LMFDB - Embedded newform 2627.1.x.b.354.3

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			354.3
Root			$-0.411287 + 0.911506i$ of defining polynomial
Character	$\chi$	$=$	2627.354
Dual form			2627.1.x.b.141.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.296794 + 0.815435i) q^{2} +(-0.233690 + 0.0850561i) q^{3} +(0.189197 + 0.158755i) q^{4} +(-1.96900 - 0.347188i) q^{5} -0.215803i q^{6} +(-0.937116 + 0.541044i) q^{8} +(-0.718668 + 0.603034i) q^{9} +O(q^{10})$	\(q+(-0.296794 + 0.815435i) q^{2} +(-0.233690 + 0.0850561i) q^{3} +(0.189197 + 0.158755i) q^{4} +(-1.96900 - 0.347188i) q^{5} -0.215803i q^{6} +(-0.937116 + 0.541044i) q^{8} +(-0.718668 + 0.603034i) q^{9} +(0.867498 - 1.50255i) q^{10} +(-0.0577166 - 0.0210071i) q^{12} +(0.489666 - 0.0863414i) q^{15} +(-0.120168 - 0.681508i) q^{16} +(-0.278439 - 0.765004i) q^{18} +(-0.623507 - 1.71307i) q^{19} +(-0.317412 - 0.378277i) q^{20} +(0.172975 - 0.206144i) q^{24} +(2.81674 + 1.02521i) q^{25} +(0.240997 - 0.417420i) q^{27} +(0.510531 - 0.294755i) q^{29} +(-0.0749242 + 0.424917i) q^{30} +(-0.474258 - 0.0836246i) q^{32} -0.231705 q^{36} +(0.411287 - 0.911506i) q^{37} +1.58195 q^{38} +(2.03303 - 0.739962i) q^{40} +1.49956i q^{43} +(1.62443 - 0.937863i) q^{45} +(0.0860485 + 0.149040i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(-1.67198 + 1.99259i) q^{50} +(0.268852 + 0.320405i) q^{54} +(0.291414 + 0.347294i) q^{57} +(0.0888311 + 0.503786i) q^{58} +(0.106351 + 0.0614016i) q^{60} +(0.554958 - 0.961216i) q^{64} +(0.939693 - 0.342020i) q^{71} +(0.347207 - 0.953944i) q^{72} +1.75644 q^{73} +(0.621206 + 0.605907i) q^{74} -0.745444 q^{75} +(0.153993 - 0.423094i) q^{76} +(-0.941976 - 0.166096i) q^{79} +1.38361i q^{80} +(0.142094 - 0.805857i) q^{81} +(1.26587 - 1.06219i) q^{83} +(-1.22280 - 0.445061i) q^{86} +(-0.0942351 + 0.112305i) q^{87} +(-1.18926 + 0.209699i) q^{89} +(0.282646 + 1.60297i) q^{90} +(0.632929 + 3.58952i) q^{95} +(0.117942 - 0.0207964i) q^{96} +(0.557790 - 0.664748i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2627\mathbb{Z}\right)^\times$.

$n$	$149$	$853$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.296794	+	0.815435i	−0.296794	+	0.815435i	0.698237	+	0.715867i	$0.253968\pi$
$2$	−0.296794	+	0.815435i	−0.296794	+	0.815435i	−0.995031	+	0.0995678i	$0.968254\pi$
$3$	−0.233690	+	0.0850561i	−0.233690	+	0.0850561i	−0.456211	−	0.889872i	$-0.650794\pi$
$3$	−0.233690	+	0.0850561i	−0.233690	+	0.0850561i	0.222521	+	0.974928i	$0.428571\pi$
$4$	0.189197	+	0.158755i	0.189197	+	0.158755i
$5$	−1.96900	−	0.347188i	−1.96900	−	0.347188i	−0.988831	−	0.149042i	$-0.952381\pi$
$5$	−1.96900	−	0.347188i	−1.96900	−	0.347188i	−0.980172	−	0.198146i	$-0.936508\pi$
$6$		−	0.215803i		−	0.215803i
$7$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$7$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$8$	−0.937116	+	0.541044i	−0.937116	+	0.541044i
$9$	−0.718668	+	0.603034i	−0.718668	+	0.603034i
$10$	0.867498	−	1.50255i	0.867498	−	1.50255i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	−0.0577166	−	0.0210071i	−0.0577166	−	0.0210071i
$13$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$13$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$14$		0			0
$15$	0.489666	−	0.0863414i	0.489666	−	0.0863414i
$16$	−0.120168	−	0.681508i	−0.120168	−	0.681508i
$17$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$17$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$18$	−0.278439	−	0.765004i	−0.278439	−	0.765004i
$19$	−0.623507	−	1.71307i	−0.623507	−	1.71307i	−0.698237	−	0.715867i	$-0.746032\pi$
$19$	−0.623507	−	1.71307i	−0.623507	−	1.71307i	0.0747301	−	0.997204i	$-0.476190\pi$
$20$	−0.317412	−	0.378277i	−0.317412	−	0.378277i
$21$		0			0
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	0.172975	−	0.206144i	0.172975	−	0.206144i
$25$	2.81674	+	1.02521i	2.81674	+	1.02521i
$26$		0			0
$27$	0.240997	−	0.417420i	0.240997	−	0.417420i
$28$		0			0
$29$	0.510531	−	0.294755i	0.510531	−	0.294755i	−0.222521	−	0.974928i	$-0.571429\pi$
$29$	0.510531	−	0.294755i	0.510531	−	0.294755i	0.733052	+	0.680173i	$0.238095\pi$
$30$	−0.0749242	+	0.424917i	−0.0749242	+	0.424917i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−0.474258	−	0.0836246i	−0.474258	−	0.0836246i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.231705			−0.231705
$37$	0.411287	−	0.911506i	0.411287	−	0.911506i
$37$	0.411287	−	0.911506i	0.411287	−	0.911506i
$38$	1.58195			1.58195
$39$		0			0
$40$	2.03303	−	0.739962i	2.03303	−	0.739962i
$41$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$41$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$42$		0			0
$43$			1.49956i			1.49956i	0.661686	+	0.749781i	$0.269841\pi$
$43$			1.49956i			1.49956i	−0.661686	+	0.749781i	$0.730159\pi$
$44$		0			0
$45$	1.62443	−	0.937863i	1.62443	−	0.937863i
$46$		0			0
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	0.0860485	+	0.149040i	0.0860485	+	0.149040i
$49$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$50$	−1.67198	+	1.99259i	−1.67198	+	1.99259i
$51$		0			0
$52$		0			0
$53$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$53$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$54$	0.268852	+	0.320405i	0.268852	+	0.320405i
$55$		0			0
$56$		0			0
$57$	0.291414	+	0.347294i	0.291414	+	0.347294i
$58$	0.0888311	+	0.503786i	0.0888311	+	0.503786i
$59$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$59$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$60$	0.106351	+	0.0614016i	0.106351	+	0.0614016i
$61$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$61$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$62$		0			0
$63$		0			0
$64$	0.554958	−	0.961216i	0.554958	−	0.961216i
$65$		0			0
$66$		0			0
$67$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$67$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.939693	−	0.342020i	0.939693	−	0.342020i
