LMFDB - Embedded newform 2627.1.x.b.1064.3

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			1064.3
Root			$0.698237 + 0.715867i$ of defining polynomial
Character	$\chi$	$=$	2627.1064
Dual form			2627.1.x.b.1632.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.854584 + 0.150686i) q^{2} +(0.346865 - 1.96717i) q^{3} +(-0.232085 + 0.0844720i) q^{4} +(1.21863 - 1.45231i) q^{5} +1.73338i q^{6} +(0.937116 - 0.541044i) q^{8} +(-2.80974 - 1.02266i) q^{9} +O(q^{10})$	\(q+(-0.854584 + 0.150686i) q^{2} +(0.346865 - 1.96717i) q^{3} +(-0.232085 + 0.0844720i) q^{4} +(1.21863 - 1.45231i) q^{5} +1.73338i q^{6} +(0.937116 - 0.541044i) q^{8} +(-2.80974 - 1.02266i) q^{9} +(-0.822581 + 1.42475i) q^{10} +(0.0856685 + 0.485850i) q^{12} +(-2.43423 - 2.90101i) q^{15} +(-0.530119 + 0.444823i) q^{16} +(2.55526 + 0.450561i) q^{18} +(1.40998 + 0.248618i) q^{19} +(-0.160147 + 0.439999i) q^{20} +(-0.739272 - 2.03113i) q^{24} +(-0.450489 - 2.55485i) q^{25} +(-1.98759 + 3.44260i) q^{27} +(-1.17809 + 0.680173i) q^{29} +(2.51740 + 2.11235i) q^{30} +(-0.309550 + 0.368908i) q^{32} +0.738484 q^{36} +(-0.698237 - 0.715867i) q^{37} -1.24241 q^{38} +(0.356236 - 2.02032i) q^{40} -1.99938i q^{43} +(-4.90926 + 2.83436i) q^{45} +(0.691161 + 1.19713i) q^{48} +(0.173648 + 0.984808i) q^{49} +(0.769962 + 2.11545i) q^{50} +(1.17981 - 3.24150i) q^{54} +(0.978146 - 2.68743i) q^{57} +(0.904288 - 0.758787i) q^{58} +(0.810003 + 0.467655i) q^{60} +(0.554958 - 0.961216i) q^{64} +(-0.173648 + 0.984808i) q^{71} +(-3.18636 + 0.561841i) q^{72} +1.96034 q^{73} +(0.704573 + 0.506554i) q^{74} -5.18208 q^{75} +(-0.348237 + 0.0614036i) q^{76} +(0.254732 - 0.303578i) q^{79} +1.31197i q^{80} +(3.79223 + 3.18206i) q^{81} +(-0.140447 - 0.0511184i) q^{83} +(0.301279 + 1.70864i) q^{86} +(0.929374 + 2.55344i) q^{87} +(1.07992 + 1.28699i) q^{89} +(3.76827 - 3.16196i) q^{90} +(2.07932 - 1.74476i) q^{95} +(0.618331 + 0.736898i) q^{96} +(-0.296794 - 0.815435i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2627\mathbb{Z}\right)^\times$.

$n$	$149$	$853$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.854584	+	0.150686i	−0.854584	+	0.150686i	−0.583744	−	0.811938i	$-0.698413\pi$
$2$	−0.854584	+	0.150686i	−0.854584	+	0.150686i	−0.270840	+	0.962624i	$0.587302\pi$
$3$	0.346865	−	1.96717i	0.346865	−	1.96717i	0.124344	−	0.992239i	$-0.460317\pi$
$3$	0.346865	−	1.96717i	0.346865	−	1.96717i	0.222521	−	0.974928i	$-0.428571\pi$
$4$	−0.232085	+	0.0844720i	−0.232085	+	0.0844720i
$5$	1.21863	−	1.45231i	1.21863	−	1.45231i	0.365341	−	0.930874i	$-0.380952\pi$
$5$	1.21863	−	1.45231i	1.21863	−	1.45231i	0.853291	−	0.521435i	$-0.174603\pi$
$6$			1.73338i			1.73338i
$7$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$7$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$8$	0.937116	−	0.541044i	0.937116	−	0.541044i
$9$	−2.80974	−	1.02266i	−2.80974	−	1.02266i
$10$	−0.822581	+	1.42475i	−0.822581	+	1.42475i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	0.0856685	+	0.485850i	0.0856685	+	0.485850i
$13$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$13$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$14$		0			0
$15$	−2.43423	−	2.90101i	−2.43423	−	2.90101i
$16$	−0.530119	+	0.444823i	−0.530119	+	0.444823i
$17$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$17$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$18$	2.55526	+	0.450561i	2.55526	+	0.450561i
$19$	1.40998	+	0.248618i	1.40998	+	0.248618i	0.826239	−	0.563320i	$-0.190476\pi$
$19$	1.40998	+	0.248618i	1.40998	+	0.248618i	0.583744	+	0.811938i	$0.301587\pi$
$20$	−0.160147	+	0.439999i	−0.160147	+	0.439999i
$21$		0			0
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−0.739272	−	2.03113i	−0.739272	−	2.03113i
$25$	−0.450489	−	2.55485i	−0.450489	−	2.55485i
$26$		0			0
$27$	−1.98759	+	3.44260i	−1.98759	+	3.44260i
$28$		0			0
$29$	−1.17809	+	0.680173i	−1.17809	+	0.680173i	−0.955573	−	0.294755i	$-0.904762\pi$
$29$	−1.17809	+	0.680173i	−1.17809	+	0.680173i	−0.222521	+	0.974928i	$0.571429\pi$
$30$	2.51740	+	2.11235i	2.51740	+	2.11235i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−0.309550	+	0.368908i	−0.309550	+	0.368908i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.738484			0.738484
$37$	−0.698237	−	0.715867i	−0.698237	−	0.715867i
$37$	−0.698237	−	0.715867i	−0.698237	−	0.715867i
$38$	−1.24241			−1.24241
$39$		0			0
$40$	0.356236	−	2.02032i	0.356236	−	2.02032i
$41$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$41$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$42$		0			0
$43$		−	1.99938i		−	1.99938i	−0.0249307	−	0.999689i	$-0.507937\pi$
$43$		−	1.99938i		−	1.99938i	0.0249307	−	0.999689i	$-0.492063\pi$
$44$		0			0
$45$	−4.90926	+	2.83436i	−4.90926	+	2.83436i
$46$		0			0
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	0.691161	+	1.19713i	0.691161	+	1.19713i
$49$	0.173648	+	0.984808i	0.173648	+	0.984808i
$50$	0.769962	+	2.11545i	0.769962	+	2.11545i
$51$		0			0
$52$		0			0
$53$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$53$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$54$	1.17981	−	3.24150i	1.17981	−	3.24150i
