$0.751687\pi$
$62$	−4.80098	−	8.31553i	−0.609725	−	1.05607i
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.0107575	−	1.64557i	−0.00133430	−	0.204108i
$66$		0			0
$67$	−1.78993			−0.218674			−0.109337	−	0.994005i	$-0.534873\pi$
$67$	−1.78993			−0.218674			−0.109337	+	0.994005i	$0.534873\pi$
$68$	0.775934	−	1.34396i	0.0940959	−	0.162979i
$69$		0			0
$70$	1.11991	−	0.451626i	0.133855	−	0.0539796i
$71$	5.06527	−	8.77331i	0.601137	−	1.04120i	−0.391512	−	0.920173i	$-0.628048\pi$
$71$	5.06527	−	8.77331i	0.601137	−	1.04120i	0.992649	−	0.121027i	$-0.0386188\pi$
$72$		0			0
$73$	1.40601	−	2.43529i	0.164561	−	0.285029i	−0.771938	−	0.635698i	$-0.780712\pi$
$73$	1.40601	−	2.43529i	0.164561	−	0.285029i	0.936499	+	0.350669i	$0.114046\pi$
$74$	0.140245	+	0.242912i	0.0163032	+	0.0282379i
$75$		0			0
$76$	1.44122	+	2.49627i	0.165319	+	0.286342i
$77$	9.41517	−	3.79685i	1.07296	−	0.432692i
$78$		0			0
$79$	2.70966	+	4.69326i	0.304860	+	0.528033i	0.977230	−	0.212182i	$-0.0680570\pi$
$79$	2.70966	+	4.69326i	0.304860	+	0.528033i	−0.672370	+	0.740215i	$0.734724\pi$
$80$	−0.456409			−0.0510281
$81$		0			0
$82$	7.14554			0.789093
$83$	−1.35738			−0.148992			−0.0744959	−	0.997221i	$-0.523735\pi$
$83$	−1.35738			−0.148992			−0.0744959	+	0.997221i	$0.523735\pi$
$84$		0			0
$85$	−0.354144	+	0.613395i	−0.0384123	+	0.0665320i
$86$	−1.21716	−	2.10818i	−0.131249	−	0.227330i
$87$		0			0
$88$	−3.83707			−0.409033
$89$	−0.0898485	+	0.155622i	−0.00952392	+	0.0164959i	−0.870748	−	0.491729i	$-0.836365\pi$
$89$	−0.0898485	+	0.155622i	−0.00952392	+	0.0164959i	0.861224	+	0.508225i	$0.169698\pi$
$90$		0			0
$91$	−9.45421	−	1.27200i	−0.991070	−	0.133341i
$92$	−3.24339			−0.338147
$93$		0			0
$94$	7.86211			0.810915
$95$	−0.657787	−	1.13932i	−0.0674875	−	0.116892i
$96$		0			0
$97$	4.73894	−	8.20808i	0.481166	−	0.833405i	−0.518600	−	0.855017i	$-0.673547\pi$
$97$	4.73894	−	8.20808i	0.481166	−	0.833405i	0.999766	+	0.0216122i	$0.00687993\pi$
$98$	−1.68461	−	6.79427i	−0.170172	−	0.686325i
$99$		0			0
$100$	−4.79169			−0.479169
$101$	−6.36213			−0.633056			−0.316528	−	0.948583i	$-0.602517\pi$
$101$	−6.36213			−0.633056			−0.316528	+	0.948583i	$0.602517\pi$
$102$		0			0
$103$	−8.28934	−	14.3576i	−0.816773	−	1.41469i	−0.908048	−	0.418866i	$-0.862428\pi$
$103$	−8.28934	−	14.3576i	−0.816773	−	1.41469i	0.0912754	−	0.995826i	$-0.470906\pi$
$104$	3.13422	+	1.78233i	0.307335	+	0.174771i
$105$		0			0
$106$	0.550397	+	0.953315i	0.0534593	+	0.0925942i
$107$	8.46023	−	14.6536i	0.817882	−	1.41661i	−0.0893583	−	0.996000i	$-0.528482\pi$
$107$	8.46023	−	14.6536i	0.817882	−	1.41661i	0.907240	−	0.420613i	$-0.138185\pi$
$108$		0			0
$109$	3.95108	−	6.84346i	0.378444	−	0.655485i	−0.612392	−	0.790554i	$-0.709792\pi$
$109$	3.95108	−	6.84346i	0.378444	−	0.655485i	0.990836	+	0.135070i	$0.0431258\pi$
$110$	1.75127			0.166977
$111$		0			0
$112$	−0.369922	+	2.61976i	−0.0349543	+	0.247544i
$113$	−3.40689	+	5.90091i	−0.320494	+	0.555111i	−0.980590	−	0.196070i	$-0.937182\pi$
$113$	−3.40689	+	5.90091i	−0.320494	+	0.555111i	0.660096	+	0.751181i	$0.270515\pi$
$114$		0			0
$115$	1.48031			0.138040
$116$	2.20552	−	3.82007i	0.204777	−	0.354684i
$117$		0			0
$118$	−9.36566			−0.862179
$119$	3.23382	+	2.52992i	0.296443	+	0.231918i
$120$		0			0
$121$	3.72308			0.338462
$122$	−5.55187	+	9.61612i	−0.502643	+	0.870602i
$123$		0			0
$124$	−9.60195			−0.862281
$125$	4.46902			0.399721
$126$		0			0
$127$	10.9334	+	18.9372i	0.970183	+	1.68041i	0.694993	+	0.719016i	$0.255407\pi$
$127$	10.9334	+	18.9372i	0.970183	+	1.68041i	0.275190	+	0.961390i	$0.411259\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.43049	−	0.813470i	−0.125462	−	0.0713460i
$131$	−4.72554	−	8.18487i	−0.412872	−	0.715116i	0.582330	−	0.812952i	$-0.302141\pi$
$131$	−4.72554	−	8.18487i	−0.412872	−	0.715116i	−0.995202	+	0.0978367i	$0.968808\pi$
$132$		0			0
$133$	−7.07277	+	2.85223i	−0.613287	+	0.247320i
$134$	−0.894964	+	1.55012i	−0.0773131	+	0.133910i
$135$		0			0
$136$	−0.775934	−	1.34396i	−0.0665358	−	0.115243i
$137$	1.22396	+	2.11996i	0.104570	+	0.181121i	0.913562	−	0.406698i	$-0.133320\pi$
$137$	1.22396	+	2.11996i	0.104570	+	0.181121i	−0.808992	+	0.587819i	$0.799987\pi$
$138$		0			0
$139$	−5.37228	+	9.30505i	−0.455670	+	0.789244i	−0.998726	−	0.0504521i	$-0.983934\pi$
$139$	−5.37228	+	9.30505i	−0.455670	+	0.789244i	0.543056	+	0.839696i	$0.317267\pi$
$140$	0.168836	−	1.19568i	0.0142692	−	0.101054i
$141$		0			0
$142$	−5.06527	−	8.77331i	−0.425068	−	0.736240i
$143$	−12.0262	−	6.83890i	−1.00568	−	0.571898i
$144$		0			0
$145$	−1.00662	+	1.74351i	−0.0835951	+	0.144791i
$146$	−1.40601	−	2.43529i	−0.116362	−	0.201546i
$147$		0			0
$148$	0.280491			0.0230562
$149$	−9.30314			−0.762143			−0.381072	−	0.924546i	$-0.624445\pi$
$149$	−9.30314			−0.762143			−0.381072	+	0.924546i	$0.624445\pi$
$150$		0			0
$151$	−10.3722	+	17.9651i	−0.844075	+	1.46198i	0.0423464	+	0.999103i	$0.486517\pi$
$151$	−10.3722	+	17.9651i	−0.844075	+	1.46198i	−0.886422	+	0.462878i	$0.846817\pi$
$152$	2.88244			0.233797
$153$		0			0
$154$	1.41942	−	10.0522i	0.114380	−	0.810030i
$155$	4.38242			0.352004
$156$		0			0
$157$	3.22701	−	5.58934i	0.257543	−	0.446078i	−0.708040	−	0.706172i	$-0.750420\pi$
$157$	3.22701	−	5.58934i	0.257543	−	0.446078i	0.965583	+	0.260094i	$0.0837536\pi$
$158$	5.41931			0.431137
$159$		0			0
$160$	−0.228205	+	0.395262i	−0.0180412	+	0.0312482i
$161$	1.19980	−	8.49692i	0.0945576	−	0.669651i
$162$		0			0
$163$	8.71775			0.682827			0.341413	−	0.939913i	$-0.389094\pi$
$163$	8.71775			0.682827			0.341413	+	0.939913i	$0.389094\pi$
$164$	3.57277	−	6.18822i	0.278987	−	0.483219i
$165$		0			0
$166$	−0.678689	+	1.17552i	−0.0526765	+	0.0912384i
$167$	11.4560	+	19.8424i	0.886491	+	1.53545i	0.843995	+	0.536351i	$0.180198\pi$
$167$	11.4560	+	19.8424i	0.886491	+	1.53545i	0.0424965	+	0.999097i	$0.486469\pi$
$168$		0			0
$169$	6.64663	+	11.1724i	0.511280	+	0.859414i
$170$	0.354144	+	0.613395i	0.0271616	+	0.0470452i
$171$		0			0
$172$	−2.43431			−0.185615
$173$	−7.58716			−0.576841			−0.288421	−	0.957504i	$-0.593130\pi$
$173$	−7.58716			−0.576841			−0.288421	+	0.957504i	$0.593130\pi$
$174$		0			0
$175$	1.77255	−	12.5531i	0.133992	−	0.948925i
$176$	−1.91853	+	3.32300i	−0.144615	+	0.250480i
$177$		0			0
$178$	0.0898485	+	0.155622i	0.00673443	+	0.0116644i
$179$	−12.5041			−0.934600			−0.467300	−	0.884099i	$-0.654773\pi$
$179$	−12.5041			−0.934600			−0.467300	+	0.884099i	$0.654773\pi$
$180$		0			0
$181$	−2.26428			−0.168303			−0.0841513	−	0.996453i	$-0.526818\pi$