$71$	0.939693	−	0.342020i	0.939693	−	0.342020i
$72$	0.347207	−	0.953944i	0.347207	−	0.953944i
$73$	1.75644			1.75644			0.878222	−	0.478254i	$-0.158730\pi$
$73$	1.75644			1.75644			0.878222	+	0.478254i	$0.158730\pi$
$74$	0.621206	+	0.605907i	0.621206	+	0.605907i
$75$	−0.745444			−0.745444
$76$	0.153993	−	0.423094i	0.153993	−	0.423094i
$77$		0			0
$78$		0			0
$79$	−0.941976	−	0.166096i	−0.941976	−	0.166096i	−0.318487	−	0.947927i	$-0.603175\pi$
$79$	−0.941976	−	0.166096i	−0.941976	−	0.166096i	−0.623490	+	0.781831i	$0.714286\pi$
$80$			1.38361i			1.38361i
$81$	0.142094	−	0.805857i	0.142094	−	0.805857i
$82$		0			0
$83$	1.26587	−	1.06219i	1.26587	−	1.06219i	0.270840	−	0.962624i	$-0.412698\pi$
$83$	1.26587	−	1.06219i	1.26587	−	1.06219i	0.995031	−	0.0995678i	$-0.0317460\pi$
$84$		0			0
$85$		0			0
$86$	−1.22280	−	0.445061i	−1.22280	−	0.445061i
$87$	−0.0942351	+	0.112305i	−0.0942351	+	0.112305i
$88$		0			0
$89$	−1.18926	+	0.209699i	−1.18926	+	0.209699i	−0.733052	−	0.680173i	$-0.761905\pi$
$89$	−1.18926	+	0.209699i	−1.18926	+	0.209699i	−0.456211	+	0.889872i	$0.650794\pi$
$90$	0.282646	+	1.60297i	0.282646	+	1.60297i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.632929	+	3.58952i	0.632929	+	3.58952i
$96$	0.117942	−	0.0207964i	0.117942	−	0.0207964i
$97$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$97$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$98$	0.557790	−	0.664748i	0.557790	−	0.664748i
$99$		0			0
$100$	0.370162	+	0.641140i	0.370162	+	0.641140i
$101$	0.698237	−	1.20938i	0.698237	−	1.20938i	−0.270840	−	0.962624i	$-0.587302\pi$
$101$	0.698237	−	1.20938i	0.698237	−	1.20938i	0.969077	−	0.246757i	$-0.0793651\pi$
$102$		0			0
$103$	1.71861	−	0.992239i	1.71861	−	0.992239i	0.797133	−	0.603804i	$-0.206349\pi$
$103$	1.71861	−	0.992239i	1.71861	−	0.992239i	0.921476	−	0.388435i	$-0.126984\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$107$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$108$	0.111864	−	0.0407151i	0.111864	−	0.0407151i
$109$	0.678732	−	1.86480i	0.678732	−	1.86480i	0.222521	−	0.974928i	$-0.428571\pi$
$109$	0.678732	−	1.86480i	0.678732	−	1.86480i	0.456211	−	0.889872i	$-0.349206\pi$
$110$		0			0
$111$	−0.0185844	+	0.247992i	−0.0185844	+	0.247992i
$112$		0			0
$113$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$113$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$114$	−0.369686	+	0.134555i	−0.369686	+	0.134555i
$115$		0			0
$116$	0.143385	+	0.0252827i	0.143385	+	0.0252827i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.412160	+	0.345843i	−0.412160	+	0.345843i
$121$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.45872	−	1.99689i	−3.45872	−	1.99689i
$126$		0			0
$127$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$127$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$128$	0.309550	+	0.368908i	0.309550	+	0.368908i
$129$	−0.127547	−	0.350432i	−0.127547	−	0.350432i
$130$		0			0
$131$	−1.21863	−	1.45231i	−1.21863	−	1.45231i	−0.853291	−	0.521435i	$-0.825397\pi$
$131$	−1.21863	−	1.45231i	−1.21863	−	1.45231i	−0.365341	−	0.930874i	$-0.619048\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.619448	+	0.738229i	−0.619448	+	0.738229i
$136$		0			0
$137$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$137$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$138$		0			0
$139$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$139$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$140$		0			0
$141$		0			0
$142$			0.867767i			0.867767i
$143$		0			0
$144$	0.497334	+	0.417313i	0.497334	+	0.417313i
$145$	−1.10757	+	0.403123i	−1.10757	+	0.403123i
$146$	−0.521302	+	1.43226i	−0.521302	+	1.43226i
$147$	0.248687			0.248687
$148$	0.222521	−	0.107160i	0.222521	−	0.107160i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	0.221243	−	0.607861i	0.221243	−	0.607861i
$151$	−1.01965	+	0.371124i	−1.01965	+	0.371124i	−0.797133	−	0.603804i	$-0.793651\pi$
$151$	−1.01965	+	0.371124i	−1.01965	+	0.371124i	−0.222521	+	0.974928i	$0.571429\pi$
$152$	1.51115	+	1.26800i	1.51115	+	1.26800i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.53018	+	1.28398i	−1.53018	+	1.28398i	−0.733052	+	0.680173i	$0.761905\pi$
$157$	−1.53018	+	1.28398i	−1.53018	+	1.28398i	−0.797133	+	0.603804i	$0.793651\pi$
$158$	0.415013	−	0.718824i	0.415013	−	0.718824i
$159$		0			0
$160$	0.904783	+	0.329314i	0.904783	+	0.329314i
$161$		0			0
$162$	0.614951	+	0.355042i	0.614951	+	0.355042i
$163$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$163$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$164$		0			0
$165$		0			0
$166$	0.490445	+	1.34749i	0.490445	+	1.34749i
$167$	0.101951	+	0.280108i	0.101951	+	0.280108i	0.980172	−	0.198146i	$-0.0634921\pi$
$167$	0.101951	+	0.280108i	0.101951	+	0.280108i	−0.878222	+	0.478254i	$0.841270\pi$
$168$		0			0
$169$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$170$		0			0
$171$	1.48113	+	0.855133i	1.48113	+	0.855133i
$172$	−0.238064	+	0.283713i	−0.238064	+	0.283713i
$173$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$173$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$174$	−0.0636090	−	0.110174i	−0.0636090	−	0.110174i
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.181970	−	1.03200i	0.181970	−	1.03200i
$179$			1.86175i			1.86175i	0.365341	+	0.930874i	$0.380952\pi$
$179$			1.86175i			1.86175i	−0.365341	+	0.930874i	$0.619048\pi$
$180$	0.456228	+	0.0804453i	0.456228	+	0.0804453i
$181$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$181$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.12629	+	1.65196i	−1.12629	+	1.65196i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−3.11487	−	0.549235i	−3.11487	−	0.549235i
$191$		−	0.0996918i		−	0.0996918i	−0.998757	−	0.0498459i	$-0.984127\pi$