$55$		0			0
$56$		0			0
$57$	0.978146	−	2.68743i	0.978146	−	2.68743i
$58$	0.904288	−	0.758787i	0.904288	−	0.758787i
$59$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$59$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$60$	0.810003	+	0.467655i	0.810003	+	0.467655i
$61$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$61$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$62$		0			0
$63$		0			0
$64$	0.554958	−	0.961216i	0.554958	−	0.961216i
$65$		0			0
$66$		0			0
$67$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$67$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$71$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$72$	−3.18636	+	0.561841i	−3.18636	+	0.561841i
$73$	1.96034			1.96034			0.980172	−	0.198146i	$-0.0634921\pi$
$73$	1.96034			1.96034			0.980172	+	0.198146i	$0.0634921\pi$
$74$	0.704573	+	0.506554i	0.704573	+	0.506554i
$75$	−5.18208			−5.18208
$76$	−0.348237	+	0.0614036i	−0.348237	+	0.0614036i
$77$		0			0
$78$		0			0
$79$	0.254732	−	0.303578i	0.254732	−	0.303578i	−0.623490	−	0.781831i	$-0.714286\pi$
$79$	0.254732	−	0.303578i	0.254732	−	0.303578i	0.878222	+	0.478254i	$0.158730\pi$
$80$			1.31197i			1.31197i
$81$	3.79223	+	3.18206i	3.79223	+	3.18206i
$82$		0			0
$83$	−0.140447	−	0.0511184i	−0.140447	−	0.0511184i	0.270840	−	0.962624i	$-0.412698\pi$
$83$	−0.140447	−	0.0511184i	−0.140447	−	0.0511184i	−0.411287	+	0.911506i	$0.634921\pi$
$84$		0			0
$85$		0			0
$86$	0.301279	+	1.70864i	0.301279	+	1.70864i
$87$	0.929374	+	2.55344i	0.929374	+	2.55344i
$88$		0			0
$89$	1.07992	+	1.28699i	1.07992	+	1.28699i	0.955573	+	0.294755i	$0.0952381\pi$
$89$	1.07992	+	1.28699i	1.07992	+	1.28699i	0.124344	+	0.992239i	$0.460317\pi$
$90$	3.76827	−	3.16196i	3.76827	−	3.16196i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.07932	−	1.74476i	2.07932	−	1.74476i
$96$	0.618331	+	0.736898i	0.618331	+	0.736898i
$97$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$97$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$98$	−0.296794	−	0.815435i	−0.296794	−	0.815435i
$99$		0			0
$100$	0.320365	+	0.554889i	0.320365	+	0.554889i
$101$	−0.583744	+	1.01107i	−0.583744	+	1.01107i	0.411287	+	0.911506i	$0.365079\pi$
$101$	−0.583744	+	1.01107i	−0.583744	+	1.01107i	−0.995031	+	0.0995678i	$0.968254\pi$
$102$		0			0
$103$	−0.0863356	+	0.0498459i	−0.0863356	+	0.0498459i	−0.542546	−	0.840026i	$-0.682540\pi$
$103$	−0.0863356	+	0.0498459i	−0.0863356	+	0.0498459i	0.456211	+	0.889872i	$0.349206\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$107$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$108$	0.170486	−	0.966872i	0.170486	−	0.966872i
$109$	0.0981772	−	0.0173113i	0.0981772	−	0.0173113i	−0.124344	−	0.992239i	$-0.539683\pi$
$109$	0.0981772	−	0.0173113i	0.0981772	−	0.0173113i	0.222521	+	0.974928i	$0.428571\pi$
$110$		0			0
$111$	−1.65042	+	1.12524i	−1.65042	+	1.12524i
$112$		0			0
$113$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$113$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$114$	−0.430949	+	2.44403i	−0.430949	+	2.44403i
$115$		0			0
$116$	0.215962	−	0.257374i	0.215962	−	0.257374i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−3.85073	−	1.40155i	−3.85073	−	1.40155i
$121$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.61756	−	1.51125i	−2.61756	−	1.51125i
$126$		0			0
$127$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$127$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$128$	−0.164708	+	0.452532i	−0.164708	+	0.452532i
$129$	−3.93311	−	0.693514i	−3.93311	−	0.693514i
$130$		0			0
$131$	0.327145	−	0.898823i	0.327145	−	0.898823i	−0.661686	−	0.749781i	$-0.730159\pi$
$131$	0.327145	−	0.898823i	0.327145	−	0.898823i	0.988831	−	0.149042i	$-0.0476190\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.57759	+	7.08186i	2.57759	+	7.08186i
$136$		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		−0.939693	−	0.342020i	$-0.888889\pi$
$139$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$140$		0			0
$141$		0			0
$142$		−	0.867767i		−	0.867767i
$143$		0			0
$144$	1.94440	−	0.707704i	1.94440	−	0.707704i
$145$	−0.447842	+	2.53984i	−0.447842	+	2.53984i
$146$	−1.67528	+	0.295397i	−1.67528	+	0.295397i
$147$	1.99751			1.99751
$148$	0.222521	+	0.107160i	0.222521	+	0.107160i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	4.42852	−	0.780868i	4.42852	−	0.780868i
$151$	0.320025	−	1.81495i	0.320025	−	1.81495i	−0.222521	−	0.974928i	$-0.571429\pi$
$151$	0.320025	−	1.81495i	0.320025	−	1.81495i	0.542546	−	0.840026i	$-0.317460\pi$
$152$	1.45583	−	0.529879i	1.45583	−	0.529879i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.49812	+	0.545271i	1.49812	+	0.545271i	0.955573	−	0.294755i	$-0.0952381\pi$
$157$	1.49812	+	0.545271i	1.49812	+	0.545271i	0.542546	+	0.840026i	$0.317460\pi$
$158$	−0.171945	+	0.297817i	−0.171945	+	0.297817i
$159$		0			0
$160$	0.158540	+	0.899125i	0.158540	+	0.899125i
$161$		0			0
$162$	−3.72027	−	2.14790i	−3.72027	−	2.14790i
$163$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$163$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$164$		0			0
