LMFDB - Embedded newform 2627.1.x.b.780.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2627,1,Mod(141,2627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2627, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 9]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("2627.141");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2627 = 37 \cdot 71 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2627.x (of order $18$, degree $6$, 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:	$1.31104378819$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{63})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{36} - x^{33} + x^{27} - x^{24} + x^{18} - x^{12} + x^{9} - x^{3} + 1 $ x^36 - x^33 + x^27 - x^24 + x^18 - x^12 + x^9 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{126}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{126} - \cdots)$

Embedding invariants

Embedding label			780.6
Root			$0.921476 + 0.388435i$ of defining polynomial
Character	$\chi$	$=$	2627.780
Dual form			2627.1.x.b.1135.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25334 - 1.49368i) q^{2} +(0.0381960 - 0.0320503i) q^{3} +(-0.486551 - 2.75937i) q^{4} +(0.555398 - 1.52594i) q^{5} -0.0972225i q^{6} +(-3.04280 - 1.75676i) q^{8} +(-0.173216 + 0.982359i) q^{9} +O(q^{10})$	\(q+(1.25334 - 1.49368i) q^{2} +(0.0381960 - 0.0320503i) q^{3} +(-0.486551 - 2.75937i) q^{4} +(0.555398 - 1.52594i) q^{5} -0.0972225i q^{6} +(-3.04280 - 1.75676i) q^{8} +(-0.173216 + 0.982359i) q^{9} +(-1.58316 - 2.74212i) q^{10} +(-0.107023 - 0.0898029i) q^{12} +(-0.0276929 - 0.0760857i) q^{15} +(-3.80474 + 1.38481i) q^{16} +(1.25023 + 1.48996i) q^{18} +(0.499362 + 0.595117i) q^{19} +(-4.48087 - 0.790099i) q^{20} +(-0.172527 + 0.0304212i) q^{24} +(-1.25399 - 1.05223i) q^{25} +(0.0497994 + 0.0862551i) q^{27} +(1.61232 + 0.930874i) q^{29} +(-0.148356 - 0.0539972i) q^{30} +(-1.49849 + 4.11706i) q^{32} +2.79497 q^{36} +(-0.921476 - 0.388435i) q^{37} +1.51478 q^{38} +(-4.37068 + 3.66744i) q^{40} -1.43173i q^{43} +(1.40282 + 0.809919i) q^{45} +(-0.100942 + 0.174837i) q^{48} +(0.766044 + 0.642788i) q^{49} +(-3.14337 + 0.554261i) q^{50} +(0.191253 + 0.0337231i) q^{54} +(0.0381473 + 0.00672640i) q^{57} +(3.41122 - 1.24158i) q^{58} +(-0.196475 + 0.113435i) q^{60} +(2.24698 + 3.89188i) q^{64} +(-0.766044 + 0.642788i) q^{71} +(2.25283 - 2.68482i) q^{72} +1.99006 q^{73} +(-1.73512 + 0.889545i) q^{74} -0.0816218 q^{75} +(1.39918 - 1.66748i) q^{76} +(-0.0681084 + 0.187126i) q^{79} +6.57494i q^{80} +(-0.932690 - 0.339471i) q^{81} +(-0.254586 + 1.44383i) q^{83} +(-2.13855 - 1.79445i) q^{86} +(0.0914190 - 0.0161196i) q^{87} +(-0.327145 - 0.898823i) q^{89} +(2.96797 - 1.08025i) q^{90} +(1.18546 - 0.431472i) q^{95} +(0.0747167 + 0.205282i) q^{96} +(1.92023 - 0.338589i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{3} + 3 q^{5} - 6 q^{9}+O(q^{10}) $ 36 * q + 6 * q^3 + 3 * q^5 - 6 * q^9	$ 36 q + 6 q^{3} + 3 q^{5} - 6 q^{9} + 6 q^{12} - 3 q^{15} + 21 q^{18} + 3 q^{19} - 36 q^{20} - 21 q^{24} + 3 q^{25} + 3 q^{27} - 9 q^{29} - 21 q^{30} - 48 q^{36} - 3 q^{57} + 54 q^{60} + 24 q^{64} + 21 q^{72} - 6 q^{75} - 3 q^{76} + 6 q^{79} - 3 q^{81} - 12 q^{87} + 3 q^{89} + 42 q^{90} - 6 q^{95} - 21 q^{96}+O(q^{100}) $ 36 * q + 6 * q^3 + 3 * q^5 - 6 * q^9 + 6 * q^12 - 3 * q^15 + 21 * q^18 + 3 * q^19 - 36 * q^20 - 21 * q^24 + 3 * q^25 + 3 * q^27 - 9 * q^29 - 21 * q^30 - 48 * q^36 - 3 * q^57 + 54 * q^60 + 24 * q^64 + 21 * q^72 - 6 * q^75 - 3 * q^76 + 6 * q^79 - 3 * q^81 - 12 * q^87 + 3 * q^89 + 42 * q^90 - 6 * q^95 - 21 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2627\mathbb{Z}\right)^\times$.

$n$	$149$	$853$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	1.25334	−	1.49368i	1.25334	−	1.49368i	0.456211	−	0.889872i	$-0.349206\pi$
$2$	1.25334	−	1.49368i	1.25334	−	1.49368i	0.797133	−	0.603804i	$-0.206349\pi$
$3$	0.0381960	−	0.0320503i	0.0381960	−	0.0320503i	−0.623490	−	0.781831i	$-0.714286\pi$
$3$	0.0381960	−	0.0320503i	0.0381960	−	0.0320503i	0.661686	+	0.749781i	$0.269841\pi$
$4$	−0.486551	−	2.75937i	−0.486551	−	2.75937i
$5$	0.555398	−	1.52594i	0.555398	−	1.52594i	−0.270840	−	0.962624i	$-0.587302\pi$
$5$	0.555398	−	1.52594i	0.555398	−	1.52594i	0.826239	−	0.563320i	$-0.190476\pi$
$6$		−	0.0972225i		−	0.0972225i
$7$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$7$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$8$	−3.04280	−	1.75676i	−3.04280	−	1.75676i
$9$	−0.173216	+	0.982359i	−0.173216	+	0.982359i
$10$	−1.58316	−	2.74212i	−1.58316	−	2.74212i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	−0.107023	−	0.0898029i	−0.107023	−	0.0898029i
$13$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$13$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$14$		0			0
$15$	−0.0276929	−	0.0760857i	−0.0276929	−	0.0760857i
$16$	−3.80474	+	1.38481i	−3.80474	+	1.38481i
$17$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$17$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$18$	1.25023	+	1.48996i	1.25023	+	1.48996i
$19$	0.499362	+	0.595117i	0.499362	+	0.595117i	0.955573	−	0.294755i	$-0.0952381\pi$
$19$	0.499362	+	0.595117i	0.499362	+	0.595117i	−0.456211	+	0.889872i	$0.650794\pi$
$20$	−4.48087	−	0.790099i	−4.48087	−	0.790099i
$21$		0			0
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	−0.172527	+	0.0304212i	−0.172527	+	0.0304212i
$25$	−1.25399	−	1.05223i	−1.25399	−	1.05223i
$26$		0			0
$27$	0.0497994	+	0.0862551i	0.0497994	+	0.0862551i
$28$		0			0
$29$	1.61232	+	0.930874i	1.61232	+	0.930874i	0.988831	+	0.149042i	$0.0476190\pi$
$29$	1.61232	+	0.930874i	1.61232	+	0.930874i	0.623490	+	0.781831i	$0.285714\pi$
$30$	−0.148356	−	0.0539972i	−0.148356	−	0.0539972i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−1.49849	+	4.11706i	−1.49849	+	4.11706i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	2.79497			2.79497
$37$	−0.921476	−	0.388435i	−0.921476	−	0.388435i
$37$	−0.921476	−	0.388435i	−0.921476	−	0.388435i
$38$	1.51478			1.51478
$39$		0			0
$40$	−4.37068	+	3.66744i	−4.37068	+	3.66744i