$191$		−	0.0996918i		−	0.0996918i	0.998757	−	0.0498459i	$-0.0158730\pi$
$192$	−0.0479308	+	0.271829i	−0.0479308	+	0.271829i
$193$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$193$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$194$		0			0
$195$		0			0
$196$	−0.123490	−	0.213891i	−0.123490	−	0.213891i
$197$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$197$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$198$		0			0
$199$	−1.66731	−	0.962624i	−1.66731	−	0.962624i	−0.969077	−	0.246757i	$-0.920635\pi$
$199$	−1.66731	−	0.962624i	−1.66731	−	0.962624i	−0.698237	−	0.715867i	$-0.746032\pi$
$200$	−3.19430	+	0.563241i	−3.19430	+	0.563241i
$201$		0			0
$202$	0.778939	+	0.928304i	0.778939	+	0.928304i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	0.299034	+	1.69590i	0.299034	+	1.69590i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$		0			0
$213$	−0.190506	+	0.159853i	−0.190506	+	0.159853i
$214$	0.751509	−	0.433884i	0.751509	−	0.433884i
$215$	0.520631	−	2.95264i	0.520631	−	2.95264i
$216$			0.521561i			0.521561i
$217$		0			0
$218$	1.31918	+	1.10692i	1.31918	+	1.10692i
$219$	−0.410463	+	0.149396i	−0.410463	+	0.149396i
$220$		0			0
$221$		0			0
$222$	−0.196706	−	0.0887569i	−0.196706	−	0.0887569i
$223$	−1.99006			−1.99006			−0.995031	−	0.0995678i	$-0.968254\pi$
$223$	−1.99006			−1.99006			−0.995031	+	0.0995678i	$0.968254\pi$
$224$		0			0
$225$	−2.64254	+	0.961806i	−2.64254	+	0.961806i
$226$		0			0
$227$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$227$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$228$			0.111971i			0.111971i
$229$	0.343417	−	1.94762i	0.343417	−	1.94762i	0.0249307	−	0.999689i	$-0.492063\pi$
$229$	0.343417	−	1.94762i	0.343417	−	1.94762i	0.318487	−	0.947927i	$-0.396825\pi$
$230$		0			0
$231$		0			0
$232$	−0.318951	+	0.552440i	−0.318951	+	0.552440i
$233$	0.0747301	+	0.129436i	0.0747301	+	0.129436i	0.900969	−	0.433884i	$-0.142857\pi$
$233$	0.0747301	+	0.129436i	0.0747301	+	0.129436i	−0.826239	+	0.563320i	$0.809524\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.234258	−	0.0413060i	0.234258	−	0.0413060i
$238$		0			0
$239$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$239$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$240$	−0.117685	−	0.323336i	−0.117685	−	0.323336i
$241$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$241$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$242$	−0.557790	−	0.664748i	−0.557790	−	0.664748i
$243$	0.119035	+	0.675079i	0.119035	+	0.675079i
$244$		0			0
$245$	1.73151	+	0.999689i	1.73151	+	0.999689i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−0.205475	+	0.355893i	−0.205475	+	0.355893i
$250$	2.65486	−	2.22769i	2.65486	−	2.22769i
$251$	0.751509	−	0.433884i	0.751509	−	0.433884i	−0.0747301	−	0.997204i	$-0.523810\pi$
$251$	0.751509	−	0.433884i	0.751509	−	0.433884i	0.826239	+	0.563320i	$0.190476\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.650287	−	0.236685i	0.650287	−	0.236685i
$257$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$257$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$258$	0.323610			0.323610
$259$		0			0
$260$		0			0
$261$	−0.189155	+	0.519699i	−0.189155	+	0.519699i
$262$	1.54595	−	0.562678i	1.54595	−	0.562678i
$263$	0.0381960	+	0.0320503i	0.0381960	+	0.0320503i	0.661686	−	0.749781i	$-0.269841\pi$
$263$	0.0381960	+	0.0320503i	0.0381960	+	0.0320503i	−0.623490	+	0.781831i	$0.714286\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.260082	−	0.150159i	0.260082	−	0.150159i
$268$		0			0
$269$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$269$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$270$	−0.418129	−	0.724221i	−0.418129	−	0.724221i
$271$	−0.418203	−	0.152213i	−0.418203	−	0.152213i	0.124344	−	0.992239i	$-0.460317\pi$
$271$	−0.418203	−	0.152213i	−0.418203	−	0.152213i	−0.542546	+	0.840026i	$0.682540\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.385334	−	1.05870i	−0.385334	−	1.05870i	−0.969077	−	0.246757i	$-0.920635\pi$
$277$	−0.385334	−	1.05870i	−0.385334	−	1.05870i	0.583744	−	0.811938i	$-0.301587\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$281$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$282$		0			0
$283$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$283$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$284$	0.232085	+	0.0844720i	0.232085	+	0.0844720i
$285$	−0.453219	−	0.784999i	−0.453219	−	0.784999i
$286$		0			0
$287$		0			0
$288$	0.391263	−	0.225896i	0.391263	−	0.225896i
$289$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$290$		−	1.02280i		−	1.02280i
$291$		0			0
$292$	0.332314	+	0.278845i	0.332314	+	0.278845i
$293$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	−0.500000	−	0.866025i	$-0.666667\pi$
$293$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$294$	−0.0738089	+	0.202788i	−0.0738089	+	0.202788i
$295$		0			0
$296$	0.107741	+	1.07671i	0.107741	+	1.07671i
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−0.141036	−	0.118343i	−0.141036	−	0.118343i
$301$		0			0
$302$		−	0.941608i		−	0.941608i
$303$	−0.0603055	+	0.342009i	−0.0603055	+	0.342009i
$304$	−1.09255	+	0.630782i	−1.09255	+	0.630782i
$305$		0			0
$306$		0			0
$307$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$307$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$308$		0			0
$309$	−0.317225	+	0.378054i	−0.317225	+	0.378054i
$310$		0			0
$311$	1.59921	−	0.281983i	1.59921	−	0.281983i	0.698237	−	0.715867i	$-0.253968\pi$
$311$	1.59921	−	0.281983i	1.59921	−	0.281983i	0.900969	+	0.433884i	$0.142857\pi$
$312$		0			0
$313$	1.04381	+	1.24396i	1.04381	+	1.24396i	0.969077	+	0.246757i	$0.0793651\pi$
$313$	1.04381	+	1.24396i	1.04381	+	1.24396i	0.0747301	+	0.997204i	$0.476190\pi$
$314$	−0.592850	−	1.62884i	−0.592850	−	1.62884i
$315$		0			0
$316$	−0.151851	−	0.180969i	−0.151851	−	0.180969i