$165$		0			0
$166$	0.127726	+	0.0225216i	0.127726	+	0.0225216i
$167$	−1.83346	−	0.323289i	−1.83346	−	0.323289i	−0.853291	−	0.521435i	$-0.825397\pi$
$167$	−1.83346	−	0.323289i	−1.83346	−	0.323289i	−0.980172	+	0.198146i	$0.936508\pi$
$168$		0			0
$169$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$170$		0			0
$171$	−3.70743	−	2.14049i	−3.70743	−	2.14049i
$172$	0.168891	+	0.464026i	0.168891	+	0.464026i
$173$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$173$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$174$	−1.17900	−	2.04208i	−1.17900	−	2.04208i
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−1.11681	−	0.937116i	−1.11681	−	0.937116i
$179$			0.298085i			0.298085i	0.988831	+	0.149042i	$0.0476190\pi$
$179$			0.298085i			0.298085i	−0.988831	+	0.149042i	$0.952381\pi$
$180$	0.899940	−	1.07251i	0.899940	−	1.07251i
$181$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$181$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.89055	+	0.141677i	−1.89055	+	0.141677i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−1.51404	+	1.80437i	−1.51404	+	1.80437i
$191$		−	1.20761i		−	1.20761i	−0.797133	−	0.603804i	$-0.793651\pi$
$191$		−	1.20761i		−	1.20761i	0.797133	−	0.603804i	$-0.206349\pi$
$192$	−1.69838	−	1.42511i	−1.69838	−	1.42511i
$193$		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		−0.173648	−	0.984808i	$-0.555556\pi$
$197$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$198$		0			0
$199$	1.57877	+	0.911506i	1.57877	+	0.911506i	0.995031	+	0.0995678i	$0.0317460\pi$
$199$	1.57877	+	0.911506i	1.57877	+	0.911506i	0.583744	+	0.811938i	$0.301587\pi$
$200$	−1.80445	−	2.15046i	−1.80445	−	2.15046i
$201$		0			0
$202$	0.346503	−	0.952010i	0.346503	−	0.952010i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	0.0662700	−	0.0556071i	0.0662700	−	0.0556071i
$207$		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
$213$	1.87705	+	0.683190i	1.87705	+	0.683190i
$214$	−0.751509	+	0.433884i	−0.751509	+	0.433884i
$215$	−2.90372	−	2.43651i	−2.90372	−	2.43651i
$216$			4.30149i			4.30149i
$217$		0			0
$218$	−0.0812921	+	0.0295879i	−0.0812921	+	0.0295879i
$219$	0.679974	−	3.85633i	0.679974	−	3.85633i
$220$		0			0
$221$		0			0
$222$	1.24087	−	1.21031i	1.24087	−	1.21031i
$223$	−0.541681			−0.541681			−0.270840	−	0.962624i	$-0.587302\pi$
$223$	−0.541681			−0.541681			−0.270840	+	0.962624i	$0.587302\pi$
$224$		0			0
$225$	−1.34699	+	7.63917i	−1.34699	+	7.63917i
$226$		0			0
$227$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$227$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$228$			0.706339i			0.706339i
$229$	−0.559735	−	0.469673i	−0.559735	−	0.469673i	0.318487	−	0.947927i	$-0.396825\pi$
$229$	−0.559735	−	0.469673i	−0.559735	−	0.469673i	−0.878222	+	0.478254i	$0.841270\pi$
$230$		0			0
$231$		0			0
$232$	−0.736007	+	1.27480i	−0.736007	+	1.27480i
$233$	0.826239	+	1.43109i	0.826239	+	1.43109i	0.900969	+	0.433884i	$0.142857\pi$
$233$	0.826239	+	1.43109i	0.826239	+	1.43109i	−0.0747301	+	0.997204i	$0.523810\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.508830	−	0.606400i	−0.508830	−	0.606400i
$238$		0			0
$239$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$239$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$240$	2.58087	+	0.455077i	2.58087	+	0.455077i
$241$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$241$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$242$	0.296794	−	0.815435i	0.296794	−	0.815435i
$243$	4.52987	−	3.80102i	4.52987	−	3.80102i
$244$		0			0
$245$	1.64186	+	0.947927i	1.64186	+	0.947927i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−0.149274	+	0.258551i	−0.149274	+	0.258551i
$250$	2.46465	+	0.897058i	2.46465	+	0.897058i
$251$	−0.751509	+	0.433884i	−0.751509	+	0.433884i	−0.826239	−	0.563320i	$-0.809524\pi$
$251$	−0.751509	+	0.433884i	−0.751509	+	0.433884i	0.0747301	+	0.997204i	$0.476190\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.120168	+	0.681508i	−0.120168	+	0.681508i
$257$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$257$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$258$	3.46568			3.46568
$259$		0			0
$260$		0			0
$261$	4.00572	−	0.706317i	4.00572	−	0.706317i
$262$	−0.144133	+	0.817417i	−0.144133	+	0.817417i
$263$	−0.598559	+	0.217858i	−0.598559	+	0.217858i	−0.623490	−	0.781831i	$-0.714286\pi$
$263$	−0.598559	+	0.217858i	−0.598559	+	0.217858i	0.0249307	+	0.999689i	$0.492063\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.90632	−	1.67796i	2.90632	−	1.67796i
$268$		0			0
$269$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$269$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$270$	−3.26990	−	5.66364i	−3.26990	−	5.66364i
$271$	0.0772807	+	0.438281i	0.0772807	+	0.438281i	0.998757	+	0.0498459i	$0.0158730\pi$
$271$	0.0772807	+	0.438281i	0.0772807	+	0.438281i	−0.921476	+	0.388435i	$0.873016\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.96411	+	0.346325i	1.96411	+	0.346325i	0.995031	+	0.0995678i	$0.0317460\pi$
$277$	1.96411	+	0.346325i	1.96411	+	0.346325i	0.969077	+	0.246757i	$0.0793651\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$281$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$282$		0			0