$41$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$41$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$42$		0			0
$43$		−	1.43173i		−	1.43173i	−0.698237	−	0.715867i	$-0.746032\pi$
$43$		−	1.43173i		−	1.43173i	0.698237	−	0.715867i	$-0.253968\pi$
$44$		0			0
$45$	1.40282	+	0.809919i	1.40282	+	0.809919i
$46$		0			0
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$	−0.100942	+	0.174837i	−0.100942	+	0.174837i
$49$	0.766044	+	0.642788i	0.766044	+	0.642788i
$50$	−3.14337	+	0.554261i	−3.14337	+	0.554261i
$51$		0			0
$52$		0			0
$53$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$53$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$54$	0.191253	+	0.0337231i	0.191253	+	0.0337231i
$55$		0			0
$56$		0			0
$57$	0.0381473	+	0.00672640i	0.0381473	+	0.00672640i
$58$	3.41122	−	1.24158i	3.41122	−	1.24158i
$59$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$59$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$60$	−0.196475	+	0.113435i	−0.196475	+	0.113435i
$61$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$61$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$62$		0			0
$63$		0			0
$64$	2.24698	+	3.89188i	2.24698	+	3.89188i
$65$		0			0
$66$		0			0
$67$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$67$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$71$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$72$	2.25283	−	2.68482i	2.25283	−	2.68482i
$73$	1.99006			1.99006			0.995031	−	0.0995678i	$-0.0317460\pi$
$73$	1.99006			1.99006			0.995031	+	0.0995678i	$0.0317460\pi$
$74$	−1.73512	+	0.889545i	−1.73512	+	0.889545i
$75$	−0.0816218			−0.0816218
$76$	1.39918	−	1.66748i	1.39918	−	1.66748i
$77$		0			0
$78$		0			0
$79$	−0.0681084	+	0.187126i	−0.0681084	+	0.187126i	−0.969077	−	0.246757i	$-0.920635\pi$
$79$	−0.0681084	+	0.187126i	−0.0681084	+	0.187126i	0.900969	+	0.433884i	$0.142857\pi$
$80$			6.57494i			6.57494i
$81$	−0.932690	−	0.339471i	−0.932690	−	0.339471i
$82$		0			0
$83$	−0.254586	+	1.44383i	−0.254586	+	1.44383i	0.542546	+	0.840026i	$0.317460\pi$
$83$	−0.254586	+	1.44383i	−0.254586	+	1.44383i	−0.797133	+	0.603804i	$0.793651\pi$
$84$		0			0
$85$		0			0
$86$	−2.13855	−	1.79445i	−2.13855	−	1.79445i
$87$	0.0914190	−	0.0161196i	0.0914190	−	0.0161196i
$88$		0			0
$89$	−0.327145	−	0.898823i	−0.327145	−	0.898823i	−0.988831	−	0.149042i	$-0.952381\pi$
$89$	−0.327145	−	0.898823i	−0.327145	−	0.898823i	0.661686	−	0.749781i	$-0.269841\pi$
$90$	2.96797	−	1.08025i	2.96797	−	1.08025i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.18546	−	0.431472i	1.18546	−	0.431472i
$96$	0.0747167	+	0.205282i	0.0747167	+	0.205282i
$97$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$97$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$98$	1.92023	−	0.338589i	1.92023	−	0.338589i
$99$		0			0
$100$	−2.29335	+	3.97220i	−2.29335	+	3.97220i
$101$	0.456211	+	0.790180i	0.456211	+	0.790180i	0.998757	−	0.0498459i	$-0.0158730\pi$
$101$	0.456211	+	0.790180i	0.456211	+	0.790180i	−0.542546	+	0.840026i	$0.682540\pi$
$102$		0			0
$103$	−1.73151	−	0.999689i	−1.73151	−	0.999689i	−0.878222	−	0.478254i	$-0.841270\pi$
$103$	−1.73151	−	0.999689i	−1.73151	−	0.999689i	−0.853291	−	0.521435i	$-0.825397\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$107$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$108$	0.213780	−	0.179383i	0.213780	−	0.179383i
$109$	−1.28518	+	1.53161i	−1.28518	+	1.53161i	−0.623490	+	0.781831i	$0.714286\pi$
$109$	−1.28518	+	1.53161i	−1.28518	+	1.53161i	−0.661686	+	0.749781i	$0.730159\pi$
$110$		0			0
$111$	−0.0476462	+	0.0146969i	−0.0476462	+	0.0146969i
$112$		0			0
$113$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$113$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$114$	0.0578587	−	0.0485492i	0.0578587	−	0.0485492i
$115$		0			0
$116$	1.78415	−	4.90191i	1.78415	−	4.90191i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.0494003	+	0.280163i	−0.0494003	+	0.280163i
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.895787	+	0.517183i	−0.895787	+	0.517183i
$126$		0			0
$127$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$127$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$128$	4.31472	+	0.760802i	4.31472	+	0.760802i
$129$	−0.0458875	−	0.0546866i	−0.0458875	−	0.0546866i
$130$		0			0
$131$	−0.486017	−	0.0856979i	−0.486017	−	0.0856979i	−0.0747301	−	0.997204i	$-0.523810\pi$
$131$	−0.486017	−	0.0856979i	−0.486017	−	0.0856979i	−0.411287	+	0.911506i	$0.634921\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.159279	−	0.0280852i	0.159279	−	0.0280852i
$136$		0			0
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$139$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$140$		0			0
$141$		0			0
$142$			1.94986i			1.94986i
$143$		0			0
$144$	−0.701339	−	3.97749i	−0.701339	−	3.97749i
$145$	2.31594	−	1.94331i	2.31594	−	1.94331i
$146$	2.49423	−	2.97251i	2.49423	−	2.97251i
$147$	0.0498614			0.0498614
$148$	−0.623490	+	2.73169i	−0.623490	+	2.73169i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	−0.102300	+	0.121916i	−0.102300	+	0.121916i
$151$	1.50171	−	1.26009i	1.50171	−	1.26009i	0.623490	−	0.781831i	$-0.285714\pi$
$151$	1.50171	−	1.26009i	1.50171	−	1.26009i	0.878222	−	0.478254i	$-0.158730\pi$
$152$	−0.473981	−	2.68808i	−0.473981	−	2.68808i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.110609	+	0.627296i	−0.110609	+	0.627296i	0.878222	+	0.478254i	$0.158730\pi$
$157$	−0.110609	+	0.627296i	−0.110609	+	0.627296i	−0.988831	+	0.149042i	$0.952381\pi$
$158$	0.194143	+	0.336265i	0.194143	+	0.336265i
$159$		0			0
$160$	5.45015	+	4.57322i	5.45015	+	4.57322i
$161$		0			0
$162$	−1.67604	+	0.967662i	−1.67604	+	0.967662i
$163$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$163$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$164$		0			0
$165$		0			0
$166$	1.83753	+	2.18988i	1.83753	+	2.18988i
$167$	−0.724190	−	0.863056i	−0.724190	−	0.863056i	0.270840	−	0.962624i	$-0.412698\pi$
$167$	−0.724190	−	0.863056i	−0.724190	−	0.863056i	−0.995031	+	0.0995678i	$0.968254\pi$
$168$		0			0
$169$	0.939693	−	0.342020i	0.939693	−	0.342020i
$170$		0			0
$171$	−0.671116	+	0.387469i	−0.671116	+	0.387469i