$317$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$317$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$318$		0			0
$319$		0			0
$320$	−1.42644	+	1.69996i	−1.42644	+	1.69996i
$321$	0.233690	+	0.0850561i	0.233690	+	0.0850561i
$322$		0			0
$323$		0			0
$324$	0.154818	−	0.129908i	0.154818	−	0.129908i
$325$		0			0
$326$		0			0
$327$			0.493515i			0.493515i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$331$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$332$	0.408128			0.408128
$333$	0.254090	+	0.903090i	0.254090	+	0.903090i
$334$	−0.258668			−0.258668
$335$		0			0
$336$		0			0
$337$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$337$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$338$	0.854584	+	0.150686i	0.854584	+	0.150686i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−1.13690	+	0.953970i	−1.13690	+	0.953970i
$343$		0			0
$344$	−0.811330	−	1.40526i	−0.811330	−	1.40526i
$345$		0			0
$346$		0			0
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$	−0.0356581	+	0.00628748i	−0.0356581	+	0.00628748i
$349$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$349$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$353$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$354$		0			0
$355$	−1.96900	+	0.347188i	−1.96900	+	0.347188i
$356$	−0.258296	−	0.149127i	−0.258296	−	0.149127i
$357$		0			0
$358$	−1.51813	−	0.552555i	−1.51813	−	0.552555i
$359$	−0.661686	−	1.14607i	−0.661686	−	1.14607i	−0.980172	−	0.198146i	$-0.936508\pi$
$359$	−0.661686	−	1.14607i	−0.661686	−	1.14607i	0.318487	−	0.947927i	$-0.396825\pi$
$360$	−1.01485	+	1.75777i	−1.01485	+	1.75777i
$361$	−1.77981	+	1.49343i	−1.77981	+	1.49343i
$362$		0			0
$363$	0.0431841	−	0.244909i	0.0431841	−	0.244909i
$364$		0			0
$365$	−3.45844	−	0.609817i	−3.45844	−	0.609817i
$366$		0			0
$367$	0.598559	−	0.217858i	0.598559	−	0.217858i	−0.0249307	−	0.999689i	$-0.507937\pi$
$367$	0.598559	−	0.217858i	0.598559	−	0.217858i	0.623490	+	0.781831i	$0.285714\pi$
$368$		0			0
$369$		0			0
$370$	−1.01279	−	1.40871i	−1.01279	−	1.40871i
$371$		0			0
$372$		0			0
$373$	−0.0468544	+	0.0170536i	−0.0468544	+	0.0170536i	−0.365341	−	0.930874i	$-0.619048\pi$
$373$	−0.0468544	+	0.0170536i	−0.0468544	+	0.0170536i	0.318487	+	0.947927i	$0.396825\pi$
$374$		0			0
$375$	0.978115	+	0.172468i	0.978115	+	0.172468i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.831229	−	0.697484i	0.831229	−	0.697484i	−0.124344	−	0.992239i	$-0.539683\pi$
$379$	0.831229	−	0.697484i	0.831229	−	0.697484i	0.955573	+	0.294755i	$0.0952381\pi$
$380$	−0.450107	+	0.779608i	−0.450107	+	0.779608i
$381$		0			0
$382$	0.0812921	+	0.0295879i	0.0812921	+	0.0295879i
$383$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$383$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$384$	−0.103717	−	0.0598808i	−0.103717	−	0.0598808i
$385$		0			0
$386$		0			0
$387$	−0.904287	−	1.07769i	−0.904287	−	1.07769i
$388$		0			0
$389$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$389$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$390$		0			0
$391$		0			0
$392$	1.06565	−	0.187903i	1.06565	−	0.187903i
$393$	0.408309	+	0.235738i	0.408309	+	0.235738i
$394$		0			0
$395$	1.79709	+	0.654087i	1.79709	+	0.654087i
$396$		0			0
$397$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$397$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$398$	1.27981	−	1.07388i	1.27981	−	1.07388i
$399$		0			0
$400$	0.360206	−	2.04283i	0.360206	−	2.04283i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$		0			0
$404$	0.324100	−	0.117963i	0.324100	−	0.117963i
$405$	−0.559568	+	1.53740i	−0.559568	+	1.53740i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.465266	+	1.27831i	−0.465266	+	1.27831i	0.456211	+	0.889872i	$0.349206\pi$
$409$	−0.465266	+	1.27831i	−0.465266	+	1.27831i	−0.921476	+	0.388435i	$0.873016\pi$
$410$		0			0
$411$		0			0
$412$	0.482680	+	0.0851094i	0.482680	+	0.0851094i
$413$		0			0
$414$		0			0
$415$	−2.86129	+	1.65196i	−2.86129	+	1.65196i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.37769	−	0.501437i	−1.37769	−	0.501437i	−0.456211	−	0.889872i	$-0.650794\pi$
$419$	−1.37769	−	0.501437i	−1.37769	−	0.501437i	−0.921476	+	0.388435i	$0.873016\pi$
$420$		0			0
$421$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$421$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−0.0738089	−	0.202788i	−0.0738089	−	0.202788i
$427$		0			0
$428$	−0.0428876	−	0.243227i	−0.0428876	−	0.243227i
$429$		0			0
$430$	2.25317	+	1.30087i	2.25317	+	1.30087i
$431$	0.920301	−	1.09677i	0.920301	−	1.09677i	−0.0747301	−	0.997204i	$-0.523810\pi$
$431$	0.920301	−	1.09677i	0.920301	−	1.09677i	0.995031	−	0.0995678i	$-0.0317460\pi$
$432$	−0.313435	−	0.114081i	−0.313435	−	0.114081i
$433$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$433$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$434$		0			0
$435$	0.224540	−	0.188412i	0.224540	−	0.188412i
$436$	0.424461	−	0.245063i	0.424461	−	0.245063i
$437$		0			0
$438$		−	0.379045i		−	0.379045i
$439$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$439$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$440$		0			0
$441$	0.881577	−	0.320868i	0.881577	−	0.320868i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	−0.0428862	+	0.0439691i	−0.0428862	+	0.0439691i
$445$	2.41447			2.41447
$446$	0.590638	−	1.62277i	0.590638	−	1.62277i
$447$		0			0
$448$		0			0
$449$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$449$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$450$		−	2.44028i		−	2.44028i
$451$		0			0
$452$		0			0
$453$	0.206716	−	0.173455i	0.206716	−	0.173455i
$454$		0			0
$455$		0			0
$456$	−0.460990	−	0.167787i	−0.460990	−	0.167787i
$457$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$457$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$458$	1.48623	+	0.858075i	1.48623	+	0.858075i