$283$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$283$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$284$	−0.0428876	−	0.243227i	−0.0428876	−	0.243227i
$285$	−2.71098	−	4.69556i	−2.71098	−	4.69556i
$286$		0			0
$287$		0			0
$288$	1.24702	−	0.719969i	1.24702	−	0.719969i
$289$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$290$		−	2.23799i		−	2.23799i
$291$		0			0
$292$	−0.454966	+	0.165594i	−0.454966	+	0.165594i
$293$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$293$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$294$	−1.70704	+	0.300998i	−1.70704	+	0.300998i
$295$		0			0
$296$	−1.04164	−	0.293073i	−1.04164	−	0.293073i
$297$		0			0
$298$		0			0
$299$		0			0
$300$	1.20268	−	0.437741i	1.20268	−	0.437741i
$301$		0			0
$302$			1.59925i			1.59925i
$303$	1.78647	+	1.49903i	1.78647	+	1.49903i
$304$	−0.858050	+	0.495395i	−0.858050	+	0.495395i
$305$		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
$309$	0.0681084	+	0.187126i	0.0681084	+	0.187126i
$310$		0			0
$311$	0.317225	+	0.378054i	0.317225	+	0.378054i	0.900969	−	0.433884i	$-0.142857\pi$
$311$	0.317225	+	0.378054i	0.317225	+	0.378054i	−0.583744	+	0.811938i	$0.698413\pi$
$312$		0			0
$313$	−0.168792	+	0.463752i	−0.168792	+	0.463752i	−0.995031	−	0.0995678i	$-0.968254\pi$
$313$	−0.168792	+	0.463752i	−0.168792	+	0.463752i	0.826239	+	0.563320i	$0.190476\pi$
$314$	−1.36243	−	0.240234i	−1.36243	−	0.240234i
$315$		0			0
$316$	−0.0334756	+	0.0919735i	−0.0334756	+	0.0919735i
$317$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$317$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$318$		0			0
$319$		0			0
$320$	−0.719692	−	1.97734i	−0.719692	−	1.97734i
$321$	−0.346865	−	1.96717i	−0.346865	−	1.96717i
$322$		0			0
$323$		0			0
$324$	−1.14891	−	0.418171i	−1.14891	−	0.418171i
$325$		0			0
$326$		0			0
$327$		−	0.199136i		−	0.199136i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$331$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$332$	0.0369136			0.0369136
$333$	1.22977	+	2.72546i	1.22977	+	2.72546i
$334$	1.61556			1.61556
$335$		0			0
$336$		0			0
$337$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$337$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$338$	0.557790	−	0.664748i	0.557790	−	0.664748i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	3.49085	+	1.27057i	3.49085	+	1.27057i
$343$		0			0
$344$	−1.08175	−	1.87365i	−1.08175	−	1.87365i
$345$		0			0
$346$		0			0
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$	−0.431388	−	0.514108i	−0.431388	−	0.514108i
$349$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$349$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$353$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$354$		0			0
$355$	1.21863	+	1.45231i	1.21863	+	1.45231i
$356$	−0.359347	−	0.207469i	−0.359347	−	0.207469i
$357$		0			0
$358$	−0.0449172	−	0.254738i	−0.0449172	−	0.254738i
$359$	−0.0249307	−	0.0431812i	−0.0249307	−	0.0431812i	0.853291	−	0.521435i	$-0.174603\pi$
$359$	−0.0249307	−	0.0431812i	−0.0249307	−	0.0431812i	−0.878222	+	0.478254i	$0.841270\pi$
$360$	−3.06703	+	5.31225i	−3.06703	+	5.31225i
$361$	0.986547	+	0.359074i	0.986547	+	0.359074i
$362$		0			0
$363$	1.53018	+	1.28398i	1.53018	+	1.28398i
$364$		0			0
$365$	2.38894	−	2.84703i	2.38894	−	2.84703i
$366$		0			0
$367$	0.305003	−	1.72976i	0.305003	−	1.72976i	−0.318487	−	0.947927i	$-0.603175\pi$
$367$	0.305003	−	1.72976i	0.305003	−	1.72976i	0.623490	−	0.781831i	$-0.285714\pi$
$368$		0			0
$369$		0			0
$370$	1.59429	−	0.405956i	1.59429	−	0.405956i
$371$		0			0
$372$		0			0
$373$	0.110609	−	0.627296i	0.110609	−	0.627296i	−0.878222	−	0.478254i	$-0.841270\pi$
$373$	0.110609	−	0.627296i	0.110609	−	0.627296i	0.988831	−	0.149042i	$-0.0476190\pi$
$374$		0			0
$375$	−3.88081	+	4.62497i	−3.88081	+	4.62497i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.73181	−	0.630327i	−1.73181	−	0.630327i	−0.733052	−	0.680173i	$-0.761905\pi$
$379$	−1.73181	−	0.630327i	−1.73181	−	0.630327i	−0.998757	+	0.0498459i	$0.984127\pi$
$380$	−0.335196	+	0.580576i	−0.335196	+	0.580576i
$381$		0			0
$382$	0.181970	+	1.03200i	0.181970	+	1.03200i
$383$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$383$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$384$	0.833075	+	0.480976i	0.833075	+	0.480976i
$385$		0			0
$386$		0			0
$387$	−2.04469	+	5.61773i	−2.04469	+	5.61773i
$388$		0			0
$389$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$389$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$390$		0			0
$391$		0			0
$392$	0.695553	+	0.828928i	0.695553	+	0.828928i
$393$	−1.65466	−	0.955319i	−1.65466	−	0.955319i
$394$		0			0
$395$	−0.130464	−	0.739898i	−0.130464	−	0.739898i
$396$		0			0
$397$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$397$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$398$	−1.48655	−	0.541059i	−1.48655	−	0.541059i
$399$		0			0
$400$	1.37527	+	1.15399i	1.37527	+	1.15399i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$		0			0