$181$	−2.26428			−0.168303			−0.0841513	+	0.996453i	$0.526818\pi$
$182$	−5.82868	+	7.55158i	−0.432051	+	0.559761i
$183$		0			0
$184$	−1.62170	+	2.80886i	−0.119553	+	0.207072i
$185$	−0.128019			−0.00941211
$186$		0			0
$187$	2.97731	+	5.15686i	0.217723	+	0.377107i
$188$	3.93105	−	6.80879i	0.286702	−	0.496582i
$189$		0			0
$190$	−1.31557			−0.0954418
$191$	9.17297			0.663733			0.331867	−	0.943326i	$-0.392322\pi$
$191$	9.17297			0.663733			0.331867	+	0.943326i	$0.392322\pi$
$192$		0			0
$193$	−2.43985			−0.175624			−0.0878122	−	0.996137i	$-0.527988\pi$
$193$	−2.43985			−0.175624			−0.0878122	+	0.996137i	$0.527988\pi$
$194$	−4.73894	−	8.20808i	−0.340236	−	0.589306i
$195$		0			0
$196$	−6.72632	−	1.93822i	−0.480451	−	0.138444i
$197$	13.4334	+	23.2673i	0.957091	+	1.65773i	0.729510	+	0.683971i	$0.239748\pi$
$197$	13.4334	+	23.2673i	0.957091	+	1.65773i	0.227581	+	0.973759i	$0.426918\pi$
$198$		0			0
$199$	13.9509	+	24.1638i	0.988957	+	1.71292i	0.622828	+	0.782359i	$0.285984\pi$
$199$	13.9509	+	24.1638i	0.988957	+	1.71292i	0.366129	+	0.930564i	$0.380683\pi$
$200$	−2.39585	+	4.14973i	−0.169412	+	0.293430i
$201$		0			0
$202$	−3.18107	+	5.50977i	−0.223819	+	0.387666i
$203$	9.19180	+	7.19106i	0.645138	+	0.504713i
$204$		0			0
$205$	−1.63065	+	2.82436i	−0.113889	+	0.197262i
$206$	−16.5787			−1.15509
$207$		0			0
$208$	3.11065	−	1.82315i	0.215685	−	0.126413i
$209$	−11.0601			−0.765045
$210$		0			0
$211$	10.9871	+	19.0301i	0.756381	+	1.31009i	0.944685	+	0.327979i	$0.106367\pi$
$211$	10.9871	+	19.0301i	0.756381	+	1.31009i	−0.188305	+	0.982111i	$0.560299\pi$
$212$	1.10079			0.0756028
$213$		0			0
$214$	−8.46023	−	14.6536i	−0.578330	−	1.00170i
$215$	1.11104			0.0757725
$216$		0			0
$217$	3.55197	−	25.1548i	0.241124	−	1.70762i
$218$	−3.95108	−	6.84346i	−0.267601	−	0.463498i
$219$		0			0
$220$	0.875637	−	1.51665i	0.0590354	−	0.102252i
$221$	−0.0365772	−	5.59522i	−0.00246045	−	0.376375i
$222$		0			0
$223$	−6.87919	−	11.9151i	−0.460664	−	0.797894i	0.538330	−	0.842734i	$-0.319055\pi$
$223$	−6.87919	−	11.9151i	−0.460664	−	0.797894i	−0.998994	+	0.0448402i	$0.985722\pi$
$224$	2.08382	+	1.63024i	0.139231	+	0.108925i
$225$		0			0
$226$	3.40689	+	5.90091i	0.226623	+	0.392523i
$227$	9.41545	+	16.3080i	0.624925	+	1.08240i	0.988555	+	0.150859i	$0.0482039\pi$
$227$	9.41545	+	16.3080i	0.624925	+	1.08240i	−0.363630	+	0.931543i	$0.618463\pi$
$228$		0			0
$229$	1.74812	+	3.02784i	0.115519	+	0.200085i	0.917987	−	0.396610i	$-0.129814\pi$
$229$	1.74812	+	3.02784i	0.115519	+	0.200085i	−0.802468	+	0.596695i	$0.796480\pi$
$230$	0.740157	−	1.28199i	0.0488045	−	0.0845319i
$231$		0			0
$232$	−2.20552	−	3.82007i	−0.144799	−	0.250800i
$233$	−9.74031	−	16.8707i	−0.638109	−	1.10524i	−0.985847	−	0.167645i	$-0.946384\pi$
$233$	−9.74031	−	16.8707i	−0.638109	−	1.10524i	0.347739	−	0.937592i	$-0.386950\pi$
$234$		0			0
$235$	−1.79417	+	3.10759i	−0.117039	+	0.202717i
$236$	−4.68283	+	8.11090i	−0.304826	+	0.527974i
$237$		0			0
$238$	3.80789	−	1.53560i	0.246829	−	0.0995385i
$239$	−12.5469			−0.811592			−0.405796	−	0.913964i	$-0.633006\pi$
$239$	−12.5469			−0.811592			−0.405796	+	0.913964i	$0.633006\pi$
$240$		0			0
$241$	0.233225	+	0.403958i	0.0150234	+	0.0260212i	0.873439	−	0.486933i	$-0.161884\pi$
$241$	0.233225	+	0.403958i	0.0150234	+	0.0260212i	−0.858416	+	0.512954i	$0.828551\pi$
$242$	1.86154	−	3.22428i	0.119664	−	0.207265i
$243$		0			0
$244$	5.55187	+	9.61612i	0.355422	+	0.615609i
$245$	3.06995	+	0.884620i	0.196132	+	0.0565163i
$246$		0			0
$247$	9.03420	+	5.13745i	0.574832	+	0.326888i
$248$	−4.80098	+	8.31553i	−0.304862	+	0.528037i
$249$		0			0
$250$	2.23451	−	3.87028i	0.141323	−	0.244778i
$251$	−12.7935	+	22.1590i	−0.807517	+	1.39866i	0.107062	+	0.994252i	$0.465856\pi$
$251$	−12.7935	+	22.1590i	−0.807517	+	1.39866i	−0.914579	+	0.404408i	$0.867478\pi$
$252$		0			0
$253$	6.22256	−	10.7778i	0.391209	−	0.677594i
$254$	21.8668			1.37205
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.88805	+	3.27020i	−0.117774	+	0.203990i	−0.918885	−	0.394525i	$-0.870909\pi$
$257$	−1.88805	+	3.27020i	−0.117774	+	0.203990i	0.801112	+	0.598515i	$0.204242\pi$
$258$		0			0
$259$	−0.103760	+	0.734819i	−0.00644731	+	0.0456594i
$260$	−1.41973	+	0.832102i	−0.0880478	+	0.0516048i
$261$		0			0
$262$	−9.45108			−0.583889
$263$	−19.6872			−1.21396			−0.606981	−	0.794716i	$-0.707620\pi$
$263$	−19.6872			−1.21396			−0.606981	+	0.794716i	$0.707620\pi$
$264$		0			0
$265$	−0.502413			−0.0308630
$266$	−1.06628	+	7.55132i	−0.0653777	+	0.463001i
$267$		0			0
$268$	0.894964	+	1.55012i	0.0546686	+	0.0946888i
$269$	−4.39082	−	7.60513i	−0.267713	−	0.463693i	0.700558	−	0.713596i	$-0.252935\pi$
$269$	−4.39082	−	7.60513i	−0.267713	−	0.463693i	−0.968271	+	0.249903i	$0.919601\pi$
$270$		0			0
$271$	−14.4014	+	24.9439i	−0.874820	+	1.51523i	−0.0178654	+	0.999840i	$0.505687\pi$
$271$	−14.4014	+	24.9439i	−0.874820	+	1.51523i	−0.856955	+	0.515392i	$0.827646\pi$
$272$	−1.55187			−0.0940959
$273$		0			0
$274$	2.44792			0.147884
$275$	9.19302	−	15.9228i	0.554360	−	0.960179i
$276$		0			0
$277$	−3.47496	−	6.01880i	−0.208790	−	0.361635i	0.742544	−	0.669798i	$-0.233619\pi$
$277$	−3.47496	−	6.01880i	−0.208790	−	0.361635i	−0.951334	+	0.308163i	$0.900286\pi$
$278$	5.37228	+	9.30505i	0.322208	+	0.558080i
$279$		0			0
$280$	−0.951075	−	0.744058i	−0.0568376	−	0.0444660i
$281$	12.5116			0.746381			0.373190	−	0.927755i	$-0.378264\pi$
$281$	12.5116			0.746381			0.373190	+	0.927755i	$0.378264\pi$
$282$		0			0
$283$	11.2039			0.666003			0.333001	−	0.942926i	$-0.391939\pi$
$283$	11.2039			0.666003			0.333001	+	0.942926i	$0.391939\pi$
$284$	−10.1305			−0.601137
$285$		0			0
$286$	−11.9358	+	6.99554i	−0.705776	+	0.413655i
$287$	14.8900	+	11.6490i	0.878931	+	0.687617i
$288$		0			0
$289$	7.29585	−	12.6368i	0.429168	−	0.743340i
$290$	1.00662	+	1.74351i	0.0591107	+	0.102383i
$291$		0			0
$292$	−2.81202			−0.164561
$293$	−14.2699	+	24.7162i	−0.833657	+	1.44394i	0.0614625	+	0.998109i	$0.480424\pi$
$293$	−14.2699	+	24.7162i	−0.833657	+	1.44394i	−0.895119	+	0.445827i	$0.852910\pi$
$294$		0			0
$295$	2.13729	−	3.70189i	0.124438	−	0.215532i
$296$	0.140245	−	0.242912i	0.00815159	−	0.0141190i
$297$		0			0
$298$	−4.65157	+	8.05676i	−0.269458	+	0.466715i
$299$	−10.0891	+	5.91319i	−0.583465	+	0.341969i
$300$		0			0
$301$	0.900505	−	6.37732i	0.0519043	−	0.367583i
$302$	10.3722	+	17.9651i	0.596851	+	1.03378i
$303$		0			0
$304$	1.44122	−	2.49627i	0.0826597	−	0.143171i