$459$		0			0
$460$		0			0
$461$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$461$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$462$		0			0
$463$	−0.682128	−	1.87413i	−0.682128	−	1.87413i	−0.411287	−	0.911506i	$-0.634921\pi$
$463$	−0.682128	−	1.87413i	−0.682128	−	1.87413i	−0.270840	−	0.962624i	$-0.587302\pi$
$464$	−0.262228	−	0.312511i	−0.262228	−	0.312511i
$465$		0			0
$466$	−0.127726	+	0.0225216i	−0.127726	+	0.0225216i
$467$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$467$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.248378	−	0.430204i	0.248378	−	0.430204i
$472$		0			0
$473$		0			0
$474$	−0.0358440	+	0.203281i	−0.0358440	+	0.203281i
$475$		−	5.46450i		−	5.46450i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$479$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$480$	−0.239449			−0.239449
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.232085	+	0.0844720i	−0.232085	+	0.0844720i
$485$		0			0
$486$	−0.585811	−	0.103294i	−0.585811	−	0.103294i
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$		0			0
$489$		0			0
$490$	−1.32908	+	1.11523i	−1.32908	+	1.11523i
$491$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$491$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.229224	−	0.273179i	−0.229224	−	0.273179i
$499$	0.265705	+	0.730019i	0.265705	+	0.730019i	0.998757	+	0.0498459i	$0.0158730\pi$
$499$	0.265705	+	0.730019i	0.265705	+	0.730019i	−0.733052	+	0.680173i	$0.761905\pi$
$500$	−0.337363	−	0.926897i	−0.337363	−	0.926897i
$501$	−0.0476498	−	0.0567868i	−0.0476498	−	0.0567868i
$502$	0.130761	+	0.741580i	0.130761	+	0.741580i
$503$	1.33968	−	0.236222i	1.33968	−	0.236222i	0.542546	−	0.840026i	$-0.317460\pi$
$503$	1.33968	−	0.236222i	1.33968	−	0.236222i	0.797133	+	0.603804i	$0.206349\pi$
$504$		0			0
$505$	−1.79471	+	2.13886i	−1.79471	+	2.13886i
$506$		0			0
$507$	0.124344	+	0.215370i	0.124344	+	0.215370i
$508$		0			0
$509$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.500000	−	0.866025i	$-0.333333\pi$
$509$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.939693	−	0.342020i	$-0.111111\pi$
$510$		0			0
$511$		0			0
$512$			1.08209i			1.08209i
$513$	−0.865333	−	0.152582i	−0.865333	−	0.152582i
$514$		0			0
$515$	−3.72844	+	1.35704i	−3.72844	+	1.35704i
$516$	0.0315015	−	0.0865496i	0.0315015	−	0.0865496i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.686617	+	0.249908i	−0.686617	+	0.249908i	−0.661686	−	0.749781i	$-0.730159\pi$
$521$	−0.686617	+	0.249908i	−0.686617	+	0.249908i	−0.0249307	+	0.999689i	$0.507937\pi$
$522$	−0.367640	−	0.308487i	−0.367640	−	0.308487i
$523$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$523$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$524$		−	0.468237i		−	0.468237i
$525$		0			0
$526$	−0.0374713	+	0.0216340i	−0.0374713	+	0.0216340i
$527$		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
$534$	0.0452537	+	0.256646i	0.0452537	+	0.256646i
$535$	1.28518	+	1.53161i	1.28518	+	1.53161i
$536$		0			0
$537$	−0.158353	−	0.435071i	−0.158353	−	0.435071i
$538$		0			0
$539$		0			0
$540$	−0.234396	+	0.0413303i	−0.234396	+	0.0413303i
$541$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$541$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$542$	0.248240	−	0.295841i	0.248240	−	0.295841i
$543$		0			0
$544$		0			0
$545$	−1.98386	+	3.43615i	−1.98386	+	3.43615i
$546$		0			0
$547$	−0.427396	+	0.246757i	−0.427396	+	0.246757i	−0.698237	−	0.715867i	$-0.746032\pi$
$547$	−0.427396	+	0.246757i	−0.427396	+	0.246757i	0.270840	+	0.962624i	$0.412698\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.823256	−	0.690794i	−0.823256	−	0.690794i
$552$		0			0
$553$		0			0
$554$	0.977662			0.977662
$555$	0.122693	−	0.481845i	0.122693	−	0.481845i
$556$		0			0
$557$	0.574612	−	1.57873i	0.574612	−	1.57873i	−0.222521	−	0.974928i	$-0.571429\pi$
$557$	0.574612	−	1.57873i	0.574612	−	1.57873i	0.797133	−	0.603804i	$-0.206349\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−0.695553	+	0.828928i	−0.695553	+	0.828928i
$569$	−1.35417	−	0.781831i	−1.35417	−	0.781831i	−0.365341	−	0.930874i	$-0.619048\pi$
$569$	−1.35417	−	0.781831i	−1.35417	−	0.781831i	−0.988831	+	0.149042i	$0.952381\pi$
$570$	0.774628	−	0.136588i	0.774628	−	0.136588i
$571$	−0.0940619	−	0.533452i	−0.0940619	−	0.533452i	−0.995031	−	0.0995678i	$-0.968254\pi$
$571$	−0.0940619	−	0.533452i	−0.0940619	−	0.533452i	0.900969	−	0.433884i	$-0.142857\pi$
$572$		0			0
$573$	0.00847939	+	0.0232969i	0.00847939	+	0.0232969i
$574$		0			0
$575$		0			0
$576$	0.180815	+	1.02545i	0.180815	+	1.02545i
$577$	1.83346	−	0.323289i	1.83346	−	0.323289i	0.853291	−	0.521435i	$-0.174603\pi$
$577$	1.83346	−	0.323289i	1.83346	−	0.323289i	0.980172	+	0.198146i	$0.0634921\pi$
$578$	−0.751509	−	0.433884i	−0.751509	−	0.433884i
$579$		0			0
$580$	−0.273548	−	0.0995633i	−0.273548	−	0.0995633i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−1.64599	+	0.950313i	−1.64599	+	0.950313i
$585$		0			0
$586$		−	0.301372i		−	0.301372i
$587$	−1.33968	−	0.236222i	−1.33968	−	0.236222i	−0.542546	−	0.840026i	$-0.682540\pi$
$587$	−1.33968	−	0.236222i	−1.33968	−	0.236222i	−0.797133	+	0.603804i	$0.793651\pi$
$588$	0.0470510	+	0.0394805i	0.0470510	+	0.0394805i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.670622	−	0.170761i	−0.670622	−	0.170761i
$593$	0.445042			0.445042			0.222521	−	0.974928i	$-0.428571\pi$
$593$	0.445042			0.445042			0.222521	+	0.974928i	$0.428571\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.471511	+	0.0831402i	0.471511	+	0.0831402i
$598$		0			0
$599$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$599$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$600$	0.698567	−	0.403318i	0.698567	−	0.403318i
$601$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$601$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$602$		0			0