$172$	−3.95068	+	0.696612i	−3.95068	+	0.696612i
$173$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$173$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$174$	0.0905019	−	0.156754i	0.0905019	−	0.156754i
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−1.75258	−	0.637886i	−1.75258	−	0.637886i
$179$			1.99441i			1.99441i	0.0747301	+	0.997204i	$0.476190\pi$
$179$			1.99441i			1.99441i	−0.0747301	+	0.997204i	$0.523810\pi$
$180$	1.55232	−	4.26497i	1.55232	−	4.26497i
$181$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$181$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.10452	+	1.19039i	−1.10452	+	1.19039i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	0.841308	−	2.31148i	0.841308	−	2.31148i
$191$			1.89585i			1.89585i	0.318487	+	0.947927i	$0.396825\pi$
$191$			1.89585i			1.89585i	−0.318487	+	0.947927i	$0.603175\pi$
$192$	0.210562	+	0.0766382i	0.210562	+	0.0766382i
$193$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$193$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$194$		0			0
$195$		0			0
$196$	1.40097	−	2.42655i	1.40097	−	2.42655i
$197$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$197$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$198$		0			0
$199$	−1.45497	+	0.840026i	−1.45497	+	0.840026i	−0.998757	−	0.0498459i	$-0.984127\pi$
$199$	−1.45497	+	0.840026i	−1.45497	+	0.840026i	−0.456211	+	0.889872i	$0.650794\pi$
$200$	1.96714	+	5.40468i	1.96714	+	5.40468i
$201$		0			0
$202$	1.75206	+	0.308936i	1.75206	+	0.308936i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−3.66339	+	1.33337i	−3.66339	+	1.33337i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$	−0.00865834	+	0.0491039i	−0.00865834	+	0.0491039i
$214$	−1.68862	−	0.974928i	−1.68862	−	0.974928i
$215$	−2.18475	−	0.795182i	−2.18475	−	0.795182i
$216$		−	0.349942i		−	0.349942i
$217$		0			0
$218$	0.676967	+	3.83927i	0.676967	+	3.83927i
$219$	0.0760125	−	0.0637820i	0.0760125	−	0.0637820i
$220$		0			0
$221$		0			0
$222$	−0.0377646	+	0.0895882i	−0.0377646	+	0.0895882i
$223$	1.59427			1.59427			0.797133	−	0.603804i	$-0.206349\pi$
$223$	1.59427			1.59427			0.797133	+	0.603804i	$0.206349\pi$
$224$		0			0
$225$	1.25088	−	1.04961i	1.25088	−	1.04961i
$226$		0			0
$227$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$227$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$228$		−	0.108535i		−	0.108535i
$229$	1.55282	+	0.565181i	1.55282	+	0.565181i	0.969077	−	0.246757i	$-0.0793651\pi$
$229$	1.55282	+	0.565181i	1.55282	+	0.565181i	0.583744	+	0.811938i	$0.301587\pi$
$230$		0			0
$231$		0			0
$232$	−3.27064	−	5.66492i	−3.27064	−	5.66492i
$233$	0.955573	−	1.65510i	0.955573	−	1.65510i	0.222521	−	0.974928i	$-0.428571\pi$
$233$	0.955573	−	1.65510i	0.955573	−	1.65510i	0.733052	−	0.680173i	$-0.238095\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.00339598	+	0.00933038i	0.00339598	+	0.00933038i
$238$		0			0
$239$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$239$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$240$	0.210729	+	0.251137i	0.210729	+	0.251137i
$241$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$241$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$242$	−1.92023	−	0.338589i	−1.92023	−	0.338589i
$243$	−0.140097	+	0.0509913i	−0.140097	+	0.0509913i
$244$		0			0
$245$	1.40632	−	0.811938i	1.40632	−	0.811938i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	0.0365510	+	0.0633082i	0.0365510	+	0.0633082i
$250$	−0.350225	+	1.98622i	−0.350225	+	1.98622i
$251$	−1.68862	−	0.974928i	−1.68862	−	0.974928i	−0.955573	−	0.294755i	$-0.904762\pi$
$251$	−1.68862	−	0.974928i	−1.68862	−	0.974928i	−0.733052	−	0.680173i	$-0.761905\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	3.10165	−	2.60259i	3.10165	−	2.60259i
$257$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$257$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$258$	−0.139197			−0.139197
$259$		0			0
$260$		0			0
$261$	−1.19373	+	1.42264i	−1.19373	+	1.42264i
$262$	−0.737151	+	0.618543i	−0.737151	+	0.618543i
$263$	0.202732	+	1.14975i	0.202732	+	1.14975i	0.900969	+	0.433884i	$0.142857\pi$
$263$	0.202732	+	1.14975i	0.202732	+	1.14975i	−0.698237	+	0.715867i	$0.746032\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.0413032	−	0.0238464i	−0.0413032	−	0.0238464i
$268$		0			0
$269$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$269$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$270$	0.157681	−	0.273112i	0.157681	−	0.273112i
$271$	−0.955242	−	0.801543i	−0.955242	−	0.801543i	0.0249307	−	0.999689i	$-0.492063\pi$
$271$	−0.955242	−	0.801543i	−0.955242	−	0.801543i	−0.980172	+	0.198146i	$0.936508\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.874413	−	1.04209i	−0.874413	−	1.04209i	−0.998757	−	0.0498459i	$-0.984127\pi$
$277$	−0.874413	−	1.04209i	−0.874413	−	1.04209i	0.124344	−	0.992239i	$-0.460317\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$281$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$282$		0			0
$283$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$283$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$284$	2.14641	+	1.80105i	2.14641	+	1.80105i
$285$	0.0314511	−	0.0544748i	0.0314511	−	0.0544748i
$286$		0			0
$287$		0			0
$288$	−3.78487	−	2.18520i	−3.78487	−	2.18520i
$289$	0.939693	+	0.342020i	0.939693	+	0.342020i
$290$		−	5.89490i		−	5.89490i
$291$		0			0
$292$	−0.968267	−	5.49132i	−0.968267	−	5.49132i
$293$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$293$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$294$	0.0624934	−	0.0744768i	0.0624934	−	0.0744768i
$295$		0			0
$296$	2.12148	+	2.80074i	2.12148	+	2.80074i
$297$		0			0
$298$		0			0
$299$		0			0
$300$	0.0397132	+	0.225225i	0.0397132	+	0.225225i
$301$		0			0
$302$		−	3.82239i		−	3.82239i
$303$	0.0427509	+	0.0155601i	0.0427509	+	0.0155601i
$304$	−2.72407	−	1.57274i	−2.72407	−	1.57274i
$305$		0			0
$306$		0			0
$307$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$307$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$308$		0			0
$309$	−0.0981772	+	0.0173113i	−0.0981772	+	0.0173113i