$305$	−2.53392	−	4.38889i	−0.145092	−	0.251307i
$306$		0			0
$307$	−23.1907			−1.32356			−0.661781	−	0.749698i	$-0.730199\pi$
$307$	−23.1907			−1.32356			−0.661781	+	0.749698i	$0.730199\pi$
$308$	−7.99576	−	6.25535i	−0.455601	−	0.356432i
$309$		0			0
$310$	2.19121	−	3.79529i	0.124452	−	0.215558i
$311$	−11.6740	+	20.2200i	−0.661973	+	1.14657i	0.318123	+	0.948049i	$0.396948\pi$
$311$	−11.6740	+	20.2200i	−0.661973	+	1.14657i	−0.980096	+	0.198522i	$0.936386\pi$
$312$		0			0
$313$	7.26499	+	12.5833i	0.410641	+	0.711252i	0.994960	−	0.100273i	$-0.0319715\pi$
$313$	7.26499	+	12.5833i	0.410641	+	0.711252i	−0.584319	+	0.811524i	$0.698638\pi$
$314$	−3.22701	−	5.58934i	−0.182111	−	0.315425i
$315$		0			0
$316$	2.70966	−	4.69326i	0.152430	−	0.264017i
$317$	−1.64596	−	2.85089i	−0.0924463	−	0.160122i	0.816094	−	0.577920i	$-0.196135\pi$
$317$	−1.64596	−	2.85089i	−0.0924463	−	0.160122i	−0.908540	+	0.417798i	$0.862802\pi$
$318$		0			0
$319$	8.46271	+	14.6579i	0.473821	+	0.820682i
$320$	0.228205	+	0.395262i	0.0127570	+	0.0220958i
$321$		0			0
$322$	−6.75865	−	5.28752i	−0.376645	−	0.294662i
$323$	−2.23659	−	3.87388i	−0.124447	−	0.215549i
$324$		0			0
$325$	−14.9053	+	8.73597i	−0.826795	+	0.484584i
$326$	4.35887	−	7.54979i	0.241416	−	0.418144i
$327$		0			0
$328$	−3.57277	−	6.18822i	−0.197273	−	0.341687i
$329$	16.3832	+	12.8171i	0.903236	+	0.706632i
$330$		0			0
$331$	16.1057			0.885250			0.442625	−	0.896707i	$-0.354047\pi$
$331$	16.1057			0.885250			0.442625	+	0.896707i	$0.354047\pi$
$332$	0.678689	+	1.17552i	0.0372479	+	0.0645153i
$333$		0			0
$334$	22.9120			1.25369
$335$	−0.408470	−	0.707490i	−0.0223171	−	0.0386543i
$336$		0			0
$337$	−14.9134			−0.812383			−0.406192	−	0.913788i	$-0.633143\pi$
$337$	−14.9134			−0.812383			−0.406192	+	0.913788i	$0.633143\pi$
$338$	12.9989	−	0.169960i	0.707046	−	0.00924462i
$339$		0			0
$340$	0.708287			0.0384123
$341$	18.4217	−	31.9073i	0.997589	−	1.72787i
$342$		0			0
$343$	7.56588	−	16.9044i	0.408519	−	0.912750i
$344$	−1.21716	+	2.10818i	−0.0656246	+	0.113665i
$345$		0			0
$346$	−3.79358	+	6.57067i	−0.203944	+	0.353242i
$347$	14.4006	+	24.9425i	0.773062	+	1.33898i	0.935877	+	0.352326i	$0.114609\pi$
$347$	14.4006	+	24.9425i	0.773062	+	1.33898i	−0.162815	+	0.986657i	$0.552057\pi$
$348$		0			0
$349$	2.50740	+	4.34294i	0.134218	+	0.232472i	0.925298	−	0.379240i	$-0.123814\pi$
$349$	2.50740	+	4.34294i	0.134218	+	0.232472i	−0.791081	+	0.611712i	$0.790481\pi$
$350$	−9.98502	−	7.81162i	−0.533722	−	0.417549i
$351$		0			0
$352$	1.91853	+	3.32300i	0.102258	+	0.177116i
$353$	11.5667			0.615631			0.307816	−	0.951446i	$-0.400402\pi$
$353$	11.5667			0.615631			0.307816	+	0.951446i	$0.400402\pi$
$354$		0			0
$355$	4.62367			0.245399
$356$	0.179697			0.00952392
$357$		0			0
$358$	−6.25205	+	10.8289i	−0.330431	+	0.572324i
$359$	14.9173	+	25.8375i	0.787306	+	1.36365i	0.927612	+	0.373546i	$0.121858\pi$
$359$	14.9173	+	25.8375i	0.787306	+	1.36365i	−0.140306	+	0.990108i	$0.544809\pi$
$360$		0			0
$361$	−10.6915			−0.562712
$362$	−1.13214	+	1.96092i	−0.0595040	+	0.103064i
$363$		0			0
$364$	3.62552	+	8.82358i	0.190029	+	0.462481i
$365$	1.28343			0.0671780
$366$		0			0
$367$	7.27789			0.379903			0.189951	−	0.981793i	$-0.439167\pi$
$367$	7.27789			0.379903			0.189951	+	0.981793i	$0.439167\pi$
$368$	1.62170	+	2.80886i	0.0845368	+	0.146422i
$369$		0			0
$370$	−0.0640093	+	0.110867i	−0.00332768	+	0.00576372i
$371$	−0.407208	+	2.88382i	−0.0211412	+	0.149720i
$372$		0			0
$373$	31.0916			1.60986			0.804932	−	0.593367i	$-0.202202\pi$
$373$	31.0916			1.60986			0.804932	+	0.593367i	$0.202202\pi$
$374$	5.95462			0.307906
$375$		0			0
$376$	−3.93105	−	6.80879i	−0.202729	−	0.351136i
$377$	−0.103967	−	15.9039i	−0.00535457	−	0.819091i
$378$		0			0
$379$	−9.33146	−	16.1626i	−0.479325	−	0.830215i	0.520394	−	0.853926i	$-0.325785\pi$
$379$	−9.33146	−	16.1626i	−0.479325	−	0.830215i	−0.999719	+	0.0237115i	$0.992452\pi$
$380$	−0.657787	+	1.13932i	−0.0337438	+	0.0584459i
$381$		0			0
$382$	4.58649	−	7.94403i	0.234665	−	0.406452i
$383$	−8.96269			−0.457972			−0.228986	−	0.973430i	$-0.573541\pi$
$383$	−8.96269			−0.457972			−0.228986	+	0.973430i	$0.573541\pi$
$384$		0			0
$385$	3.64934	+	2.85500i	0.185988	+	0.145504i
$386$	−1.21993	+	2.11297i	−0.0620926	+	0.107548i
$387$		0			0
$388$	−9.47788			−0.481166
$389$	14.5103	−	25.1326i	0.735702	−	1.27427i	−0.218712	−	0.975789i	$-0.570186\pi$
$389$	14.5103	−	25.1326i	0.735702	−	1.27427i	0.954415	−	0.298484i	$-0.0964811\pi$
$390$		0			0
$391$	5.03332			0.254546
$392$	−5.04170	+	4.85605i	−0.254644	+	0.245268i
$393$		0			0
$394$	26.8668			1.35353
$395$	−1.23671	+	2.14205i	−0.0622257	+	0.107778i
$396$		0			0
$397$	−4.34889			−0.218265			−0.109132	−	0.994027i	$-0.534807\pi$
$397$	−4.34889			−0.218265			−0.109132	+	0.994027i	$0.534807\pi$
$398$	27.9019			1.39860
$399$		0			0
$400$	2.39585	+	4.14973i	0.119792	+	0.207486i
$401$	4.77562	−	8.27162i	0.238483	−	0.413065i	−0.721796	−	0.692106i	$-0.756683\pi$
$401$	4.77562	−	8.27162i	0.238483	−	0.413065i	0.960279	+	0.279041i	$0.0900165\pi$
$402$		0			0
$403$	−29.8683	+	17.5058i	−1.48785	+	0.872026i
$404$	3.18107	+	5.50977i	0.158264	+	0.274121i
$405$		0			0
$406$	10.8235	−	4.36480i	0.537163	−	0.216622i
$407$	−0.538131	+	0.932070i	−0.0266741	+	0.0462010i
$408$		0			0
$409$	−0.635121	−	1.10006i	−0.0314047	−	0.0543946i	0.849896	−	0.526951i	$-0.176665\pi$
$409$	−0.635121	−	1.10006i	−0.0314047	−	0.0543946i	−0.881301	+	0.472556i	$0.843331\pi$
$410$	1.63065	+	2.82436i	0.0805319	+	0.139485i
$411$		0			0
$412$	−8.28934	+	14.3576i	−0.408386	+	0.707346i
$413$	−19.5163	−	15.2683i	−0.960337	−	0.751304i
$414$		0			0
$415$	−0.309760	−	0.536520i	−0.0152055	−	0.0263368i
$416$	−0.0235697	−	3.60547i	−0.00115560	−	0.176773i
$417$		0			0
$418$	−5.53006	+	9.57835i	−0.270484	+	0.468492i
$419$	−5.25472	−	9.10144i	−0.256710	−	0.444634i	0.708649	−	0.705561i	$-0.249305\pi$
$419$	−5.25472	−	9.10144i	−0.256710	−	0.444634i	−0.965359	+	0.260927i	$0.915972\pi$
$420$		0			0
$421$	−1.14121			−0.0556192			−0.0278096	−	0.999613i	$-0.508853\pi$
$421$	−1.14121			−0.0556192			−0.0278096	+	0.999613i	$0.508853\pi$
$422$	21.9741			1.06968
$423$		0			0
$424$	0.550397	−	0.953315i	0.0267296	−	0.0462971i
$425$	7.43607			0.360703
$426$		0			0
$427$	−27.2457	+	10.9874i	−1.31851	+	0.531716i
$428$	−16.9205			−0.817882
$429$		0			0
$430$	0.555521	−	0.962191i	0.0267896	−	0.0464010i
$431$	−31.3274			−1.50899			−0.754493	−	0.656308i	$-0.772117\pi$
$431$	−31.3274			−1.50899			−0.754493	+	0.656308i	$0.772117\pi$