$603$		0			0
$604$	−0.251834	−	0.0916599i	−0.251834	−	0.0916599i
$605$	1.28518	−	1.53161i	1.28518	−	1.53161i
$606$	−0.260988	−	0.150681i	−0.260988	−	0.150681i
$607$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$607$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$608$	0.152449	+	0.864579i	0.152449	+	0.864579i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.254586	+	1.44383i	0.254586	+	1.44383i	0.797133	+	0.603804i	$0.206349\pi$
$613$	0.254586	+	1.44383i	0.254586	+	1.44383i	−0.542546	+	0.840026i	$0.682540\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.84212	+	0.670477i	1.84212	+	0.670477i	0.988831	+	0.149042i	$0.0476190\pi$
$617$	1.84212	+	0.670477i	1.84212	+	0.670477i	0.853291	+	0.521435i	$0.174603\pi$
$618$	−0.214128	−	0.370881i	−0.214128	−	0.370881i
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$		0			0
$622$	−0.244696	+	1.38774i	−0.244696	+	1.38774i
$623$		0			0
$624$		0			0
$625$	3.82070	+	3.20595i	3.82070	+	3.20595i
$626$	−1.32416	+	0.481957i	−1.32416	+	0.481957i
$627$		0			0
$628$	−0.493345			−0.493345
$629$		0			0
$630$		0			0
$631$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$631$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$632$	0.972606	−	0.354000i	0.972606	−	0.354000i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−0.469077	+	0.812466i	−0.469077	+	0.812466i
$640$	−0.481425	−	0.833852i	−0.481425	−	0.833852i
$641$	1.09708	+	0.399304i	1.09708	+	0.399304i	0.826239	−	0.563320i	$-0.190476\pi$
$641$	1.09708	+	0.399304i	1.09708	+	0.399304i	0.270840	+	0.962624i	$0.412698\pi$
$642$	−0.138715	+	0.165315i	−0.138715	+	0.165315i
$643$	−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
$645$	0.129474	+	0.734285i	0.129474	+	0.734285i
$646$		0			0
$647$	−0.592396	−	1.62760i	−0.592396	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$647$	−0.592396	−	1.62760i	−0.592396	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$648$	0.302845	+	0.832061i	0.302845	+	0.832061i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$653$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$654$	−0.402429	−	0.146472i	−0.402429	−	0.146472i
$655$	1.89527	+	3.28270i	1.89527	+	3.28270i
$656$		0			0
$657$	−1.26230	+	1.05920i	−1.26230	+	1.05920i
$658$		0			0
$659$	0.331867	−	1.88211i	0.331867	−	1.88211i	−0.124344	−	0.992239i	$-0.539683\pi$
$659$	0.331867	−	1.88211i	0.331867	−	1.88211i	0.456211	−	0.889872i	$-0.349206\pi$
$660$		0			0
$661$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$661$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$662$		0			0
$663$		0			0
$664$	−0.611575	+	1.68029i	−0.611575	+	1.68029i
$665$		0			0
$666$	−0.811824	−	0.0608378i	−0.811824	−	0.0608378i
$667$		0			0
$668$	−0.0251798	+	0.0691809i	−0.0251798	+	0.0691809i
$669$	0.465057	−	0.169267i	0.465057	−	0.169267i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$673$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$674$		0			0
$675$	1.10677	−	0.928690i	1.10677	−	0.928690i
$676$	0.123490	−	0.213891i	0.123490	−	0.213891i
$677$	0.797133	+	1.38067i	0.797133	+	1.38067i	0.921476	+	0.388435i	$0.126984\pi$
$677$	0.797133	+	1.38067i	0.797133	+	1.38067i	−0.124344	+	0.992239i	$0.539683\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$683$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$684$	0.144470	+	0.396927i	0.144470	+	0.396927i
$685$		0			0
$686$		0			0
$687$	0.0854036	+	0.484348i	0.0854036	+	0.484348i
$688$	1.02196	−	0.180200i	1.02196	−	0.180200i
$689$		0			0
$690$		0			0
$691$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$691$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	0.0275472	−	0.156228i	0.0275472	−	0.156228i
$697$		0			0
$698$		0			0
$699$	−0.0284730	−	0.0238917i	−0.0284730	−	0.0238917i
$700$		0			0
$701$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$701$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$702$		0			0
$703$	−1.81791	−	0.136234i	−1.81791	−	0.136234i
$704$		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	$0.5\pi$
$710$	0.301279	−	1.70864i	0.301279	−	1.70864i
$711$	0.777130	−	0.448676i	0.777130	−	0.448676i
$712$	1.00102	−	0.839956i	1.00102	−	0.839956i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.295563	+	0.352238i	−0.295563	+	0.352238i
$717$		0			0
$718$	1.13093	−	0.199414i	1.13093	−	0.199414i
$719$	0.0940619	+	0.533452i	0.0940619	+	0.533452i	0.995031	+	0.0995678i	$0.0317460\pi$
$719$	0.0940619	+	0.533452i	0.0940619	+	0.533452i	−0.900969	+	0.433884i	$0.857143\pi$
$720$	−0.834366	−	0.994358i	−0.834366	−	0.994358i
$721$		0			0
$722$	−0.689563	−	1.89456i	−0.689563	−	1.89456i
$723$		0			0
$724$		0			0
$725$	1.74022	−	0.306848i	1.74022	−	0.306848i
$726$	0.186891	+	0.107901i	0.186891	+	0.107901i
$727$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$727$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$728$		0			0
$729$	0.323908	+	0.561024i	0.323908	+	0.561024i
$730$	1.52371	−	2.63914i	1.52371	−	2.63914i
$731$		0			0
$732$		0			0
$733$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$733$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$734$			0.552745i			0.552745i
$735$	−0.489666	−	0.0863414i	−0.489666	−	0.0863414i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$739$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$740$	−0.475349	+	0.133743i	−0.475349	+	0.133743i
$741$		0			0
$742$		0			0
$743$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$743$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$744$		0			0
$745$		0			0
$746$		−	0.0432681i		−	0.0432681i
$747$	−0.269203	+	1.52673i	−0.269203	+	1.52673i
$748$		0			0
$749$		0			0
$750$	−0.430935	+	0.746402i	−0.430935	+	0.746402i
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$		0			0
$753$	−0.138715	+	0.165315i	−0.138715	+	0.165315i
$754$		0			0