$310$		0			0
$311$	0.678732	+	1.86480i	0.678732	+	1.86480i	0.456211	+	0.889872i	$0.349206\pi$
$311$	0.678732	+	1.86480i	0.678732	+	1.86480i	0.222521	+	0.974928i	$0.428571\pi$
$312$		0			0
$313$	1.95433	+	0.344601i	1.95433	+	0.344601i	0.998757	+	0.0498459i	$0.0158730\pi$
$313$	1.95433	+	0.344601i	1.95433	+	0.344601i	0.955573	+	0.294755i	$0.0952381\pi$
$314$	0.798346	+	0.951432i	0.798346	+	0.951432i
$315$		0			0
$316$	0.549489	+	0.0968897i	0.549489	+	0.0968897i
$317$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$317$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$318$		0			0
$319$		0			0
$320$	7.18677	−	1.26722i	7.18677	−	1.26722i
$321$	−0.0381960	−	0.0320503i	−0.0381960	−	0.0320503i
$322$		0			0
$323$		0			0
$324$	−0.482925	+	2.73881i	−0.482925	+	2.73881i
$325$		0			0
$326$		0			0
$327$			0.0996918i			0.0996918i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$331$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$332$	4.10793			4.10793
$333$	0.541197	−	0.837937i	0.541197	−	0.837937i
$334$	−2.19679			−2.19679
$335$		0			0
$336$		0			0
$337$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$337$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$338$	0.666890	−	1.83227i	0.666890	−	1.83227i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−0.262385	+	1.48806i	−0.262385	+	1.48806i
$343$		0			0
$344$	−2.51521	+	4.35647i	−2.51521	+	4.35647i
$345$		0			0
$346$		0			0
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$	−0.0889601	−	0.244416i	−0.0889601	−	0.244416i
$349$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$349$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$353$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$354$		0			0
$355$	0.555398	+	1.52594i	0.555398	+	1.52594i
$356$	−2.32101	+	1.34004i	−2.32101	+	1.34004i
$357$		0			0
$358$	2.97900	+	2.49968i	2.97900	+	2.49968i
$359$	0.698237	−	1.20938i	0.698237	−	1.20938i	−0.270840	−	0.962624i	$-0.587302\pi$
$359$	0.698237	−	1.20938i	0.698237	−	1.20938i	0.969077	−	0.246757i	$-0.0793651\pi$
$360$	−2.84567	−	4.92884i	−2.84567	−	4.92884i
$361$	0.0688469	−	0.390450i	0.0688469	−	0.390450i
$362$		0			0
$363$	−0.0468544	−	0.0170536i	−0.0468544	−	0.0170536i
$364$		0			0
$365$	1.10528	−	3.03672i	1.10528	−	3.03672i
$366$		0			0
$367$	−1.48471	+	1.24582i	−1.48471	+	1.24582i	−0.583744	+	0.811938i	$0.698413\pi$
$367$	−1.48471	+	1.24582i	−1.48471	+	1.24582i	−0.900969	+	0.433884i	$0.857143\pi$
$368$		0			0
$369$		0			0
$370$	0.393712	+	3.14175i	0.393712	+	3.14175i
$371$		0			0
$372$		0			0
$373$	0.894347	−	0.750446i	0.894347	−	0.750446i	−0.0747301	−	0.997204i	$-0.523810\pi$
$373$	0.894347	−	0.750446i	0.894347	−	0.750446i	0.969077	+	0.246757i	$0.0793651\pi$
$374$		0			0
$375$	−0.0176397	+	0.0484646i	−0.0176397	+	0.0484646i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.340410	−	1.93056i	0.340410	−	1.93056i	−0.0249307	−	0.999689i	$-0.507937\pi$
$379$	0.340410	−	1.93056i	0.340410	−	1.93056i	0.365341	−	0.930874i	$-0.380952\pi$
$380$	−1.76738	−	3.06119i	−1.76738	−	3.06119i
$381$		0			0
$382$	2.83179	+	2.37616i	2.83179	+	2.37616i
$383$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$383$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$384$	0.189189	−	0.109228i	0.189189	−	0.109228i
$385$		0			0
$386$		0			0
$387$	1.40648	+	0.248000i	1.40648	+	0.248000i
$388$		0			0
$389$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$389$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$390$		0			0
$391$		0			0
$392$	−1.20169	−	3.30163i	−1.20169	−	3.30163i
$393$	−0.0213106	+	0.0123037i	−0.0213106	+	0.0123037i
$394$		0			0
$395$	0.247717	+	0.207859i	0.247717	+	0.207859i
$396$		0			0
$397$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$397$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$398$	−0.568847	+	3.22609i	−0.568847	+	3.22609i
$399$		0			0
$400$	6.22825	+	2.26690i	6.22825	+	2.26690i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$		0			0
$404$	1.95843	−	1.64332i	1.95843	−	1.64332i
$405$	−1.03603	+	1.23469i	−1.03603	+	1.23469i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.191605	−	0.228346i	0.191605	−	0.228346i	−0.661686	−	0.749781i	$-0.730159\pi$
$409$	0.191605	−	0.228346i	0.191605	−	0.228346i	0.853291	+	0.521435i	$0.174603\pi$
$410$		0			0
$411$		0			0
$412$	−1.91604	+	5.26428i	−1.91604	+	5.26428i
$413$		0			0
$414$		0			0
$415$	2.06181	+	1.19039i	2.06181	+	1.19039i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.51498	+	1.27122i	1.51498	+	1.27122i	0.853291	+	0.521435i	$0.174603\pi$
$419$	1.51498	+	1.27122i	1.51498	+	1.27122i	0.661686	+	0.749781i	$0.269841\pi$
$420$		0			0
$421$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$421$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	0.0624934	+	0.0744768i	0.0624934	+	0.0744768i
$427$		0			0
$428$	−2.63296	+	0.958319i	−2.63296	+	0.958319i
$429$		0			0
$430$	−3.92598	+	2.26667i	−3.92598	+	2.26667i
$431$	−1.75271	+	0.309049i	−1.75271	+	0.309049i	−0.955573	−	0.294755i	$-0.904762\pi$
$431$	−1.75271	+	0.309049i	−1.75271	+	0.309049i	−0.797133	+	0.603804i	$0.793651\pi$
$432$	−0.308921	−	0.259215i	−0.308921	−	0.259215i
$433$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$433$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$434$		0			0
$435$	0.0261763	−	0.148453i	0.0261763	−	0.148453i
$436$	4.85159	+	2.80107i	4.85159	+	2.80107i
$437$		0			0
$438$		−	0.193479i		−	0.193479i
$439$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$439$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$440$		0			0
$441$	−0.764140	+	0.641190i	−0.764140	+	0.641190i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	0.0637365	+	0.124323i	0.0637365	+	0.124323i
$445$	−1.55325			−1.55325
$446$	1.99816	−	2.38132i	1.99816	−	2.38132i
$447$		0			0
$448$		0			0
$449$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$449$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$450$		−	3.18393i		−	3.18393i
$451$		0			0
$452$		0			0
$453$	0.0169733	−	0.0962605i	0.0169733	−	0.0962605i
$454$		0			0
$455$		0			0
$456$	−0.104258	−	0.0874827i	−0.104258	−	0.0874827i