$404$	0.0500707	−	0.283965i	0.0500707	−	0.283965i
$405$	9.24267	−	1.62973i	9.24267	−	1.62973i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.580554	+	0.102367i	−0.580554	+	0.102367i	−0.456211	−	0.889872i	$-0.650794\pi$
$409$	−0.580554	+	0.102367i	−0.580554	+	0.102367i	−0.124344	+	0.992239i	$0.539683\pi$
$410$		0			0
$411$		0			0
$412$	0.0158266	−	0.0188614i	0.0158266	−	0.0188614i
$413$		0			0
$414$		0			0
$415$	−0.245392	+	0.141677i	−0.245392	+	0.141677i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.331867	−	1.88211i	−0.331867	−	1.88211i	−0.456211	−	0.889872i	$-0.650794\pi$
$419$	−0.331867	−	1.88211i	−0.331867	−	1.88211i	0.124344	−	0.992239i	$-0.460317\pi$
$420$		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
$426$	−1.70704	−	0.300998i	−1.70704	−	0.300998i
$427$		0			0
$428$	−0.189197	+	0.158755i	−0.189197	+	0.158755i
$429$		0			0
$430$	2.84862	+	1.64465i	2.84862	+	1.64465i
$431$	−0.555398	−	1.52594i	−0.555398	−	1.52594i	−0.826239	−	0.563320i	$-0.809524\pi$
$431$	−0.555398	−	1.52594i	−0.555398	−	1.52594i	0.270840	−	0.962624i	$-0.412698\pi$
$432$	−0.477690	−	2.70911i	−0.477690	−	2.70911i
$433$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$433$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$434$		0			0
$435$	4.84094	+	1.76196i	4.84094	+	1.76196i
$436$	−0.0213231	+	0.0123109i	−0.0213231	+	0.0123109i
$437$		0			0
$438$			3.39802i			3.39802i
$439$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$439$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$440$		0			0
$441$	0.519219	−	2.94464i	0.519219	−	2.94464i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	0.287987	−	0.400566i	0.287987	−	0.400566i
$445$	3.18513			3.18513
$446$	0.462912	−	0.0816239i	0.462912	−	0.0816239i
$447$		0			0
$448$		0			0
$449$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$449$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$450$		−	6.73128i		−	6.73128i
$451$		0			0
$452$		0			0
$453$	−3.45931	−	1.25909i	−3.45931	−	1.25909i
$454$		0			0
$455$		0			0
$456$	−0.537384	−	3.04766i	−0.537384	−	3.04766i
$457$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$457$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$458$	0.549114	+	0.317031i	0.549114	+	0.317031i
$459$		0			0
$460$		0			0
$461$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$461$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$462$		0			0
$463$	1.10952	+	0.195639i	1.10952	+	0.195639i	0.698237	−	0.715867i	$-0.253968\pi$
$463$	1.10952	+	0.195639i	1.10952	+	0.195639i	0.411287	+	0.911506i	$0.365079\pi$
$464$	0.321974	−	0.884616i	0.321974	−	0.884616i
$465$		0			0
$466$	−0.921736	−	1.09848i	−0.921736	−	1.09848i
$467$		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
$471$	1.59228	−	2.75792i	1.59228	−	2.75792i
$472$		0			0
$473$		0			0
$474$	0.526214	+	0.441546i	0.526214	+	0.441546i
$475$		−	3.71430i		−	3.71430i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$479$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$480$	1.82372			1.82372
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.0428876	−	0.243227i	0.0428876	−	0.243227i
$485$		0			0
$486$	−3.29840	+	3.93088i	−3.29840	+	3.93088i
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$		0			0
$489$		0			0
$490$	−1.54595	−	0.562678i	−1.54595	−	0.562678i
$491$		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
$498$	0.0886075	−	0.243447i	0.0886075	−	0.243447i
$499$	1.75271	+	0.309049i	1.75271	+	0.309049i	0.955573	−	0.294755i	$-0.0952381\pi$
$499$	1.75271	+	0.309049i	1.75271	+	0.309049i	0.797133	+	0.603804i	$0.206349\pi$
$500$	0.735154	+	0.129627i	0.735154	+	0.129627i
$501$	−1.27193	+	3.49459i	−1.27193	+	3.49459i
$502$	0.576847	−	0.484032i	0.576847	−	0.484032i
$503$	0.378930	+	0.451591i	0.378930	+	0.451591i	0.921476	−	0.388435i	$-0.126984\pi$
$503$	0.378930	+	0.451591i	0.378930	+	0.451591i	−0.542546	+	0.840026i	$0.682540\pi$
$504$		0			0
$505$	0.757023	+	2.07990i	0.757023	+	2.07990i
$506$		0			0
$507$	0.998757	+	1.72990i	0.998757	+	1.72990i
$508$		0			0
$509$	0.326352	+	0.118782i	0.326352	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$509$	0.326352	+	0.118782i	0.326352	+	0.118782i	−0.173648	+	0.984808i	$0.555556\pi$
$510$		0			0
$511$		0			0
$512$		−	1.08209i		−	1.08209i
$513$	−3.65836	+	4.35986i	−3.65836	+	4.35986i
$514$		0			0
$515$	−0.0328197	+	0.186130i	−0.0328197	+	0.186130i
$516$	0.971398	−	0.171284i	0.971398	−	0.171284i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.343417	+	1.94762i	−0.343417	+	1.94762i	−0.0249307	+	0.999689i	$0.507937\pi$
$521$	−0.343417	+	1.94762i	−0.343417	+	1.94762i	−0.318487	+	0.947927i	$0.603175\pi$
$522$	−3.31679	+	1.20721i	−3.31679	+	1.20721i
$523$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$523$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$524$			0.236238i			0.236238i
$525$		0			0
$526$	0.478691	−	0.276372i	0.478691	−	0.276372i
$527$		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
$534$	−2.23085	+	1.87190i	−2.23085	+	1.87190i
$535$	0.648420	−	1.78152i	0.648420	−	1.78152i
$536$		0			0
$537$	0.586382	+	0.103395i	0.586382	+	0.103395i