$755$	2.13655	−	0.376732i	2.13655	−	0.376732i
$756$		0			0
$757$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$757$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$758$	0.322049	+	0.884822i	0.322049	+	0.884822i
$759$		0			0
$760$	−2.53521	−	3.02135i	−2.53521	−	3.02135i
$761$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$761$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$762$		0			0
$763$		0			0
$764$	0.0158266	−	0.0188614i	0.0158266	−	0.0188614i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.131834	+	0.110622i	−0.131834	+	0.110622i
$769$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$769$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$773$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$774$	1.14717	−	0.417536i	1.14717	−	0.417536i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		−	0.284141i		−	0.284141i
$784$	−0.120168	+	0.681508i	−0.120168	+	0.681508i
$785$	3.45872	−	1.99689i	3.45872	−	1.99689i
$786$	−0.313412	+	0.262984i	−0.313412	+	0.262984i
$787$	−0.797133	+	1.38067i	−0.797133	+	1.38067i	0.124344	+	0.992239i	$0.460317\pi$
$787$	−0.797133	+	1.38067i	−0.797133	+	1.38067i	−0.921476	+	0.388435i	$0.873016\pi$
$788$		0			0
$789$	−0.0116521	−	0.00424101i	−0.0116521	−	0.00424101i
$790$	−1.06673	+	1.27128i	−1.06673	+	1.27128i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.162630	−	0.446821i	−0.162630	−	0.446821i
$797$	0.920301	+	1.09677i	0.920301	+	1.09677i	0.995031	+	0.0995678i	$0.0317460\pi$
$797$	0.920301	+	1.09677i	0.920301	+	1.09677i	−0.0747301	+	0.997204i	$0.523810\pi$
$798$		0			0
$799$		0			0
$800$	−1.25013	−	0.721763i	−1.25013	−	0.721763i
$801$	0.728229	−	0.867870i	0.728229	−	0.867870i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$			1.51111i			1.51111i
$809$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$809$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$810$	−1.08757	−	0.912583i	−1.08757	−	0.912583i
$811$	1.60366	−	0.583685i	1.60366	−	0.583685i	0.623490	−	0.781831i	$-0.285714\pi$
$811$	1.60366	−	0.583685i	1.60366	−	0.583685i	0.980172	+	0.198146i	$0.0634921\pi$
$812$		0			0
$813$	0.110676			0.110676
$814$		0			0
$815$		0			0
$816$		0			0
$817$	2.56886	−	0.934987i	2.56886	−	0.934987i
$818$	−0.904288	−	0.758787i	−0.904288	−	0.758787i
$819$		0			0
$820$		0			0
$821$	0.142839	−	0.810077i	0.142839	−	0.810077i	−0.826239	−	0.563320i	$-0.809524\pi$
$821$	0.142839	−	0.810077i	0.142839	−	0.810077i	0.969077	−	0.246757i	$-0.0793651\pi$
$822$		0			0
$823$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$823$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$824$	−1.07369	+	1.85969i	−1.07369	+	1.85969i
$825$		0			0
$826$		0			0
$827$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$827$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$828$		0			0
$829$	1.40998	−	0.248618i	1.40998	−	0.248618i	0.583744	−	0.811938i	$-0.301587\pi$
$829$	1.40998	−	0.248618i	1.40998	−	0.248618i	0.826239	+	0.563320i	$0.190476\pi$
$830$	−0.497856	−	2.82348i	−0.497856	−	2.82348i
$831$	0.180097	+	0.214631i	0.180097	+	0.214631i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.103491	−	0.586929i	−0.103491	−	0.586929i
$836$		0			0
$837$		0			0
$838$	0.817778	−	0.974590i	0.817778	−	0.974590i
$839$	−1.55282	−	0.565181i	−1.55282	−	0.565181i	−0.583744	−	0.811938i	$-0.698413\pi$
$839$	−1.55282	−	0.565181i	−1.55282	−	0.565181i	−0.969077	+	0.246757i	$0.920635\pi$
$840$		0			0
$841$	−0.326239	+	0.565062i	−0.326239	+	0.565062i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			1.99938i			1.99938i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	−0.0614207			−0.0614207
$853$	0.265705	−	0.730019i	0.265705	−	0.730019i	−0.733052	−	0.680173i	$-0.761905\pi$
$853$	0.265705	−	0.730019i	0.265705	−	0.730019i	0.998757	−	0.0498459i	$-0.0158730\pi$
$854$		0			0
$855$	−2.61947	−	2.19799i	−2.61947	−	2.19799i
$856$	1.06565	+	0.187903i	1.06565	+	0.187903i
$857$		−	0.776870i		−	0.776870i	−0.921476	−	0.388435i	$-0.873016\pi$
$857$		−	0.776870i		−	0.776870i	0.921476	−	0.388435i	$-0.126984\pi$
$858$		0			0
$859$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$859$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$860$	0.567250	−	0.475979i	0.567250	−	0.475979i
$861$		0			0
$862$	0.621206	+	1.07596i	0.621206	+	1.07596i
$863$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$863$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$864$	−0.149202	+	0.177811i	−0.149202	+	0.177811i
$865$		0			0
$866$		0			0
$867$	−0.0431841	−	0.244909i	−0.0431841	−	0.244909i
$868$		0			0
$869$		0			0
$870$	0.0869952	+	0.239017i	0.0869952	+	0.239017i
$871$		0			0
$872$	0.372889	+	2.11476i	0.372889	+	2.11476i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−0.101376	−	0.0368978i	−0.101376	−	0.0368978i
$877$	0.365341	+	0.632789i	0.365341	+	0.632789i	0.988831	−	0.149042i	$-0.0476190\pi$
$877$	0.365341	+	0.632789i	0.365341	+	0.632789i	−0.623490	+	0.781831i	$0.714286\pi$
$878$		0			0
$879$	0.0661619	−	0.0555164i	0.0661619	−	0.0555164i
$880$		0			0
$881$	−0.216536	+	1.22804i	−0.216536	+	1.22804i	0.661686	+	0.749781i	$0.269841\pi$
$881$	−0.216536	+	1.22804i	−0.216536	+	1.22804i	−0.878222	+	0.478254i	$0.841270\pi$
$882$			0.814100i			0.814100i
$883$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$883$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$	−0.116759	−	0.242452i	−0.116759	−	0.242452i
$889$		0			0
$890$	−0.716599	+	1.96884i	−0.716599	+	1.96884i
$891$		0			0
$892$	−0.376514	−	0.315933i	−0.376514	−	0.315933i
$893$		0			0
$894$		0			0
$895$	0.646377	−	3.66579i	0.646377	−	3.66579i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.652653	−	0.237546i	−0.652653	−	0.237546i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	0.0800895	+	0.220044i	0.0800895	+	0.220044i