$457$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$457$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$458$	2.79041	−	1.61105i	2.79041	−	1.61105i
$459$		0			0
$460$		0			0
$461$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$461$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$462$		0			0
$463$	0.378930	+	0.451591i	0.378930	+	0.451591i	0.921476	−	0.388435i	$-0.126984\pi$
$463$	0.378930	+	0.451591i	0.378930	+	0.451591i	−0.542546	+	0.840026i	$0.682540\pi$
$464$	−7.42354	−	1.30897i	−7.42354	−	1.30897i
$465$		0			0
$466$	−1.27452	−	3.50173i	−1.27452	−	3.50173i
$467$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$467$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.0158802	+	0.0275053i	0.0158802	+	0.0275053i
$472$		0			0
$473$		0			0
$474$	0.0181929	+	0.00662167i	0.0181929	+	0.00662167i
$475$		−	1.27171i		−	1.27171i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$479$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$480$	0.354747			0.354747
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−2.14641	+	1.80105i	−2.14641	+	1.80105i
$485$		0			0
$486$	−0.0994257	+	0.273170i	−0.0994257	+	0.273170i
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$		0			0
$489$		0			0
$490$	0.549826	−	3.11822i	0.549826	−	3.11822i
$491$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$491$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.140373	+	0.0247515i	0.140373	+	0.0247515i
$499$	−0.670344	−	0.798885i	−0.670344	−	0.798885i	0.318487	−	0.947927i	$-0.396825\pi$
$499$	−0.670344	−	0.798885i	−0.670344	−	0.798885i	−0.988831	+	0.149042i	$0.952381\pi$
$500$	1.86295	+	2.22017i	1.86295	+	2.22017i
$501$	−0.0553224	−	0.00975483i	−0.0553224	−	0.00975483i
$502$	−3.57265	+	1.30034i	−3.57265	+	1.30034i
$503$	0.101951	+	0.280108i	0.101951	+	0.280108i	0.980172	−	0.198146i	$-0.0634921\pi$
$503$	0.101951	+	0.280108i	0.101951	+	0.280108i	−0.878222	+	0.478254i	$0.841270\pi$
$504$		0			0
$505$	1.45915	−	0.257287i	1.45915	−	0.257287i
$506$		0			0
$507$	0.0249307	−	0.0431812i	0.0249307	−	0.0431812i
$508$		0			0
$509$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	0.500000	+	0.866025i	$0.333333\pi$
$509$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	−0.766044	+	0.642788i	$0.777778\pi$
$510$		0			0
$511$		0			0
$512$		−	3.51352i		−	3.51352i
$513$	−0.0264639	+	0.0727090i	−0.0264639	+	0.0727090i
$514$		0			0
$515$	−2.48715	+	2.08697i	−2.48715	+	2.08697i
$516$	−0.128574	+	0.153228i	−0.128574	+	0.153228i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.114493	−	0.0960712i	0.114493	−	0.0960712i	−0.583744	−	0.811938i	$-0.698413\pi$
$521$	0.114493	−	0.0960712i	0.114493	−	0.0960712i	0.698237	+	0.715867i	$0.253968\pi$
$522$	0.628800	+	3.56610i	0.628800	+	3.56610i
$523$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$523$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$524$			1.38280i			1.38280i
$525$		0			0
$526$	1.97145	+	1.13822i	1.97145	+	1.13822i
$527$		0			0
$528$		0			0
$529$	0.500000	−	0.866025i	0.500000	−	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−0.0873859	+	0.0318059i	−0.0873859	+	0.0318059i
$535$	−1.59921	−	0.281983i	−1.59921	−	0.281983i
$536$		0			0
$537$	0.0639213	+	0.0761785i	0.0639213	+	0.0761785i
$538$		0			0
$539$		0			0
$540$	−0.154995	−	0.425845i	−0.154995	−	0.425845i
$541$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$541$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$542$	−2.39449	+	0.422213i	−2.39449	+	0.422213i
$543$		0			0
$544$		0			0
$545$	1.62337	+	2.81176i	1.62337	+	2.81176i
$546$		0			0
$547$	0.0863356	+	0.0498459i	0.0863356	+	0.0498459i	0.542546	−	0.840026i	$-0.317460\pi$
$547$	0.0863356	+	0.0498459i	0.0863356	+	0.0498459i	−0.456211	+	0.889872i	$0.650794\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.251153	+	1.42436i	0.251153	+	1.42436i
$552$		0			0
$553$		0			0
$554$	−2.65248			−2.65248
$555$	−0.00403596	+	0.0808681i	−0.00403596	+	0.0808681i
$556$		0			0
$557$	−0.254732	+	0.303578i	−0.254732	+	0.303578i	−0.878222	−	0.478254i	$-0.841270\pi$
$557$	−0.254732	+	0.303578i	−0.254732	+	0.303578i	0.623490	+	0.781831i	$0.285714\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$	3.46014	−	0.610116i	3.46014	−	0.610116i
$569$	0.751509	−	0.433884i	0.751509	−	0.433884i	−0.0747301	−	0.997204i	$-0.523810\pi$
$569$	0.751509	−	0.433884i	0.751509	−	0.433884i	0.826239	+	0.563320i	$0.190476\pi$
$570$	−0.0419488	−	0.115253i	−0.0419488	−	0.115253i
$571$	1.01965	−	0.371124i	1.01965	−	0.371124i	0.222521	−	0.974928i	$-0.428571\pi$
$571$	1.01965	−	0.371124i	1.01965	−	0.371124i	0.797133	+	0.603804i	$0.206349\pi$
$572$		0			0
$573$	0.0607627	+	0.0724141i	0.0607627	+	0.0724141i
$574$		0			0
$575$		0			0
$576$	−4.21244	+	1.53320i	−4.21244	+	1.53320i
$577$	0.682128	+	1.87413i	0.682128	+	1.87413i	0.411287	+	0.911506i	$0.365079\pi$
$577$	0.682128	+	1.87413i	0.682128	+	1.87413i	0.270840	+	0.962624i	$0.412698\pi$
$578$	1.68862	−	0.974928i	1.68862	−	0.974928i
$579$		0			0
$580$	−6.48912	−	5.44502i	−6.48912	−	5.44502i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−6.05535	−	3.49606i	−6.05535	−	3.49606i
$585$		0			0
$586$			3.66453i			3.66453i
$587$	−0.101951	+	0.280108i	−0.101951	+	0.280108i	−0.980172	−	0.198146i	$-0.936508\pi$
$587$	−0.101951	+	0.280108i	−0.101951	+	0.280108i	0.878222	+	0.478254i	$0.158730\pi$
$588$	−0.0242601	−	0.137586i	−0.0242601	−	0.137586i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	4.04388	+	0.201822i	4.04388	+	0.201822i
$593$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$593$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.0286509	+	0.0787178i	−0.0286509	+	0.0787178i
$598$		0			0
$599$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$599$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$600$	0.248358	+	0.143390i	0.248358	+	0.143390i
$601$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$601$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$602$		0			0
$603$		0			0
$604$	−4.20770	−	3.53068i	−4.20770	−	3.53068i
$605$	−1.59921	+	0.281983i	−1.59921	+	0.281983i