$432$		0			0
$433$	−7.06113	+	12.2302i	−0.339336	+	0.587748i	−0.984308	−	0.176459i	$-0.943536\pi$
$433$	−7.06113	+	12.2302i	−0.339336	+	0.587748i	0.644972	+	0.764206i	$0.276869\pi$
$434$	−20.0087	−	15.6535i	−0.960450	−	0.751393i
$435$		0			0
$436$	−7.90215			−0.378444
$437$	−4.67445	+	8.09638i	−0.223609	+	0.387302i
$438$		0			0
$439$	3.23066	−	5.59567i	0.154191	−	0.267067i	−0.778573	−	0.627554i	$-0.784056\pi$
$439$	3.23066	−	5.59567i	0.154191	−	0.267067i	0.932764	+	0.360487i	$0.117390\pi$
$440$	−0.875637	−	1.51665i	−0.0417443	−	0.0723033i
$441$		0			0
$442$	−4.86389	−	2.76593i	−0.231352	−	0.131562i
$443$	5.70730	+	9.88534i	0.271162	+	0.469667i	0.969160	−	0.246434i	$-0.0792587\pi$
$443$	5.70730	+	9.88534i	0.271162	+	0.469667i	−0.697998	+	0.716100i	$0.745925\pi$
$444$		0			0
$445$	−0.0820154			−0.00388790
$446$	−13.7584			−0.651478
$447$		0			0
$448$	2.45374	−	0.989520i	0.115928	−	0.0467504i
$449$	19.8942	−	34.4578i	0.938867	−	1.62617i	0.171278	−	0.985223i	$-0.445210\pi$
$449$	19.8942	−	34.4578i	0.938867	−	1.62617i	0.767589	−	0.640942i	$-0.221456\pi$
$450$		0			0
$451$	13.7090	+	23.7446i	0.645530	+	1.11809i
$452$	6.81379			0.320494
$453$		0			0
$454$	18.8309			0.883778
$455$	−1.65472	−	4.02717i	−0.0775746	−	0.188796i
$456$		0			0
$457$	2.62643	−	4.54910i	0.122859	−	0.212798i	−0.798035	−	0.602611i	$-0.794127\pi$
$457$	2.62643	−	4.54910i	0.122859	−	0.212798i	0.920894	+	0.389813i	$0.127460\pi$
$458$	3.49624			0.163369
$459$		0			0
$460$	−0.740157	−	1.28199i	−0.0345100	−	0.0597731i
$461$	−9.59122	+	16.6125i	−0.446707	+	0.773720i	−0.998169	−	0.0604800i	$-0.980737\pi$
$461$	−9.59122	+	16.6125i	−0.446707	+	0.773720i	0.551462	+	0.834200i	$0.314070\pi$
$462$		0			0
$463$	−17.5580			−0.815988			−0.407994	−	0.912985i	$-0.633772\pi$
$463$	−17.5580			−0.815988			−0.407994	+	0.912985i	$0.633772\pi$
$464$	−4.41103			−0.204777
$465$		0			0
$466$	−19.4806			−0.902422
$467$	1.54111	+	2.66928i	0.0713141	+	0.123520i	0.899477	−	0.436967i	$-0.143947\pi$
$467$	1.54111	+	2.66928i	0.0713141	+	0.123520i	−0.828163	+	0.560487i	$0.810614\pi$
$468$		0			0
$469$	−4.39202	+	1.77117i	−0.202805	+	0.0817849i
$470$	1.79417	+	3.10759i	0.0827589	+	0.143343i
$471$		0			0
$472$	4.68283	+	8.11090i	0.215545	+	0.373334i
$473$	4.67031	−	8.08921i	0.214741	−	0.371942i
$474$		0			0
$475$	−6.90589	+	11.9613i	−0.316864	+	0.548824i
$476$	0.574070	−	4.06553i	0.0263125	−	0.186343i
$477$		0			0
$478$	−6.27346	+	10.8659i	−0.286941	+	0.496997i
$479$	−18.3621			−0.838985			−0.419493	−	0.907759i	$-0.637792\pi$
$479$	−18.3621			−0.838985			−0.419493	+	0.907759i	$0.637792\pi$
$480$		0			0
$481$	0.872507	−	0.511376i	0.0397829	−	0.0233168i
$482$	0.466451			0.0212463
$483$		0			0
$484$	−1.86154	−	3.22428i	−0.0846155	−	0.146558i
$485$	4.32579			0.196424
$486$		0			0
$487$	−9.00530	−	15.5976i	−0.408069	−	0.706796i	0.586604	−	0.809874i	$-0.300464\pi$
$487$	−9.00530	−	15.5976i	−0.408069	−	0.706796i	−0.994673	+	0.103077i	$0.967131\pi$
$488$	11.1037			0.502643
$489$		0			0
$490$	2.30108	−	2.21635i	0.103952	−	0.100124i
$491$	7.98794	+	13.8355i	0.360491	+	0.624388i	0.988042	−	0.154187i	$-0.0492759\pi$
$491$	7.98794	+	13.8355i	0.360491	+	0.624388i	−0.627551	+	0.778576i	$0.715943\pi$
$492$		0			0
$493$	−3.42267	+	5.92824i	−0.154149	+	0.266995i
$494$	8.96626	−	5.25512i	0.403411	−	0.236439i
$495$		0			0
$496$	4.80098	+	8.31553i	0.215570	+	0.373379i
$497$	3.74751	−	26.5396i	0.168099	−	1.19046i
$498$		0			0
$499$	−4.06656	−	7.04348i	−0.182044	−	0.315309i	0.760532	−	0.649300i	$-0.224938\pi$
$499$	−4.06656	−	7.04348i	−0.182044	−	0.315309i	−0.942576	+	0.333990i	$0.891605\pi$
$500$	−2.23451	−	3.87028i	−0.0999303	−	0.173084i
$501$		0			0
$502$	12.7935	+	22.1590i	0.571001	+	0.989002i
$503$	18.8326	−	32.6190i	0.839705	−	1.45441i	−0.0504368	−	0.998727i	$-0.516061\pi$
$503$	18.8326	−	32.6190i	0.839705	−	1.45441i	0.890142	−	0.455684i	$-0.150605\pi$
$504$		0			0
$505$	−1.45187	−	2.51471i	−0.0646073	−	0.111903i
$506$	−6.22256	−	10.7778i	−0.276626	−	0.479131i
$507$		0			0
$508$	10.9334	−	18.9372i	0.485092	−	0.840203i
$509$	−13.8779	+	24.0372i	−0.615127	+	1.06543i	0.375236	+	0.926929i	$0.377562\pi$
$509$	−13.8779	+	24.0372i	−0.615127	+	1.06543i	−0.990362	+	0.138501i	$0.955772\pi$
$510$		0			0
$511$	1.04023	−	7.36684i	0.0460170	−	0.325890i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	1.88805	+	3.27020i	0.0832785	+	0.144243i
$515$	3.78333	−	6.55292i	0.166713	−	0.288756i
$516$		0			0
$517$	15.0837	+	26.1258i	0.663381	+	1.14901i
$518$	0.584492	+	0.457268i	0.0256811	+	0.0200912i
$519$		0			0
$520$	0.0107575	+	1.64557i	0.000471745	+	0.0721631i
$521$	7.66182	−	13.2707i	0.335671	−	0.581398i	−0.647943	−	0.761689i	$-0.724370\pi$
$521$	7.66182	−	13.2707i	0.335671	−	0.581398i	0.983613	+	0.180291i	$0.0577038\pi$
$522$		0			0
$523$	−12.5383	+	21.7170i	−0.548263	+	0.949620i	0.450130	+	0.892963i	$0.351378\pi$
$523$	−12.5383	+	21.7170i	−0.548263	+	0.949620i	−0.998394	+	0.0566571i	$0.981956\pi$
$524$	−4.72554	+	8.18487i	−0.206436	+	0.357558i
$525$		0			0
$526$	−9.84358	+	17.0496i	−0.429201	+	0.743397i
$527$	14.9010			0.649096
$528$		0			0
$529$	6.24020	+	10.8083i	0.271313	+	0.469928i
$530$	−0.251206	+	0.435102i	−0.0109117	+	0.0188996i
$531$		0			0
$532$	6.00649	+	4.69908i	0.260414	+	0.203731i
$533$	−0.168419	−	25.7631i	−0.00729502	−	1.11592i
$534$		0			0
$535$	7.72266			0.333880
$536$	1.78993			0.0773131
$537$		0			0
$538$	−8.78165			−0.378604
$539$	19.3453	−	18.6330i	0.833263	−	0.802580i
$540$		0			0
$541$	−14.2260	−	24.6402i	−0.611624	−	1.05936i	−0.990967	−	0.134107i	$-0.957183\pi$
$541$	−14.2260	−	24.6402i	−0.611624	−	1.05936i	0.379343	−	0.925256i	$-0.376150\pi$
$542$	14.4014	+	24.9439i	0.618591	+	1.07143i
$543$		0			0
$544$	−0.775934	+	1.34396i	−0.0332679	+	0.0576217i
$545$	3.60662			0.154490
$546$		0			0
$547$	4.99706			0.213659			0.106829	−	0.994277i	$-0.465930\pi$
$547$	4.99706			0.213659			0.106829	+	0.994277i	$0.465930\pi$
$548$	1.22396	−	2.11996i	0.0522851	−	0.0905604i
$549$		0			0
$550$	−9.19302	−	15.9228i	−0.391992	−	0.678949i
$551$	−6.35728	−	11.0111i	−0.270829	−	0.469090i
$552$		0			0
$553$	11.2929	+	8.83480i	0.480222	+	0.375694i
$554$	−6.94992			−0.295274
$555$		0			0
$556$	10.7446			0.455670
$557$	−31.7130			−1.34372			−0.671861	−	0.740677i	$-0.734505\pi$
$557$	−31.7130			−1.34372			−0.671861	+	0.740677i	$0.734505\pi$
$558$		0			0
$559$	−7.57228	+	4.43811i	−0.320274	+	0.187712i
$560$	−1.11991	+	0.451626i	−0.0473249	+	0.0190847i
$561$		0			0