$907$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$907$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$908$		0			0
$909$	0.227498	+	1.29020i	0.227498	+	1.29020i
$910$		0			0
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$	0.201665	−	0.240335i	0.201665	−	0.240335i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.374168	−	0.313965i	0.374168	−	0.313965i
$917$		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
$925$	2.09297	−	2.14582i	2.09297	−	2.14582i
$926$	1.73068			1.73068
$927$	−0.636755	+	1.74947i	−0.636755	+	1.74947i
$928$	−0.266772	+	0.0970972i	−0.266772	+	0.0970972i
$929$	−1.38036	−	1.15826i	−1.38036	−	1.15826i	−0.969077	−	0.246757i	$-0.920635\pi$
$929$	−1.38036	−	1.15826i	−1.38036	−	1.15826i	−0.411287	−	0.911506i	$-0.634921\pi$
$930$		0			0
$931$			1.82301i			1.82301i
$932$	−0.00640998	+	0.0363528i	−0.00640998	+	0.0363528i
$933$	−0.349734	+	0.201919i	−0.349734	+	0.201919i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$937$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$938$		0			0
$939$	−0.349734	−	0.201919i	−0.349734	−	0.201919i
$940$		0			0
$941$	0.336557	+	1.90871i	0.336557	+	1.90871i	0.411287	+	0.911506i	$0.365079\pi$
$941$	0.336557	+	1.90871i	0.336557	+	1.90871i	−0.0747301	+	0.997204i	$0.523810\pi$
$942$	0.277086	+	0.330218i	0.277086	+	0.330218i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.47678	−	0.260396i	1.47678	−	0.260396i	0.623490	−	0.781831i	$-0.285714\pi$
$947$	1.47678	−	0.260396i	1.47678	−	0.260396i	0.853291	+	0.521435i	$0.174603\pi$
$948$	0.0508785	+	0.0293747i	0.0508785	+	0.0293747i
$949$		0			0
$950$	4.45595	+	1.62183i	4.45595	+	1.62183i
$951$		0			0
$952$		0			0
$953$	1.30732	−	1.09697i	1.30732	−	1.09697i	0.318487	−	0.947927i	$-0.396825\pi$
$953$	1.30732	−	1.09697i	1.30732	−	1.09697i	0.988831	−	0.149042i	$-0.0476190\pi$
$954$		0			0
$955$	−0.0346118	+	0.196293i	−0.0346118	+	0.196293i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.188752	−	0.518591i	0.188752	−	0.518591i
$961$	−1.00000			−1.00000
$962$		0			0
$963$	0.938155			0.938155
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$967$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$968$		−	1.08209i		−	1.08209i
$969$		0			0
$970$		0			0
$971$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.500000	−	0.866025i	$-0.333333\pi$
$971$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.939693	−	0.342020i	$-0.111111\pi$
$972$	−0.0846514	+	0.146620i	−0.0846514	+	0.146620i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.75271	+	0.309049i	−1.75271	+	0.309049i	−0.955573	−	0.294755i	$-0.904762\pi$
$977$	−1.75271	+	0.309049i	−1.75271	+	0.309049i	−0.797133	+	0.603804i	$0.793651\pi$
$978$		0			0
$979$		0			0
$980$	0.168891	+	0.464026i	0.168891	+	0.464026i
$981$	0.636755	+	1.74947i	0.636755	+	1.74947i
$982$		0			0
$983$	−0.312903	−	1.77456i	−0.312903	−	1.77456i	−0.583744	−	0.811938i	$-0.698413\pi$
$983$	−0.312903	−	1.77456i	−0.312903	−	1.77456i	0.270840	−	0.962624i	$-0.412698\pi$
$984$		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	$-0.166667\pi$
$991$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.94874	+	2.47428i	2.94874	+	2.47428i
$996$	−0.0953754	+	0.0347138i	−0.0953754	+	0.0347138i
$997$	0.135540	−	0.372393i	0.135540	−	0.372393i	−0.853291	−	0.521435i	$-0.825397\pi$
$997$	0.135540	−	0.372393i	0.135540	−	0.372393i	0.988831	+	0.149042i	$0.0476190\pi$
$998$	−0.674142			−0.674142
$999$	−0.281361	−	0.391350i	−0.281361	−	0.391350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2627.1.x.b.354.3	yes	36
37.30	even	18	inner	2627.1.x.b.141.3	✓	36
71.70	odd	2	CM	2627.1.x.b.354.3	yes	36
2627.141	odd	18	inner	2627.1.x.b.141.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2627.1.x.b.141.3	✓	36	37.30	even	18	inner
2627.1.x.b.141.3	✓	36	2627.141	odd	18	inner
2627.1.x.b.354.3	yes	36	1.1	even	1	trivial
2627.1.x.b.354.3	yes	36	71.70	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(-0.296794 + 0.815435i) q^{2} +(-0.233690 + 0.0850561i) q^{3} +(0.189197 + 0.158755i) q^{4} +(-1.96900 - 0.347188i) q^{5} -0.215803i q^{6} +(-0.937116 + 0.541044i) q^{8} +(-0.718668 + 0.603034i) q^{9} +O(q^{10})\)	\(q+(-0.296794 + 0.815435i) q^{2} +(-0.233690 + 0.0850561i) q^{3} +(0.189197 + 0.158755i) q^{4} +(-1.96900 - 0.347188i) q^{5} -0.215803i q^{6} +(-0.937116 + 0.541044i) q^{8} +(-0.718668 + 0.603034i) q^{9} +(0.867498 - 1.50255i) q^{10} +(-0.0577166 - 0.0210071i) q^{12} +(0.489666 - 0.0863414i) q^{15} +(-0.120168 - 0.681508i) q^{16} +(-0.278439 - 0.765004i) q^{18} +(-0.623507 - 1.71307i) q^{19} +(-0.317412 - 0.378277i) q^{20} +(0.172975 - 0.206144i) q^{24} +(2.81674 + 1.02521i) q^{25} +(0.240997 - 0.417420i) q^{27} +(0.510531 - 0.294755i) q^{29} +(-0.0749242 + 0.424917i) q^{30} +(-0.474258 - 0.0836246i) q^{32} -0.231705 q^{36} +(0.411287 - 0.911506i) q^{37} +1.58195 q^{38} +(2.03303 - 0.739962i) q^{40} +1.49956i q^{43} +(1.62443 - 0.937863i) q^{45} +(0.0860485 + 0.149040i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(-1.67198 + 1.99259i) q^{50} +(0.268852 + 0.320405i) q^{54} +(0.291414 + 0.347294i) q^{57} +(0.0888311 + 0.503786i) q^{58} +(0.106351 + 0.0614016i) q^{60} +(0.554958 - 0.961216i) q^{64} +(0.939693 - 0.342020i) q^{71} +(0.347207 - 0.953944i) q^{72} +1.75644 q^{73} +(0.621206 + 0.605907i) q^{74} -0.745444 q^{75} +(0.153993 - 0.423094i) q^{76} +(-0.941976 - 0.166096i) q^{79} +1.38361i q^{80} +(0.142094 - 0.805857i) q^{81} +(1.26587 - 1.06219i) q^{83} +(-1.22280 - 0.445061i) q^{86} +(-0.0942351 + 0.112305i) q^{87} +(-1.18926 + 0.209699i) q^{89} +(0.282646 + 1.60297i) q^{90} +(0.632929 + 3.58952i) q^{95} +(0.117942 - 0.0207964i) q^{96} +(0.557790 - 0.664748i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{3} + 3 q^{5} - 6 q^{9}+O(q^{10}) \) 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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