$606$	0.0768233	−	0.0443539i	0.0768233	−	0.0443539i
$607$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$607$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$608$	−3.19842	+	1.16413i	−3.19842	+	1.16413i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.85839	+	0.676400i	−1.85839	+	0.676400i	−0.878222	+	0.478254i	$0.841270\pi$
$613$	−1.85839	+	0.676400i	−1.85839	+	0.676400i	−0.980172	+	0.198146i	$0.936508\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.414952	−	0.348186i	−0.414952	−	0.348186i	0.411287	−	0.911506i	$-0.365079\pi$
$617$	−0.414952	−	0.348186i	−0.414952	−	0.348186i	−0.826239	+	0.563320i	$0.809524\pi$
$618$	−0.0971923	+	0.168342i	−0.0971923	+	0.168342i
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$		0			0
$622$	3.63609	+	1.32343i	3.63609	+	1.32343i
$623$		0			0
$624$		0			0
$625$	0.00741622	+	0.0420595i	0.00741622	+	0.0420595i
$626$	2.96417	−	2.48723i	2.96417	−	2.48723i
$627$		0			0
$628$	1.78476			1.78476
$629$		0			0
$630$		0			0
$631$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$631$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$632$	0.535976	−	0.449737i	0.535976	−	0.449737i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−0.498757	−	0.863872i	−0.498757	−	0.863872i
$640$	3.55733	−	6.16148i	3.55733	−	6.16148i
$641$	−0.190506	−	0.159853i	−0.190506	−	0.159853i	0.542546	−	0.840026i	$-0.317460\pi$
$641$	−0.190506	−	0.159853i	−0.190506	−	0.159853i	−0.733052	+	0.680173i	$0.761905\pi$
$642$	−0.0957455	+	0.0168825i	−0.0957455	+	0.0168825i
$643$	−1.50000	+	0.866025i	−1.50000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$643$	−1.50000	+	0.866025i	−1.50000	+	0.866025i	−1.00000			$\pi$
$644$		0			0
$645$	−0.108934	+	0.0396489i	−0.108934	+	0.0396489i
$646$		0			0
$647$	−1.11334	−	1.32683i	−1.11334	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$647$	−1.11334	−	1.32683i	−1.11334	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$648$	2.24162	+	2.67145i	2.24162	+	2.67145i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$653$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$654$	0.148907	+	0.124948i	0.148907	+	0.124948i
$655$	−0.400703	+	0.694039i	−0.400703	+	0.694039i
$656$		0			0
$657$	−0.344711	+	1.95496i	−0.344711	+	1.95496i
$658$		0			0
$659$	−0.686617	−	0.249908i	−0.686617	−	0.249908i	−0.0249307	−	0.999689i	$-0.507937\pi$
$659$	−0.686617	−	0.249908i	−0.686617	−	0.249908i	−0.661686	+	0.749781i	$0.730159\pi$
$660$		0			0
$661$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$661$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$662$		0			0
$663$		0			0
$664$	3.31112	−	3.94604i	3.31112	−	3.94604i
$665$		0			0
$666$	−0.573301	−	1.85860i	−0.573301	−	1.85860i
$667$		0			0
$668$	−2.02914	+	2.41823i	−2.02914	+	2.41823i
$669$	0.0608946	−	0.0510966i	0.0608946	−	0.0510966i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$673$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$674$		0			0
$675$	0.0283117	−	0.160564i	0.0283117	−	0.160564i
$676$	−1.40097	−	2.42655i	−1.40097	−	2.42655i
$677$	−0.878222	+	1.52112i	−0.878222	+	1.52112i	−0.0249307	+	0.999689i	$0.507937\pi$
$677$	−0.878222	+	1.52112i	−0.878222	+	1.52112i	−0.853291	+	0.521435i	$0.825397\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$683$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$684$	1.39570	+	1.66333i	1.39570	+	1.66333i
$685$		0			0
$686$		0			0
$687$	0.0774258	−	0.0281807i	0.0774258	−	0.0281807i
$688$	1.98268	+	5.44737i	1.98268	+	5.44737i
$689$		0			0
$690$		0			0
$691$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$691$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	−0.306488	−	0.111552i	−0.306488	−	0.111552i
$697$		0			0
$698$		0			0
$699$	−0.0165473	−	0.0938447i	−0.0165473	−	0.0938447i
$700$		0			0
$701$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$701$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$702$		0			0
$703$	−0.228986	−	0.742355i	−0.228986	−	0.742355i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0			−	1.00000i	$-0.5\pi$
$709$		0			0				1.00000i	$0.5\pi$
$710$	2.97537	+	1.08295i	2.97537	+	1.08295i
$711$	−0.172028	−	0.0993203i	−0.172028	−	0.0993203i
$712$	−0.583581	+	3.30965i	−0.583581	+	3.30965i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	5.50331	−	0.970382i	5.50331	−	0.970382i
$717$		0			0
$718$	−0.931294	−	2.55871i	−0.931294	−	2.55871i
$719$	−1.01965	+	0.371124i	−1.01965	+	0.371124i	−0.797133	−	0.603804i	$-0.793651\pi$
$719$	−1.01965	+	0.371124i	−1.01965	+	0.371124i	−0.222521	+	0.974928i	$0.571429\pi$
$720$	−6.45895	−	1.13889i	−6.45895	−	1.13889i
$721$		0			0
$722$	−0.496918	−	0.592203i	−0.496918	−	0.592203i
$723$		0			0
$724$		0			0
$725$	−1.04235	−	2.86384i	−1.04235	−	2.86384i
$726$	−0.0841972	+	0.0486113i	−0.0841972	+	0.0486113i
$727$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$727$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$728$		0			0
$729$	0.492557	−	0.853134i	0.492557	−	0.853134i
$730$	−3.15059	−	5.45698i	−3.15059	−	5.45698i
$731$		0			0
$732$		0			0
$733$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$733$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$734$			3.77912i			3.77912i
$735$	0.0276929	−	0.0760857i	0.0276929	−	0.0760857i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$739$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$740$	3.82212	+	2.46859i	3.82212	+	2.46859i
$741$		0			0
$742$		0			0
$743$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$743$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$744$		0			0
$745$		0			0
$746$		−	2.27643i		−	2.27643i
$747$	−1.37426	−	0.500190i	−1.37426	−	0.500190i
$748$		0			0
$749$		0			0
$750$	0.0502818	+	0.0870907i	0.0502818	+	0.0870907i
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$	−0.0957455	+	0.0168825i	−0.0957455	+	0.0168825i
$754$		0			0
$755$	−1.08877	−	2.99138i	−1.08877	−	2.99138i
$756$		0			0
$757$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$757$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$758$	−2.45698	−	2.92812i	−2.45698	−	2.92812i
$759$		0			0
$760$	−4.36511	−	0.769686i	−4.36511	−	0.769686i