$562$	6.25581	−	10.8354i	0.263885	−	0.457063i
$563$	11.9474	+	20.6935i	0.503523	+	0.872127i	0.999992	+	0.00407268i	$0.00129638\pi$
$563$	11.9474	+	20.6935i	0.503523	+	0.872127i	−0.496469	+	0.868055i	$0.665370\pi$
$564$		0			0
$565$	−3.10988			−0.130833
$566$	5.60195	−	9.70287i	0.235468	−	0.407842i
$567$		0			0
$568$	−5.06527	+	8.77331i	−0.212534	+	0.368120i
$569$	−19.2320	+	33.3109i	−0.806249	+	1.39646i	0.109196	+	0.994020i	$0.465172\pi$
$569$	−19.2320	+	33.3109i	−0.806249	+	1.39646i	−0.915445	+	0.402443i	$0.868161\pi$
$570$		0			0
$571$	15.8854	−	27.5143i	0.664782	−	1.15144i	−0.314563	−	0.949237i	$-0.601858\pi$
$571$	15.8854	−	27.5143i	0.664782	−	1.15144i	0.979344	−	0.202199i	$-0.0648088\pi$
$572$	0.0904387	+	13.8344i	0.00378143	+	0.578447i
$573$		0			0
$574$	17.5333	−	7.07066i	0.731827	−	0.295123i
$575$	−7.77067	−	13.4592i	−0.324059	−	0.561287i
$576$		0			0
$577$	10.1750	−	17.6236i	0.423591	−	0.733682i	−0.572696	−	0.819768i	$-0.694103\pi$
$577$	10.1750	−	17.6236i	0.423591	−	0.733682i	0.996288	+	0.0860858i	$0.0274359\pi$
$578$	−7.29585	−	12.6368i	−0.303467	−	0.525621i
$579$		0			0
$580$	2.01324			0.0835951
$581$	−3.33066	+	1.34315i	−0.138179	+	0.0557234i
$582$		0			0
$583$	−2.11191	+	3.65793i	−0.0874664	+	0.151496i
$584$	−1.40601	+	2.43529i	−0.0581812	+	0.100773i
$585$		0			0
$586$	14.2699	+	24.7162i	0.589484	+	1.02102i
$587$	11.7425	+	20.3386i	0.484664	+	0.839462i	0.999845	−	0.0176191i	$-0.00560863\pi$
$587$	11.7425	+	20.3386i	0.484664	+	0.839462i	−0.515181	+	0.857081i	$0.672275\pi$
$588$		0			0
$589$	−13.8385	+	23.9691i	−0.570207	+	0.987628i
$590$	−2.13729	−	3.70189i	−0.0879907	−	0.152404i
$591$		0			0
$592$	−0.140245	−	0.242912i	−0.00576405	−	0.00998362i
$593$	0.268350	+	0.464796i	0.0110198	+	0.0190869i	0.871483	−	0.490426i	$-0.163159\pi$
$593$	0.268350	+	0.464796i	0.0110198	+	0.0190869i	−0.860463	+	0.509513i	$0.829826\pi$
$594$		0			0
$595$	−0.262011	+	1.85555i	−0.0107414	+	0.0760699i
$596$	4.65157	+	8.05676i	0.190536	+	0.330018i
$597$		0			0
$598$	0.0764459	+	11.6940i	0.00312611	+	0.478202i
$599$	−9.68962	+	16.7829i	−0.395907	+	0.685731i	−0.993217	−	0.116280i	$-0.962903\pi$
$599$	−9.68962	+	16.7829i	−0.395907	+	0.685731i	0.597309	+	0.802011i	$0.296236\pi$
$600$		0			0
$601$	7.74999	+	13.4234i	0.316129	+	0.547551i	0.979677	−	0.200583i	$-0.0642835\pi$
$601$	7.74999	+	13.4234i	0.316129	+	0.547551i	−0.663548	+	0.748134i	$0.730950\pi$
$602$	−5.07267	−	3.96852i	−0.206747	−	0.161745i
$603$		0			0
$604$	20.7443			0.844075
$605$	0.849624	+	1.47159i	0.0345421	+	0.0598287i
$606$		0			0
$607$	15.7526			0.639379			0.319690	−	0.947522i	$-0.396421\pi$
$607$	15.7526			0.639379			0.319690	+	0.947522i	$0.396421\pi$
$608$	−1.44122	−	2.49627i	−0.0584492	−	0.101237i
$609$		0			0
$610$	−5.06785			−0.205191
$611$	−0.185308	−	28.3466i	−0.00749675	−	1.14678i
$612$		0			0
$613$	31.0881			1.25564			0.627818	−	0.778360i	$-0.283948\pi$
$613$	31.0881			1.25564			0.627818	+	0.778360i	$0.283948\pi$
$614$	−11.5953	+	20.0837i	−0.467950	+	0.810512i
$615$		0			0
$616$	−9.41517	+	3.79685i	−0.379348	+	0.152980i
$617$	−9.39918	+	16.2799i	−0.378397	+	0.655403i	−0.990829	−	0.135120i	$-0.956858\pi$
$617$	−9.39918	+	16.2799i	−0.378397	+	0.655403i	0.612432	+	0.790523i	$0.290191\pi$
$618$		0			0
$619$	−10.6461	+	18.4396i	−0.427904	+	0.741152i	−0.996687	−	0.0813361i	$-0.974081\pi$
$619$	−10.6461	+	18.4396i	−0.427904	+	0.741152i	0.568783	+	0.822488i	$0.307415\pi$
$620$	−2.19121	−	3.79529i	−0.0880011	−	0.152422i
$621$		0			0
$622$	11.6740	+	20.2200i	0.468086	+	0.810749i
$623$	−0.0664738	+	0.470763i	−0.00266322	+	0.0188607i
$624$		0			0
$625$	−10.9594	−	18.9822i	−0.438375	−	0.759288i
$626$	14.5300			0.580735
$627$		0			0
$628$	−6.45402			−0.257543
$629$	−0.435285			−0.0173559
$630$		0			0
$631$	−4.63522	+	8.02844i	−0.184525	+	0.319607i	−0.943416	−	0.331610i	$-0.892408\pi$
$631$	−4.63522	+	8.02844i	−0.184525	+	0.319607i	0.758891	+	0.651218i	$0.225741\pi$
$632$	−2.70966	−	4.69326i	−0.107784	−	0.186688i
$633$		0			0
$634$	−3.29192			−0.130739
$635$	−4.99011	+	8.64312i	−0.198026	+	0.342992i
$636$		0			0
$637$	−24.4569	+	6.23397i	−0.969016	+	0.246999i
$638$	16.9254			0.670084
$639$		0			0
$640$	0.456409			0.0180412
$641$	21.8796	+	37.8967i	0.864194	+	1.49683i	0.867845	+	0.496835i	$0.165505\pi$
$641$	21.8796	+	37.8967i	0.864194	+	1.49683i	−0.00365084	+	0.999993i	$0.501162\pi$
$642$		0			0
$643$	10.6905	−	18.5165i	0.421593	−	0.730220i	−0.574503	−	0.818503i	$-0.694805\pi$
$643$	10.6905	−	18.5165i	0.421593	−	0.730220i	0.996095	+	0.0882825i	$0.0281378\pi$
$644$	−7.95845	+	3.20940i	−0.313607	+	0.126468i
$645$		0			0
$646$	−4.47317			−0.175995
$647$	8.13845			0.319955			0.159978	−	0.987121i	$-0.448858\pi$
$647$	8.13845			0.319955			0.159978	+	0.987121i	$0.448858\pi$
$648$		0			0
$649$	−17.9683	−	31.1221i	−0.705318	−	1.22165i
$650$	0.112939	+	17.2763i	0.00442983	+	0.677633i
$651$		0			0
$652$	−4.35887	−	7.54979i	−0.170707	−	0.295673i
$653$	−9.93944	+	17.2156i	−0.388960	+	0.673699i	−0.992310	−	0.123778i	$-0.960499\pi$
$653$	−9.93944	+	17.2156i	−0.388960	+	0.673699i	0.603350	+	0.797477i	$0.293832\pi$
$654$		0			0
$655$	2.15678	−	3.73565i	0.0842723	−	0.145964i
$656$	−7.14554			−0.278987
$657$		0			0
$658$	19.2916	−	7.77971i	0.752064	−	0.303285i
$659$	4.78352	−	8.28530i	0.186339	−	0.322749i	−0.757688	−	0.652617i	$-0.773671\pi$
$659$	4.78352	−	8.28530i	0.186339	−	0.322749i	0.944027	+	0.329868i	$0.107004\pi$
$660$		0			0
$661$	−11.4187			−0.444135			−0.222068	−	0.975031i	$-0.571281\pi$
$661$	−11.4187			−0.444135			−0.222068	+	0.975031i	$0.571281\pi$
$662$	8.05285	−	13.9480i	0.312983	−	0.542103i
$663$		0			0
$664$	1.35738			0.0526765
$665$	−2.74142	−	2.14471i	−0.106308	−	0.0831681i
$666$		0			0
$667$	14.3067			0.553958
$668$	11.4560	−	19.8424i	0.443246	−	0.767724i
$669$		0			0
$670$	−0.816939			−0.0315611
$671$	−42.6058			−1.64478
$672$		0			0
$673$	−7.10491	−	12.3061i	−0.273874	−	0.474364i	0.695976	−	0.718065i	$-0.254972\pi$
$673$	−7.10491	−	12.3061i	−0.273874	−	0.474364i	−0.969850	+	0.243701i	$0.921639\pi$
$674$	−7.45669	+	12.9154i	−0.287221	+	0.497481i
$675$		0			0
$676$	6.35225	−	11.3423i	0.244317	−	0.436244i
$677$	−7.31125	−	12.6635i	−0.280994	−	0.486696i	0.690636	−	0.723203i	$-0.257331\pi$
$677$	−7.31125	−	12.6635i	−0.280994	−	0.486696i	−0.971630	+	0.236507i	$0.923997\pi$
$678$		0			0
$679$	3.50608	−	24.8298i	0.134551	−	0.952880i
$680$	0.354144	−	0.613395i	0.0135808	−	0.0235226i
$681$		0			0
$682$	−18.4217	−	31.9073i	−0.705402	−	1.22179i