$538$		0			0
$539$		0			0
$540$	−1.19644	−	1.42586i	−1.19644	−	1.42586i
$541$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$541$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$542$	−0.132086	−	0.362903i	−0.132086	−	0.362903i
$543$		0			0
$544$		0			0
$545$	0.0945006	−	0.163680i	0.0945006	−	0.163680i
$546$		0			0
$547$	0.172457	−	0.0995678i	0.172457	−	0.0995678i	−0.411287	−	0.911506i	$-0.634921\pi$
$547$	0.172457	−	0.0995678i	0.172457	−	0.0995678i	0.583744	+	0.811938i	$0.301587\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.83019	+	0.666136i	−1.83019	+	0.666136i
$552$		0			0
$553$		0			0
$554$	−1.73068			−1.73068
$555$	−0.377063	+	3.76818i	−0.377063	+	3.76818i
$556$		0			0
$557$	−0.765067	+	0.134902i	−0.765067	+	0.134902i	−0.542546	−	0.840026i	$-0.682540\pi$
$557$	−0.765067	+	0.134902i	−0.765067	+	0.134902i	−0.222521	+	0.974928i	$0.571429\pi$
$558$		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
$568$	0.370096	+	1.01683i	0.370096	+	1.01683i
$569$	1.35417	+	0.781831i	1.35417	+	0.781831i	0.988831	−	0.149042i	$-0.0476190\pi$
$569$	1.35417	+	0.781831i	1.35417	+	0.781831i	0.365341	+	0.930874i	$0.380952\pi$
$570$	3.02432	+	3.60425i	3.02432	+	3.60425i
$571$	0.630128	−	0.528741i	0.630128	−	0.528741i	−0.270840	−	0.962624i	$-0.587302\pi$
$571$	0.630128	−	0.528741i	0.630128	−	0.528741i	0.900969	+	0.433884i	$0.142857\pi$
$572$		0			0
$573$	−2.37557	−	0.418877i	−2.37557	−	0.418877i
$574$		0			0
$575$		0			0
$576$	−2.54229	+	2.13323i	−2.54229	+	2.13323i
$577$	−0.191605	−	0.228346i	−0.191605	−	0.228346i	0.661686	−	0.749781i	$-0.269841\pi$
$577$	−0.191605	−	0.228346i	−0.191605	−	0.228346i	−0.853291	+	0.521435i	$0.825397\pi$
$578$	0.751509	+	0.433884i	0.751509	+	0.433884i
$579$		0			0
$580$	−0.110608	−	0.627288i	−0.110608	−	0.627288i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	1.83707	−	1.06063i	1.83707	−	1.06063i
$585$		0			0
$586$			1.32950i			1.32950i
$587$	−0.378930	+	0.451591i	−0.378930	+	0.451591i	−0.921476	−	0.388435i	$-0.873016\pi$
$587$	−0.378930	+	0.451591i	−0.378930	+	0.451591i	0.542546	+	0.840026i	$0.317460\pi$
$588$	−0.463593	+	0.168734i	−0.463593	+	0.168734i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.688583	+	0.0689031i	0.688583	+	0.0689031i
$593$	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
$597$	2.34071	−	2.78954i	2.34071	−	2.78954i
$598$		0			0
$599$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$599$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$600$	−4.85621	+	2.80373i	−4.85621	+	2.80373i
$601$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$601$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$602$		0			0
$603$		0			0
$604$	0.0790397	+	0.448257i	0.0790397	+	0.448257i
$605$	0.648420	+	1.78152i	0.648420	+	1.78152i
$606$	−1.75257	−	1.01185i	−1.75257	−	1.01185i
$607$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$607$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$608$	−0.528177	+	0.443193i	−0.528177	+	0.443193i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.46402	+	1.22846i	−1.46402	+	1.22846i	−0.542546	+	0.840026i	$0.682540\pi$
$613$	−1.46402	+	1.22846i	−1.46402	+	1.22846i	−0.921476	+	0.388435i	$0.873016\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.296345	+	1.68065i	0.296345	+	1.68065i	0.661686	+	0.749781i	$0.269841\pi$
$617$	0.296345	+	1.68065i	0.296345	+	1.68065i	−0.365341	+	0.930874i	$0.619048\pi$
$618$	−0.0864017	−	0.149652i	−0.0864017	−	0.149652i
$619$		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
$622$	−0.328063	−	0.275278i	−0.328063	−	0.275278i
$623$		0			0
$624$		0			0
$625$	−2.94683	+	1.07256i	−2.94683	+	1.07256i
$626$	0.0743659	−	0.421750i	0.0743659	−	0.421750i
$627$		0			0
$628$	−0.393751			−0.393751
$629$		0			0
$630$		0			0
$631$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$631$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$632$	0.0744644	−	0.422308i	0.0744644	−	0.422308i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.49503	−	2.58947i	1.49503	−	2.58947i
$640$	0.456498	+	0.790677i	0.456498	+	0.790677i
$641$	−0.336557	−	1.90871i	−0.336557	−	1.90871i	−0.411287	−	0.911506i	$-0.634921\pi$
$641$	−0.336557	−	1.90871i	−0.336557	−	1.90871i	0.0747301	−	0.997204i	$-0.476190\pi$
$642$	0.592850	+	1.62884i	0.592850	+	1.62884i
$643$	−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
$645$	−5.80021	+	4.86695i	−5.80021	+	4.86695i
$646$		0			0
$647$	1.70574	+	0.300767i	1.70574	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$647$	1.70574	+	0.300767i	1.70574	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$648$	5.27540	+	0.930195i	5.27540	+	0.930195i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$653$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$654$	0.0300070	+	0.170178i	0.0300070	+	0.170178i
$655$	−0.906700	−	1.57045i	−0.906700	−	1.57045i
$656$		0			0
$657$	−5.50806	−	2.00477i	−5.50806	−	2.00477i
$658$		0			0
$659$	−1.12310	−	0.942393i	−1.12310	−	0.942393i	−0.124344	−	0.992239i	$-0.539683\pi$
$659$	−1.12310	−	0.942393i	−1.12310	−	0.942393i	−0.998757	+	0.0498459i	$0.984127\pi$