$761$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$761$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$762$		0			0
$763$		0			0
$764$	5.23136	−	0.922431i	5.23136	−	0.922431i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.0350569	−	0.198818i	0.0350569	−	0.198818i
$769$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$769$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$773$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$774$	2.13323	−	1.78999i	2.13323	−	1.78999i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$			0.185428i			0.185428i
$784$	−3.80474	−	1.38481i	−3.80474	−	1.38481i
$785$	0.895787	+	0.517183i	0.895787	+	0.517183i
$786$	−0.00833177	+	0.0472518i	−0.00833177	+	0.0472518i
$787$	0.878222	+	1.52112i	0.878222	+	1.52112i	0.853291	+	0.521435i	$0.174603\pi$
$787$	0.878222	+	1.52112i	0.878222	+	1.52112i	0.0249307	+	0.999689i	$0.492063\pi$
$788$		0			0
$789$	0.0445934	+	0.0374183i	0.0445934	+	0.0374183i
$790$	0.620949	−	0.109490i	0.620949	−	0.109490i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	3.02586	+	3.60608i	3.02586	+	3.60608i
$797$	−1.75271	−	0.309049i	−1.75271	−	0.309049i	−0.797133	−	0.603804i	$-0.793651\pi$
$797$	−1.75271	−	0.309049i	−1.75271	−	0.309049i	−0.955573	+	0.294755i	$0.904762\pi$
$798$		0			0
$799$		0			0
$800$	6.21118	−	3.58602i	6.21118	−	3.58602i
$801$	0.939635	−	0.165683i	0.939635	−	0.165683i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		−	3.20581i		−	3.20581i
$809$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$809$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$810$	0.545729	+	3.09498i	0.545729	+	3.09498i
$811$	−0.630128	+	0.528741i	−0.630128	+	0.528741i	−0.900969	−	0.433884i	$-0.857143\pi$
$811$	−0.630128	+	0.528741i	−0.630128	+	0.528741i	0.270840	+	0.962624i	$0.412698\pi$
$812$		0			0
$813$	−0.0621761			−0.0621761
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.852049	−	0.714954i	0.852049	−	0.714954i
$818$	−0.100928	−	0.572392i	−0.100928	−	0.572392i
$819$		0			0
$820$		0			0
$821$	1.73181	+	0.630327i	1.73181	+	0.630327i	0.998757	−	0.0498459i	$-0.0158730\pi$
$821$	1.73181	+	0.630327i	1.73181	+	0.630327i	0.733052	+	0.680173i	$0.238095\pi$
$822$		0			0
$823$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$823$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$824$	3.51243	+	6.08370i	3.51243	+	6.08370i
$825$		0			0
$826$		0			0
$827$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$827$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$828$		0			0
$829$	−0.608708	−	1.67241i	−0.608708	−	1.67241i	−0.733052	−	0.680173i	$-0.761905\pi$
$829$	−0.608708	−	1.67241i	−0.608708	−	1.67241i	0.124344	−	0.992239i	$-0.460317\pi$
$830$	4.36220	−	1.58771i	4.36220	−	1.58771i
$831$	−0.0667982	−	0.0117783i	−0.0667982	−	0.0117783i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.71919	+	0.625734i	−1.71919	+	0.625734i
$836$		0			0
$837$		0			0
$838$	3.79757	−	0.669614i	3.79757	−	0.669614i
$839$	−1.12310	−	0.942393i	−1.12310	−	0.942393i	−0.124344	−	0.992239i	$-0.539683\pi$
$839$	−1.12310	−	0.942393i	−1.12310	−	0.942393i	−0.998757	+	0.0498459i	$0.984127\pi$
$840$		0			0
$841$	1.23305	+	2.13571i	1.23305	+	2.13571i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	1.62388i		−	1.62388i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	0.139708			0.139708
$853$	−0.670344	+	0.798885i	−0.670344	+	0.798885i	−0.988831	−	0.149042i	$-0.952381\pi$
$853$	−0.670344	+	0.798885i	−0.670344	+	0.798885i	0.318487	+	0.947927i	$0.396825\pi$
$854$		0			0
$855$	0.218519	+	1.23929i	0.218519	+	1.23929i
$856$	−1.20169	+	3.30163i	−1.20169	+	3.30163i
$857$		−	1.04287i		−	1.04287i	−0.853291	−	0.521435i	$-0.825397\pi$
$857$		−	1.04287i		−	1.04287i	0.853291	−	0.521435i	$-0.174603\pi$
$858$		0			0
$859$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$859$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$860$	−1.13121	+	6.41542i	−1.13121	+	6.41542i
$861$		0			0
$862$	−1.73512	+	3.00532i	−1.73512	+	3.00532i
$863$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$863$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$864$	−0.429741	+	0.0757750i	−0.429741	+	0.0757750i
$865$		0			0
$866$		0			0
$867$	0.0468544	−	0.0170536i	0.0468544	−	0.0170536i
$868$		0			0
$869$		0			0
$870$	−0.188933	−	0.225162i	−0.188933	−	0.225162i
$871$		0			0
$872$	6.60120	−	2.40264i	6.60120	−	2.40264i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−0.212982	−	0.178713i	−0.212982	−	0.178713i
$877$	0.0747301	−	0.129436i	0.0747301	−	0.129436i	−0.826239	−	0.563320i	$-0.809524\pi$
$877$	0.0747301	−	0.129436i	0.0747301	−	0.129436i	0.900969	+	0.433884i	$0.142857\pi$
$878$		0			0
$879$	−0.0162724	+	0.0922851i	−0.0162724	+	0.0922851i
$880$		0			0
$881$	−1.69327	−	0.616299i	−1.69327	−	0.616299i	−0.698237	−	0.715867i	$-0.746032\pi$
$881$	−1.69327	−	0.616299i	−1.69327	−	0.616299i	−0.995031	+	0.0995678i	$0.968254\pi$
$882$			1.94501i			1.94501i
$883$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$883$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$	0.170797	+	0.0389832i	0.170797	+	0.0389832i
$889$		0			0
$890$	−1.94676	+	2.32005i	−1.94676	+	2.32005i
$891$		0			0
$892$	−0.775692	−	4.39917i	−0.775692	−	4.39917i
$893$		0			0
$894$		0			0
$895$	3.04335	+	1.10769i	3.04335	+	1.10769i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−3.50488	−	2.94094i	−3.50488	−	2.94094i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−0.122509	−	0.146000i	−0.122509	−	0.146000i
$907$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$907$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$908$		0			0
$909$	−0.855264	+	0.311291i	−0.855264	+	0.311291i
$910$		0			0
$911$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$911$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$912$	−0.154455	+	0.0272346i	−0.154455	+	0.0272346i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.804015	−	4.55980i	0.804015	−	4.55980i
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.746805	+	1.45670i	0.746805	+	1.45670i
$926$	1.14946			1.14946