$683$	−17.5855	−	30.4589i	−0.672890	−	1.16548i	−0.977081	−	0.212868i	$-0.931720\pi$
$683$	−17.5855	−	30.4589i	−0.672890	−	1.16548i	0.304191	−	0.952611i	$-0.401614\pi$
$684$		0			0
$685$	−0.558628	+	0.967572i	−0.0213441	+	0.0369690i
$686$	−10.8567	−	15.0044i	−0.414510	−	0.572872i
$687$		0			0
$688$	1.21716	+	2.10818i	0.0464036	+	0.0803734i
$689$	3.42418	−	2.00691i	0.130451	−	0.0764572i
$690$		0			0
$691$	−6.90574	+	11.9611i	−0.262707	+	0.455021i	−0.966960	−	0.254927i	$-0.917948\pi$
$691$	−6.90574	+	11.9611i	−0.262707	+	0.455021i	0.704254	+	0.709948i	$0.251282\pi$
$692$	3.79358	+	6.57067i	0.144210	+	0.249779i
$693$		0			0
$694$	28.8011			1.09327
$695$	−4.90391			−0.186016
$696$		0			0
$697$	−5.54447	+	9.60331i	−0.210012	+	0.363751i
$698$	5.01479			0.189813
$699$		0			0
$700$	−11.7576	+	4.74147i	−0.444394	+	0.179211i
$701$	17.6965			0.668387			0.334193	−	0.942504i	$-0.391536\pi$
$701$	17.6965			0.668387			0.334193	+	0.942504i	$0.391536\pi$
$702$		0			0
$703$	0.404249	−	0.700180i	0.0152465	−	0.0264078i
$704$	3.83707			0.144615
$705$		0			0
$706$	5.78333	−	10.0170i	0.217659	−	0.376996i
$707$	−15.6110	+	6.29545i	−0.587113	+	0.236765i
$708$		0			0
$709$	34.8684			1.30951			0.654755	−	0.755842i	$-0.272772\pi$
$709$	34.8684			1.30951			0.654755	+	0.755842i	$0.272772\pi$
$710$	2.31184	−	4.00422i	0.0867617	−	0.150276i
$711$		0			0
$712$	0.0898485	−	0.155622i	0.00336721	−	0.00583218i
$713$	−15.5715	−	26.9705i	−0.583155	−	1.01005i
$714$		0			0
$715$	−0.0412771	−	6.31417i	−0.00154367	−	0.236137i
$716$	6.25205	+	10.8289i	0.233650	+	0.404694i
$717$		0			0
$718$	29.8346			1.11342
$719$	−3.11104			−0.116022			−0.0580112	−	0.998316i	$-0.518476\pi$
$719$	−3.11104			−0.116022			−0.0580112	+	0.998316i	$0.518476\pi$
$720$		0			0
$721$	−34.5470	−	27.0273i	−1.28660	−	1.00655i
$722$	−5.34576	+	9.25913i	−0.198949	+	0.344589i
$723$		0			0
$724$	1.13214	+	1.96092i	0.0420757	+	0.0728772i
$725$	21.1363			0.784983
$726$		0			0
$727$	22.0591			0.818128			0.409064	−	0.912506i	$-0.365855\pi$
$727$	22.0591			0.818128			0.409064	+	0.912506i	$0.365855\pi$
$728$	9.45421	+	1.27200i	0.350396	+	0.0471433i
$729$		0			0
$730$	0.641717	−	1.11149i	0.0237510	−	0.0411380i
$731$	3.77773			0.139724
$732$		0			0
$733$	−24.6272	−	42.6555i	−0.909626	−	1.57552i	−0.814585	−	0.580045i	$-0.803035\pi$
$733$	−24.6272	−	42.6555i	−0.909626	−	1.57552i	−0.0950410	−	0.995473i	$-0.530298\pi$
$734$	3.63895	−	6.30284i	0.134316	−	0.232642i
$735$		0			0
$736$	3.24339			0.119553
$737$	−6.86807			−0.252989
$738$		0			0
$739$	−34.1376			−1.25577			−0.627886	−	0.778305i	$-0.716080\pi$
$739$	−34.1376			−1.25577			−0.627886	+	0.778305i	$0.716080\pi$
$740$	0.0640093	+	0.110867i	0.00235303	+	0.00407556i
$741$		0			0
$742$	2.29386	+	1.79456i	0.0842101	+	0.0658804i
$743$	20.1806	+	34.9539i	0.740356	+	1.28233i	0.952333	+	0.305060i	$0.0986765\pi$
$743$	20.1806	+	34.9539i	0.740356	+	1.28233i	−0.211977	+	0.977275i	$0.567990\pi$
$744$		0			0
$745$	−2.12302	−	3.67718i	−0.0777815	−	0.134721i
$746$	15.5458	−	26.9261i	0.569173	−	0.985836i
$747$		0			0
$748$	2.97731	−	5.15686i	0.108861	−	0.188553i
$749$	6.25925	−	44.3276i	0.228708	−	1.61970i
$750$		0			0
$751$	16.9285	−	29.3210i	0.617729	−	1.06994i	−0.372170	−	0.928164i	$-0.621386\pi$
$751$	16.9285	−	29.3210i	0.617729	−	1.06994i	0.989899	−	0.141773i	$-0.0452803\pi$
$752$	−7.86211			−0.286702
$753$		0			0
$754$	−13.8251	−	7.86190i	−0.503482	−	0.286313i
$755$	−9.46791			−0.344573
$756$		0			0
$757$	−10.3752	−	17.9704i	−0.377094	−	0.653146i	0.613544	−	0.789660i	$-0.289743\pi$
$757$	−10.3752	−	17.9704i	−0.377094	−	0.653146i	−0.990638	+	0.136515i	$0.956410\pi$
$758$	−18.6629			−0.677867
$759$		0			0
$760$	0.657787	+	1.13932i	0.0238604	+	0.0413275i
$761$	−1.15718			−0.0419477			−0.0209739	−	0.999780i	$-0.506677\pi$
$761$	−1.15718			−0.0419477			−0.0209739	+	0.999780i	$0.506677\pi$
$762$		0			0
$763$	2.92318	−	20.7018i	0.105826	−	0.749454i
$764$	−4.58649	−	7.94403i	−0.165933	−	0.287405i
$765$		0			0
$766$	−4.48135	+	7.76192i	−0.161918	+	0.280450i
$767$	0.220746	+	33.7676i	0.00797068	+	1.21928i
$768$		0			0
$769$	16.9810	+	29.4120i	0.612352	+	1.06063i	0.990843	+	0.135020i	$0.0431099\pi$
$769$	16.9810	+	29.4120i	0.612352	+	1.06063i	−0.378491	+	0.925605i	$0.623557\pi$
$770$	4.29717	−	1.73292i	0.154859	−	0.0624501i
$771$		0			0
$772$	1.21993	+	2.11297i	0.0439061	+	0.0760476i
$773$	−12.7584	−	22.0983i	−0.458889	−	0.794819i	0.540013	−	0.841656i	$-0.318419\pi$
$773$	−12.7584	−	22.0983i	−0.458889	−	0.794819i	−0.998903	+	0.0468371i	$0.985086\pi$
$774$		0			0
$775$	−23.0048	−	39.8455i	−0.826357	−	1.43129i
$776$	−4.73894	+	8.20808i	−0.170118	+	0.294653i
$777$		0			0
$778$	−14.5103	−	25.1326i	−0.520220	−	0.901048i
$779$	−10.2983	−	17.8372i	−0.368975	−	0.639084i
$780$		0			0
$781$	19.4358	−	33.6638i	0.695467	−	1.20458i
$782$	2.51666	−	4.35898i	0.0899956	−	0.155877i
$783$		0			0
$784$	1.68461	+	6.79427i	0.0601648	+	0.242652i
$785$	2.94567			0.105136
$786$		0			0
$787$	−25.0068	−	43.3130i	−0.891395	−	1.54394i	−0.838204	−	0.545357i	$-0.816394\pi$
$787$	−25.0068	−	43.3130i	−0.891395	−	1.54394i	−0.0531913	−	0.998584i	$-0.516939\pi$
$788$	13.4334	−	23.2673i	0.478545	−	0.828865i
$789$		0			0
$790$	1.23671	+	2.14205i	0.0440002	+	0.0762107i
$791$	−2.52057	+	17.8505i	−0.0896211	+	0.634691i
$792$		0			0
$793$	34.8015	+	19.7905i	1.23584	+	0.702780i
$794$	−2.17445	+	3.76625i	−0.0771682	+	0.133659i
$795$		0			0
$796$	13.9509	−	24.1638i	0.494478	−	0.856462i
$797$	−3.59277	+	6.22286i	−0.127262	+	0.220425i	−0.922615	−	0.385722i	$-0.873952\pi$
$797$	−3.59277	+	6.22286i	−0.127262	+	0.220425i	0.795353	+	0.606147i	$0.207286\pi$
$798$		0			0
$799$	−6.10048	+	10.5663i	−0.215819	+	0.373810i
$800$	4.79169			0.169412
$801$		0			0
$802$	−4.77562	−	8.27162i	−0.168633	−	0.292081i
$803$	5.39496	−	9.34435i	0.190384	−	0.329755i
$804$		0			0
$805$	3.63231	−	1.46480i	0.128022	−	0.0516274i
$806$	0.226316	+	34.6196i	0.00797163	+	1.21942i
$807$		0			0
$808$	6.36213			0.223819
$809$	−19.8527			−0.697984			−0.348992	−	0.937126i	$-0.613476\pi$
$809$	−19.8527			−0.697984			−0.348992	+	0.937126i	$0.613476\pi$
$810$		0			0
$811$	−49.7806			−1.74803			−0.874016	−	0.485897i	$-0.838493\pi$
$811$	−49.7806			−1.74803			−0.874016	+	0.485897i	$0.838493\pi$
$812$	1.63174	−	11.5559i	0.0572628	−	0.405531i
$813$		0			0
$814$	0.538131	+	0.932070i	0.0188615	+	0.0326690i
$815$	1.98943	+	3.44579i	0.0696867	+	0.120701i
$816$		0			0
$817$	−3.50838	+	6.07670i	−0.122743	+	0.212597i