$660$		0			0
$661$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$661$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$662$		0			0
$663$		0			0
$664$	−0.159272	+	0.0280840i	−0.159272	+	0.0280840i
$665$		0			0
$666$	−1.46163	−	2.14382i	−1.46163	−	2.14382i
$667$		0			0
$668$	0.452828	−	0.0798458i	0.452828	−	0.0798458i
$669$	−0.187890	+	1.06558i	−0.187890	+	1.06558i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$673$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$674$		0			0
$675$	9.69073	+	3.52714i	9.69073	+	3.52714i
$676$	0.123490	−	0.213891i	0.123490	−	0.213891i
$677$	−0.542546	−	0.939718i	−0.542546	−	0.939718i	−0.998757	−	0.0498459i	$-0.984127\pi$
$677$	−0.542546	−	0.939718i	−0.542546	−	0.939718i	0.456211	−	0.889872i	$-0.349206\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$683$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$684$	1.04125	+	0.183600i	1.04125	+	0.183600i
$685$		0			0
$686$		0			0
$687$	−1.11808	+	0.938179i	−1.11808	+	0.938179i
$688$	0.889369	+	1.05991i	0.889369	+	1.05991i
$689$		0			0
$690$		0			0
$691$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$691$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	2.25245	+	1.89003i	2.25245	+	1.89003i
$697$		0			0
$698$		0			0
$699$	3.10178	−	1.12896i	3.10178	−	1.12896i
$700$		0			0
$701$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$701$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$702$		0			0
$703$	−0.806524	−	1.18295i	−0.806524	−	1.18295i
$704$		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	$0.5\pi$
$710$	−1.26027	−	1.05749i	−1.26027	−	1.05749i
$711$	−1.02619	+	0.592469i	−1.02619	+	0.592469i
$712$	1.70833	+	0.621780i	1.70833	+	0.621780i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.0251798	−	0.0691809i	−0.0251798	−	0.0691809i
$717$		0			0
$718$	0.0278122	+	0.0331453i	0.0278122	+	0.0331453i
$719$	−0.630128	+	0.528741i	−0.630128	+	0.528741i	−0.900969	−	0.433884i	$-0.857143\pi$
$719$	−0.630128	+	0.528741i	−0.630128	+	0.528741i	0.270840	+	0.962624i	$0.412698\pi$
$720$	1.34170	−	3.68630i	1.34170	−	3.68630i
$721$		0			0
$722$	−0.897195	−	0.158200i	−0.897195	−	0.158200i
$723$		0			0
$724$		0			0
$725$	2.26846	+	2.70344i	2.26846	+	2.70344i
$726$	−1.50115	−	0.866689i	−1.50115	−	0.866689i
$727$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$727$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$728$		0			0
$729$	−3.43078	−	5.94228i	−3.43078	−	5.94228i
$730$	−1.61254	+	2.79300i	−1.61254	+	2.79300i
$731$		0			0
$732$		0			0
$733$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$733$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$734$			1.52418i			1.52418i
$735$	2.43423	−	2.90101i	2.43423	−	2.90101i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$739$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$740$	0.426801	−	0.192580i	0.426801	−	0.192580i
$741$		0			0
$742$		0			0
$743$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$743$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$744$		0			0
$745$		0			0
$746$			0.552745i			0.552745i
$747$	0.342342	+	0.287259i	0.342342	+	0.287259i
$748$		0			0
$749$		0			0
$750$	2.61956	−	4.53722i	2.61956	−	4.53722i
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$		0			0
$753$	0.592850	+	1.62884i	0.592850	+	1.62884i
$754$		0			0
$755$	−2.24588	−	2.67654i	−2.24588	−	2.67654i
$756$		0			0
$757$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$757$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$758$	1.57496	+	0.277708i	1.57496	+	0.277708i
$759$		0			0
$760$	1.00457	−	2.76004i	1.00457	−	2.76004i
$761$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$761$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$762$		0			0
$763$		0			0
$764$	0.102009	+	0.280268i	0.102009	+	0.280268i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.29896	+	0.472782i	1.29896	+	0.472782i
$769$		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		0.939693	−	0.342020i	$-0.111111\pi$
$773$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$774$	0.900842	−	5.10893i	0.900842	−	5.10893i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		−	5.40761i		−	5.40761i
$784$	−0.530119	−	0.444823i	−0.530119	−	0.444823i
$785$	2.61756	−	1.51125i	2.61756	−	1.51125i
$786$	1.55800	+	0.567066i	1.55800	+	0.567066i
$787$	0.542546	−	0.939718i	0.542546	−	0.939718i	−0.456211	−	0.889872i	$-0.650794\pi$
$787$	0.542546	−	0.939718i	0.542546	−	0.939718i	0.998757	−	0.0498459i	$-0.0158730\pi$
$788$		0			0
$789$	0.220944	+	1.25303i	0.220944	+	1.25303i
$790$	0.222985	+	0.612646i	0.222985	+	0.612646i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.443406	−	0.0781845i	−0.443406	−	0.0781845i
$797$	−0.555398	+	1.52594i	−0.555398	+	1.52594i	0.270840	+	0.962624i	$0.412698\pi$
$797$	−0.555398	+	1.52594i	−0.555398	+	1.52594i	−0.826239	+	0.563320i	$0.809524\pi$
$798$		0			0
$799$		0			0
$800$	1.08195	+	0.624666i	1.08195	+	0.624666i
$801$	−1.71812	−	4.72051i	−1.71812	−	4.72051i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$			1.26332i			1.26332i