$927$	1.28198	−	1.52780i	1.28198	−	1.52780i
$928$	−6.24851	+	5.24312i	−6.24851	+	5.24312i
$929$	−0.0772807	−	0.438281i	−0.0772807	−	0.438281i	−0.998757	−	0.0498459i	$-0.984127\pi$
$929$	−0.0772807	−	0.438281i	−0.0772807	−	0.438281i	0.921476	−	0.388435i	$-0.126984\pi$
$930$		0			0
$931$			0.776870i			0.776870i
$932$	−5.03197	−	1.83149i	−5.03197	−	1.83149i
$933$	0.0856922	+	0.0494744i	0.0856922	+	0.0494744i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$937$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$938$		0			0
$939$	0.0856922	−	0.0494744i	0.0856922	−	0.0494744i
$940$		0			0
$941$	−1.87705	+	0.683190i	−1.87705	+	0.683190i	−0.921476	+	0.388435i	$0.873016\pi$
$941$	−1.87705	+	0.683190i	−1.87705	+	0.683190i	−0.955573	+	0.294755i	$0.904762\pi$
$942$	0.0609873	+	0.0107537i	0.0609873	+	0.0107537i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.489682	−	1.34539i	−0.489682	−	1.34539i	−0.900969	−	0.433884i	$-0.857143\pi$
$947$	−0.489682	−	1.34539i	−0.489682	−	1.34539i	0.411287	−	0.911506i	$-0.365079\pi$
$948$	0.0240936	−	0.0139105i	0.0240936	−	0.0139105i
$949$		0			0
$950$	−1.89953	−	1.59390i	−1.89953	−	1.59390i
$951$		0			0
$952$		0			0
$953$	0.142839	−	0.810077i	0.142839	−	0.810077i	−0.826239	−	0.563320i	$-0.809524\pi$
$953$	0.142839	−	0.810077i	0.142839	−	0.810077i	0.969077	−	0.246757i	$-0.0793651\pi$
$954$		0			0
$955$	2.89297	+	1.05295i	2.89297	+	1.05295i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.233891	−	0.278741i	0.233891	−	0.278741i
$961$	−1.00000			−1.00000
$962$		0			0
$963$	0.997514			0.997514
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$967$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$968$			3.51352i			3.51352i
$969$		0			0
$970$		0			0
$971$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	0.500000	+	0.866025i	$0.333333\pi$
$971$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	−0.766044	+	0.642788i	$0.777778\pi$
$972$	0.208868	+	0.361771i	0.208868	+	0.361771i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.512881	+	1.40913i	0.512881	+	1.40913i	0.878222	+	0.478254i	$0.158730\pi$
$977$	0.512881	+	1.40913i	0.512881	+	1.40913i	−0.365341	+	0.930874i	$0.619048\pi$
$978$		0			0
$979$		0			0
$980$	−2.92468	−	3.48550i	−2.92468	−	3.48550i
$981$	−1.28198	−	1.52780i	−1.28198	−	1.52780i
$982$		0			0
$983$	0.418203	−	0.152213i	0.418203	−	0.152213i	−0.124344	−	0.992239i	$-0.539683\pi$
$983$	0.418203	−	0.152213i	0.418203	−	0.152213i	0.542546	+	0.840026i	$0.317460\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$991$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.473746	+	2.68675i	0.473746	+	2.68675i
$996$	0.156907	−	0.131660i	0.156907	−	0.131660i
$997$	−1.23753	+	1.47483i	−1.23753	+	1.47483i	−0.411287	+	0.911506i	$0.634921\pi$
$997$	−1.23753	+	1.47483i	−1.23753	+	1.47483i	−0.826239	+	0.563320i	$0.809524\pi$
$998$	−2.03345			−2.03345
$999$	−0.0123845	−	0.0988258i	−0.0123845	−	0.0988258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2627.1.x.b.780.6	✓	36
37.25	even	18	inner	2627.1.x.b.1135.6	yes	36
71.70	odd	2	CM	2627.1.x.b.780.6	✓	36
2627.1135	odd	18	inner	2627.1.x.b.1135.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2627.1.x.b.780.6	✓	36	1.1	even	1	trivial
2627.1.x.b.780.6	✓	36	71.70	odd	2	CM
2627.1.x.b.1135.6	yes	36	37.25	even	18	inner
2627.1.x.b.1135.6	yes	36	2627.1135	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2627 = 37 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2627.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25334 - 1.49368i) q^{2} +(0.0381960 - 0.0320503i) q^{3} +(-0.486551 - 2.75937i) q^{4} +(0.555398 - 1.52594i) q^{5} -0.0972225i q^{6} +(-3.04280 - 1.75676i) q^{8} +(-0.173216 + 0.982359i) q^{9} +O(q^{10})\)	\(q+(1.25334 - 1.49368i) q^{2} +(0.0381960 - 0.0320503i) q^{3} +(-0.486551 - 2.75937i) q^{4} +(0.555398 - 1.52594i) q^{5} -0.0972225i q^{6} +(-3.04280 - 1.75676i) q^{8} +(-0.173216 + 0.982359i) q^{9} +(-1.58316 - 2.74212i) q^{10} +(-0.107023 - 0.0898029i) q^{12} +(-0.0276929 - 0.0760857i) q^{15} +(-3.80474 + 1.38481i) q^{16} +(1.25023 + 1.48996i) q^{18} +(0.499362 + 0.595117i) q^{19} +(-4.48087 - 0.790099i) q^{20} +(-0.172527 + 0.0304212i) q^{24} +(-1.25399 - 1.05223i) q^{25} +(0.0497994 + 0.0862551i) q^{27} +(1.61232 + 0.930874i) q^{29} +(-0.148356 - 0.0539972i) q^{30} +(-1.49849 + 4.11706i) q^{32} +2.79497 q^{36} +(-0.921476 - 0.388435i) q^{37} +1.51478 q^{38} +(-4.37068 + 3.66744i) q^{40} -1.43173i q^{43} +(1.40282 + 0.809919i) q^{45} +(-0.100942 + 0.174837i) q^{48} +(0.766044 + 0.642788i) q^{49} +(-3.14337 + 0.554261i) q^{50} +(0.191253 + 0.0337231i) q^{54} +(0.0381473 + 0.00672640i) q^{57} +(3.41122 - 1.24158i) q^{58} +(-0.196475 + 0.113435i) q^{60} +(2.24698 + 3.89188i) q^{64} +(-0.766044 + 0.642788i) q^{71} +(2.25283 - 2.68482i) q^{72} +1.99006 q^{73} +(-1.73512 + 0.889545i) q^{74} -0.0816218 q^{75} +(1.39918 - 1.66748i) q^{76} +(-0.0681084 + 0.187126i) q^{79} +6.57494i q^{80} +(-0.932690 - 0.339471i) q^{81} +(-0.254586 + 1.44383i) q^{83} +(-2.13855 - 1.79445i) q^{86} +(0.0914190 - 0.0161196i) q^{87} +(-0.327145 - 0.898823i) q^{89} +(2.96797 - 1.08025i) q^{90} +(1.18546 - 0.431472i) q^{95} +(0.0747167 + 0.205282i) q^{96} +(1.92023 - 0.338589i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{3} + 3 q^{5} - 6 q^{9}+O(q^{10}) \) 36 * q + 6 * q^3 + 3 * q^5 - 6 * q^9	\( 36 q + 6 q^{3} + 3 q^{5} - 6 q^{9} + 6 q^{12} - 3 q^{15} + 21 q^{18} + 3 q^{19} - 36 q^{20} - 21 q^{24} + 3 q^{25} + 3 q^{27} - 9 q^{29} - 21 q^{30} - 48 q^{36} - 3 q^{57} + 54 q^{60} + 24 q^{64} + 21 q^{72} - 6 q^{75} - 3 q^{76} + 6 q^{79} - 3 q^{81} - 12 q^{87} + 3 q^{89} + 42 q^{90} - 6 q^{95} - 21 q^{96}+O(q^{100}) \) 36 * q + 6 * q^3 + 3 * q^5 - 6 * q^9 + 6 * q^12 - 3 * q^15 + 21 * q^18 + 3 * q^19 - 36 * q^20 - 21 * q^24 + 3 * q^25 + 3 * q^27 - 9 * q^29 - 21 * q^30 - 48 * q^36 - 3 * q^57 + 54 * q^60 + 24 * q^64 + 21 * q^72 - 6 * q^75 - 3 * q^76 + 6 * q^79 - 3 * q^81 - 12 * q^87 + 3 * q^89 + 42 * q^90 - 6 * q^95 - 21 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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