$818$	−1.27024			−0.0444130
$819$		0			0
$820$	3.26129			0.113889
$821$	−6.57078	+	11.3809i	−0.229322	+	0.397197i	−0.957607	−	0.288077i	$-0.906984\pi$
$821$	−6.57078	+	11.3809i	−0.229322	+	0.397197i	0.728286	+	0.685274i	$0.240317\pi$
$822$		0			0
$823$	−16.5241	−	28.6206i	−0.575995	−	0.997653i	−0.995933	−	0.0901000i	$-0.971281\pi$
$823$	−16.5241	−	28.6206i	−0.575995	−	0.997653i	0.419937	−	0.907553i	$-0.362052\pi$
$824$	8.28934	+	14.3576i	0.288773	+	0.500169i
$825$		0			0
$826$	−22.9809	+	9.26750i	−0.799608	+	0.322458i
$827$	−14.9763			−0.520779			−0.260389	−	0.965504i	$-0.583851\pi$
$827$	−14.9763			−0.520779			−0.260389	+	0.965504i	$0.583851\pi$
$828$		0			0
$829$	−55.7966			−1.93789			−0.968947	−	0.247267i	$-0.920468\pi$
$829$	−55.7966			−1.93789			−0.968947	+	0.247267i	$0.920468\pi$
$830$	−0.619520			−0.0215039
$831$		0			0
$832$	−3.13422	−	1.78233i	−0.108659	−	0.0617910i
$833$	10.4384	+	3.00786i	0.361668	+	0.104216i
$834$		0			0
$835$	−5.22862	+	9.05624i	−0.180944	+	0.313404i
$836$	5.53006	+	9.57835i	0.191261	+	0.331274i
$837$		0			0
$838$	−10.5094			−0.363042
$839$	−26.0623	+	45.1412i	−0.899770	+	1.55845i	−0.0719812	+	0.997406i	$0.522932\pi$
$839$	−26.0623	+	45.1412i	−0.899770	+	1.55845i	−0.827788	+	0.561041i	$0.810401\pi$
$840$		0			0
$841$	4.77139	−	8.26429i	0.164531	−	0.284976i
$842$	−0.570606	+	0.988318i	−0.0196644	+	0.0340597i
$843$		0			0
$844$	10.9871	−	19.0301i	0.378190	−	0.655045i
$845$	−2.89923	+	5.17675i	−0.0997365	+	0.178086i
$846$		0			0
$847$	9.13548	−	3.68406i	0.313899	−	0.126586i
$848$	−0.550397	−	0.953315i	−0.0189007	−	0.0327370i
$849$		0			0
$850$	3.71804	−	6.43983i	0.127528	−	0.220884i
$851$	0.454871	+	0.787859i	0.0155928	+	0.0270075i
$852$		0			0
$853$	23.6670			0.810344			0.405172	−	0.914241i	$-0.367212\pi$
$853$	23.6670			0.810344			0.405172	+	0.914241i	$0.367212\pi$
$854$	−4.10752	+	29.0892i	−0.140556	+	0.995411i
$855$		0			0
$856$	−8.46023	+	14.6536i	−0.289165	+	0.500848i
$857$	24.0347	−	41.6292i	0.821008	−	1.42203i	−0.0839243	−	0.996472i	$-0.526745\pi$
$857$	24.0347	−	41.6292i	0.821008	−	1.42203i	0.904932	−	0.425556i	$-0.139921\pi$
$858$		0			0
$859$	7.34891	+	12.7287i	0.250742	+	0.434297i	0.963730	−	0.266878i	$-0.0859922\pi$
$859$	7.34891	+	12.7287i	0.250742	+	0.434297i	−0.712989	+	0.701176i	$0.752659\pi$
$860$	−0.555521	−	0.962191i	−0.0189431	−	0.0328104i
$861$		0			0
$862$	−15.6637	+	27.1303i	−0.533507	+	0.924062i
$863$	13.6332	+	23.6134i	0.464080	+	0.803810i	0.999159	−	0.0409917i	$-0.0130517\pi$
$863$	13.6332	+	23.6134i	0.464080	+	0.803810i	−0.535080	+	0.844802i	$0.679718\pi$
$864$		0			0
$865$	−1.73143	−	2.99892i	−0.0588702	−	0.101966i
$866$	7.06113	+	12.2302i	0.239947	+	0.415600i
$867$		0			0
$868$	−23.5607	+	9.50132i	−0.799703	+	0.322496i
$869$	10.3971	+	18.0084i	0.352698	+	0.610892i
$870$		0			0
$871$	5.61002	+	3.19023i	0.190088	+	0.108097i
$872$	−3.95108	+	6.84346i	−0.133800	+	0.231749i
$873$		0			0
$874$	4.67445	+	8.09638i	0.158116	+	0.273864i
$875$	10.9658	−	4.42218i	0.370712	−	0.149497i
$876$		0			0
$877$	−27.2132			−0.918923			−0.459461	−	0.888198i	$-0.651958\pi$
$877$	−27.2132			−0.918923			−0.459461	+	0.888198i	$0.651958\pi$
$878$	−3.23066	−	5.59567i	−0.109030	−	0.188845i
$879$		0			0
$880$	−1.75127			−0.0590354
$881$	−5.52376	−	9.56743i	−0.186100	−	0.322335i	0.757847	−	0.652433i	$-0.226252\pi$
$881$	−5.52376	−	9.56743i	−0.186100	−	0.322335i	−0.943947	+	0.330098i	$0.892918\pi$
$882$		0			0
$883$	42.1202			1.41746			0.708729	−	0.705481i	$-0.249269\pi$
$883$	42.1202			1.41746			0.708729	+	0.705481i	$0.249269\pi$
$884$	−4.82732	+	2.82929i	−0.162360	+	0.0951593i
$885$		0			0
$886$	11.4146			0.383481
$887$	22.7345	−	39.3773i	0.763349	−	1.32216i	−0.177765	−	0.984073i	$-0.556887\pi$
$887$	22.7345	−	39.3773i	0.763349	−	1.32216i	0.941115	−	0.338087i	$-0.109780\pi$
$888$		0			0
$889$	45.5665	+	35.6482i	1.52825	+	1.19560i
$890$	−0.0410077	+	0.0710274i	−0.00137458	+	0.00238084i
$891$		0			0
$892$	−6.87919	+	11.9151i	−0.230332	+	0.398947i
$893$	−11.3310	−	19.6259i	−0.379179	−	0.656757i
$894$		0			0
$895$	−2.85349	−	4.94240i	−0.0953818	−	0.165206i
$896$	0.369922	−	2.61976i	0.0123582	−	0.0875201i
$897$		0			0
$898$	−19.8942	−	34.4578i	−0.663879	−	1.14987i
$899$	42.3545			1.41260
$900$		0			0
$901$	−1.70829			−0.0569113
$902$	27.4179			0.912917
$903$		0			0
$904$	3.40689	−	5.90091i	0.113312	−	0.196261i
$905$	−0.516719	−	0.894984i	−0.0171763	−	0.0297503i
$906$		0			0
$907$	−41.6270			−1.38220			−0.691101	−	0.722758i	$-0.742874\pi$
$907$	−41.6270			−1.38220			−0.691101	+	0.722758i	$0.742874\pi$
$908$	9.41545	−	16.3080i	0.312463	−	0.541201i
$909$		0			0
$910$	−4.31499	−	0.580551i	−0.143040	−	0.0192451i
$911$	−50.3137			−1.66697			−0.833484	−	0.552544i	$-0.813657\pi$
$911$	−50.3137			−1.66697			−0.833484	+	0.552544i	$0.813657\pi$
$912$		0			0
$913$	−5.20835			−0.172371
$914$	−2.62643	−	4.54910i	−0.0868744	−	0.150471i
$915$		0			0
$916$	1.74812	−	3.02784i	0.0577596	−	0.100043i
$917$	−19.6943	−	15.4076i	−0.650364	−	0.508802i
$918$		0			0
$919$	27.6186			0.911052			0.455526	−	0.890222i	$-0.349451\pi$
$919$	27.6186			0.911052			0.455526	+	0.890222i	$0.349451\pi$
$920$	−1.48031			−0.0488045
$921$		0			0
$922$	9.59122	+	16.6125i	0.315870	+	0.547103i
$923$	−31.5125	+	18.4695i	−1.03725	+	0.607931i
$924$		0			0
$925$	0.672012	+	1.16396i	0.0220956	+	0.0382707i
$926$	−8.77898	+	15.2056i	−0.288495	+	0.499688i
$927$		0			0
$928$	−2.20552	+	3.82007i	−0.0723996	+	0.125400i
$929$	−12.2941			−0.403355			−0.201677	−	0.979452i	$-0.564639\pi$
$929$	−12.2941			−0.403355			−0.201677	+	0.979452i	$0.564639\pi$
$930$		0			0
$931$	−14.5324	+	13.9973i	−0.476281	+	0.458743i
$932$	−9.74031	+	16.8707i	−0.319054	+	0.552618i
$933$		0			0
$934$	3.08222			0.100853
$935$	−1.35887	+	2.35364i	−0.0444399	+	0.0769722i
$936$		0			0
$937$	10.2719			0.335569			0.167785	−	0.985824i	$-0.446339\pi$
$937$	10.2719			0.335569			0.167785	+	0.985824i	$0.446339\pi$
$938$	−0.662133	+	4.68918i	−0.0216194	+	0.153107i
$939$		0			0
$940$	3.58834			0.117039
$941$	22.3097	−	38.6416i	0.727276	−	1.25968i	−0.230754	−	0.973012i	$-0.574119\pi$
$941$	22.3097	−	38.6416i	0.727276	−	1.25968i	0.958030	−	0.286667i	$-0.0925473\pi$
$942$		0			0
$943$	23.1758			0.754708
$944$	9.36566			0.304826
$945$		0			0
$946$	−4.67031	−	8.08921i	−0.151845	−	0.263003i
$947$	−13.7054	+	23.7385i	−0.445366	+	0.771397i	−0.998078	−	0.0619759i	$-0.980260\pi$
$947$	−13.7054	+	23.7385i	−0.445366	+	0.771397i	0.552712	+	0.833373i	$0.313593\pi$
$948$		0			0
$949$	−8.74722	+	5.12674i	−0.283947	+	0.166421i
$950$	6.90589	+	11.9613i	0.224057	+	0.388077i
$951$		0			0
$952$	−3.23382	−	2.52992i	−0.104809	−	0.0819953i
$953$	21.0794	−	36.5107i	0.682830	−	1.18270i	−0.291284	−	0.956637i	$-0.594082\pi$
$953$	21.0794	−	36.5107i	0.682830	−	1.18270i	0.974114	−	0.226059i	$-0.0725843\pi$
$954$		0			0
$955$	2.09332	+	3.62573i	0.0677381	+	0.117326i
$956$	6.27346	+	10.8659i	0.202898	+	0.351430i
$957$		0			0
$958$	−9.18104	+	15.9020i	−0.296626	+	0.513771i
$959$	5.10103	+	3.99071i	0.164721	+	0.128867i
$960$		0			0
$961$	−30.5987	−	52.9986i	−0.987056	−	1.70963i
$962$	−0.00661109	−	1.01130i	−0.000213150	−	0.0326057i
$963$		0			0
$964$	0.233225	−	0.403958i	0.00751169	−	0.0130106i
$965$	−0.556786	−	0.964381i	−0.0179236	−	0.0310445i
$966$		0			0
$967$	49.9926			1.60765			0.803827	−	0.594863i	$-0.202794\pi$
$967$	49.9926			1.60765			0.803827	+	0.594863i	$0.202794\pi$
$968$	−3.72308			−0.119664
$969$		0			0
$970$	2.16290	−	3.74625i	0.0694464	−	0.120285i
$971$	11.0753			0.355424			0.177712	−	0.984083i	$-0.443130\pi$
$971$	11.0753			0.355424			0.177712	+	0.984083i	$0.443130\pi$
$972$		0			0
$973$	−3.97464	+	28.1482i	−0.127421	+	0.902389i
$974$	−18.0106			−0.577097
$975$		0			0
$976$	5.55187	−	9.61612i	0.177711	−	0.307804i
$977$	−52.2443			−1.67144			−0.835722	−	0.549153i	$-0.814950\pi$
$977$	−52.2443			−1.67144			−0.835722	+	0.549153i	$0.814950\pi$
$978$		0			0
$979$	−0.344755	+	0.597132i	−0.0110184	+	0.0190844i
$980$	−0.768874	−	3.10097i	−0.0245608	−	0.0990568i
$981$		0			0
$982$	15.9759			0.509811
$983$	−18.4322	+	31.9255i	−0.587896	+	1.01827i	0.406611	+	0.913601i	$0.366710\pi$
$983$	−18.4322	+	31.9255i	−0.587896	+	1.01827i	−0.994508	+	0.104665i	$0.966623\pi$
$984$		0			0
$985$	−6.13113	+	10.6194i	−0.195354	+	0.338363i
$986$	3.42267	+	5.92824i	0.109000	+	0.188794i
$987$		0			0
$988$	−0.0679384	−	10.3926i	−0.00216141	−	0.330632i
$989$	−3.94771	−	6.83764i	−0.125530	−	0.217424i
$990$		0			0
$991$	52.3315			1.66236			0.831182	−	0.556000i	$-0.187664\pi$
$991$	52.3315			1.66236			0.831182	+	0.556000i	$0.187664\pi$
$992$	9.60195			0.304862
$993$		0			0
$994$	−21.1102	−	16.5152i	−0.669576	−	0.523832i
$995$	−6.36734	+	11.0286i	−0.201858	+	0.349629i
$996$		0			0
$997$	10.0429	+	17.3949i	0.318063	+	0.550902i	0.980084	−	0.198584i	$-0.0636342\pi$
$997$	10.0429	+	17.3949i	0.318063	+	0.550902i	−0.662021	+	0.749486i	$0.730301\pi$
$998$	−8.13311			−0.257449
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.p.i.991.3		8
3.2	odd	2		546.2.k.b.445.2	yes	8
7.2	even	3		1638.2.m.g.289.3		8
13.9	even	3		1638.2.m.g.1621.3		8
21.2	odd	6		546.2.j.d.289.2	✓	8
39.35	odd	6		546.2.j.d.529.2	yes	8
91.9	even	3	inner	1638.2.p.i.919.3		8
273.191	odd	6		546.2.k.b.373.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.d.289.2	✓	8	21.2	odd	6
546.2.j.d.529.2	yes	8	39.35	odd	6
546.2.k.b.373.2	yes	8	273.191	odd	6
546.2.k.b.445.2	yes	8	3.2	odd	2
1638.2.m.g.289.3		8	7.2	even	3
1638.2.m.g.1621.3		8	13.9	even	3
1638.2.p.i.919.3		8	91.9	even	3	inner
1638.2.p.i.991.3		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.p (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.228205 + 0.395262i) q^{5} +(2.45374 - 0.989520i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.228205 + 0.395262i) q^{5} +(2.45374 - 0.989520i) q^{7} -1.00000 q^{8} +0.456409 q^{10} +3.83707 q^{11} +(-3.13422 - 1.78233i) q^{13} +(0.369922 - 2.61976i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.775934 + 1.34396i) q^{17} -2.88244 q^{19} +(0.228205 - 0.395262i) q^{20} +(1.91853 - 3.32300i) q^{22} +(1.62170 - 2.80886i) q^{23} +(2.39585 - 4.14973i) q^{25} +(-3.11065 + 1.82315i) q^{26} +(-2.08382 - 1.63024i) q^{28} +(2.20552 + 3.82007i) q^{29} +(4.80098 - 8.31553i) q^{31} +(0.500000 + 0.866025i) q^{32} +1.55187 q^{34} +(0.951075 + 0.744058i) q^{35} +(-0.140245 + 0.242912i) q^{37} +(-1.44122 + 2.49627i) q^{38} +(-0.228205 - 0.395262i) q^{40} +(3.57277 + 6.18822i) q^{41} +(1.21716 - 2.10818i) q^{43} +(-1.91853 - 3.32300i) q^{44} +(-1.62170 - 2.80886i) q^{46} +(3.93105 + 6.80879i) q^{47} +(5.04170 - 4.85605i) q^{49} +(-2.39585 - 4.14973i) q^{50} +(0.0235697 + 3.60547i) q^{52} +(-0.550397 + 0.953315i) q^{53} +(0.875637 + 1.51665i) q^{55} +(-2.45374 + 0.989520i) q^{56} +4.41103 q^{58} +(-4.68283 - 8.11090i) q^{59} -11.1037 q^{61} +(-4.80098 - 8.31553i) q^{62} +1.00000 q^{64} +(-0.0107575 - 1.64557i) q^{65} -1.78993 q^{67} +(0.775934 - 1.34396i) q^{68} +(1.11991 - 0.451626i) q^{70} +(5.06527 - 8.77331i) q^{71} +(1.40601 - 2.43529i) q^{73} +(0.140245 + 0.242912i) q^{74} +(1.44122 + 2.49627i) q^{76} +(9.41517 - 3.79685i) q^{77} +(2.70966 + 4.69326i) q^{79} -0.456409 q^{80} +7.14554 q^{82} -1.35738 q^{83} +(-0.354144 + 0.613395i) q^{85} +(-1.21716 - 2.10818i) q^{86} -3.83707 q^{88} +(-0.0898485 + 0.155622i) q^{89} +(-9.45421 - 1.27200i) q^{91} -3.24339 q^{92} +7.86211 q^{94} +(-0.657787 - 1.13932i) q^{95} +(4.73894 - 8.20808i) q^{97} +(-1.68461 - 6.79427i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8	\( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} - 4 q^{10} - 12 q^{11} - 11 q^{13} + 3 q^{14} - 4 q^{16} - 4 q^{17} - 12 q^{19} - 2 q^{20} - 6 q^{22} + 10 q^{23} - 18 q^{25} - 10 q^{26} - 2 q^{29} + 6 q^{31} + 4 q^{32} - 8 q^{34} - 18 q^{35} - 28 q^{37} - 6 q^{38} + 2 q^{40} - 6 q^{43} + 6 q^{44} - 10 q^{46} - q^{47} - 7 q^{49} + 18 q^{50} + q^{52} - 7 q^{53} + q^{55} - 3 q^{56} - 4 q^{58} - 2 q^{59} - 48 q^{61} - 6 q^{62} + 8 q^{64} - 19 q^{65} + 30 q^{67} - 4 q^{68} - 18 q^{70} - 6 q^{71} + q^{73} + 28 q^{74} + 6 q^{76} + 22 q^{77} - 12 q^{79} + 4 q^{80} + 32 q^{83} - 13 q^{85} + 6 q^{86} + 12 q^{88} - 25 q^{89} + 34 q^{91} - 20 q^{92} - 2 q^{94} + 8 q^{95} - q^{97} - 2 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 - 4 * q^10 - 12 * q^11 - 11 * q^13 + 3 * q^14 - 4 * q^16 - 4 * q^17 - 12 * q^19 - 2 * q^20 - 6 * q^22 + 10 * q^23 - 18 * q^25 - 10 * q^26 - 2 * q^29 + 6 * q^31 + 4 * q^32 - 8 * q^34 - 18 * q^35 - 28 * q^37 - 6 * q^38 + 2 * q^40 - 6 * q^43 + 6 * q^44 - 10 * q^46 - q^47 - 7 * q^49 + 18 * q^50 + q^52 - 7 * q^53 + q^55 - 3 * q^56 - 4 * q^58 - 2 * q^59 - 48 * q^61 - 6 * q^62 + 8 * q^64 - 19 * q^65 + 30 * q^67 - 4 * q^68 - 18 * q^70 - 6 * q^71 + q^73 + 28 * q^74 + 6 * q^76 + 22 * q^77 - 12 * q^79 + 4 * q^80 + 32 * q^83 - 13 * q^85 + 6 * q^86 + 12 * q^88 - 25 * q^89 + 34 * q^91 - 20 * q^92 - 2 * q^94 + 8 * q^95 - q^97 - 2 * q^98

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