$809$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$809$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$810$	−7.65306	+	2.78549i	−7.65306	+	2.78549i
$811$	−0.229801	+	1.30327i	−0.229801	+	1.30327i	0.623490	+	0.781831i	$0.285714\pi$
$811$	−0.229801	+	1.30327i	−0.229801	+	1.30327i	−0.853291	+	0.521435i	$0.825397\pi$
$812$		0			0
$813$	0.888977			0.888977
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.497081	−	2.81909i	0.497081	−	2.81909i
$818$	0.480707	−	0.174963i	0.480707	−	0.174963i
$819$		0			0
$820$		0			0
$821$	−1.06976	−	0.897636i	−1.06976	−	0.897636i	−0.0747301	−	0.997204i	$-0.523810\pi$
$821$	−1.06976	−	0.897636i	−1.06976	−	0.897636i	−0.995031	+	0.0995678i	$0.968254\pi$
$822$		0			0
$823$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$823$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$824$	−0.0539377	+	0.0934228i	−0.0539377	+	0.0934228i
$825$		0			0
$826$		0			0
$827$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$827$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$828$		0			0
$829$	1.04381	+	1.24396i	1.04381	+	1.24396i	0.969077	+	0.246757i	$0.0793651\pi$
$829$	1.04381	+	1.24396i	1.04381	+	1.24396i	0.0747301	+	0.997204i	$0.476190\pi$
$830$	0.188360	−	0.158053i	0.188360	−	0.158053i
$831$	1.36256	−	3.74360i	1.36256	−	3.74360i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−2.70383	+	2.26878i	−2.70383	+	2.26878i
$836$		0			0
$837$		0			0
$838$	0.567216	+	1.55841i	0.567216	+	1.55841i
$839$	0.0259535	+	0.147190i	0.0259535	+	0.147190i	0.995031	−	0.0995678i	$-0.0317460\pi$
$839$	0.0259535	+	0.147190i	0.0259535	+	0.147190i	−0.969077	+	0.246757i	$0.920635\pi$
$840$		0			0
$841$	0.425270	−	0.736589i	0.425270	−	0.736589i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			1.89585i			1.89585i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	−0.493345			−0.493345
$853$	1.75271	−	0.309049i	1.75271	−	0.309049i	0.797133	−	0.603804i	$-0.206349\pi$
$853$	1.75271	−	0.309049i	1.75271	−	0.309049i	0.955573	+	0.294755i	$0.0952381\pi$
$854$		0			0
$855$	−7.62664	+	2.77587i	−7.62664	+	2.77587i
$856$	0.695553	−	0.828928i	0.695553	−	0.828928i
$857$			1.77974i			1.77974i	0.456211	+	0.889872i	$0.349206\pi$
$857$			1.77974i			1.77974i	−0.456211	+	0.889872i	$0.650794\pi$
$858$		0			0
$859$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$859$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$860$	0.879725	+	0.320194i	0.879725	+	0.320194i
$861$		0			0
$862$	0.704573	+	1.22036i	0.704573	+	1.22036i
$863$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$863$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$864$	−0.654744	−	1.79889i	−0.654744	−	1.79889i
$865$		0			0
$866$		0			0
$867$	−1.53018	+	1.28398i	−1.53018	+	1.28398i
$868$		0			0
$869$		0			0
$870$	−4.40250	−	0.776279i	−4.40250	−	0.776279i
$871$		0			0
$872$	0.0826373	−	0.0693409i	0.0826373	−	0.0693409i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	0.167940	+	0.952434i	0.167940	+	0.952434i
$877$	−0.988831	−	1.71271i	−0.988831	−	1.71271i	−0.623490	−	0.781831i	$-0.714286\pi$
$877$	−0.988831	−	1.71271i	−0.988831	−	1.71271i	−0.365341	−	0.930874i	$-0.619048\pi$
$878$		0			0
$879$	−2.87581	−	1.04671i	−2.87581	−	1.04671i
$880$		0			0
$881$	−0.955242	−	0.801543i	−0.955242	−	0.801543i	0.0249307	−	0.999689i	$-0.492063\pi$
$881$	−0.955242	−	0.801543i	−0.955242	−	0.801543i	−0.980172	+	0.198146i	$0.936508\pi$
$882$			2.59468i			2.59468i
$883$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$883$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$	−0.937834	+	1.94743i	−0.937834	+	1.94743i
$889$		0			0
$890$	−2.72197	+	0.479956i	−2.72197	+	0.479956i
$891$		0			0
$892$	0.125716	−	0.0457569i	0.125716	−	0.0457569i
$893$		0			0
$894$		0			0
$895$	0.432911	+	0.363255i	0.432911	+	0.363255i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.332679	−	1.88672i	−0.332679	−	1.88672i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	3.14600	+	0.554725i	3.14600	+	0.554725i
$907$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$907$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$908$		0			0
$909$	2.67415	−	2.24388i	2.67415	−	2.24388i
$910$		0			0
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$	0.676898	+	1.85976i	0.676898	+	1.85976i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.169580	+	0.0617222i	0.169580	+	0.0617222i
$917$		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
$925$	−1.51439	+	2.10638i	−1.51439	+	2.10638i
$926$	−0.977662			−0.977662
$927$	0.293556	−	0.0517618i	0.293556	−	0.0517618i
$928$	0.113758	−	0.645155i	0.113758	−	0.645155i
$929$	1.69327	−	0.616299i	1.69327	−	0.616299i	0.698237	−	0.715867i	$-0.253968\pi$
$929$	1.69327	−	0.616299i	1.69327	−	0.616299i	0.995031	+	0.0995678i	$0.0317460\pi$
$930$		0			0
$931$			1.43173i			1.43173i
$932$	−0.312644	−	0.262340i	−0.312644	−	0.262340i
$933$	0.853730	−	0.492901i	0.853730	−	0.492901i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$937$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$938$		0			0
$939$	0.853730	+	0.492901i	0.853730	+	0.492901i
$940$		0			0
$941$	−1.52448	+	1.27919i	−1.52448	+	1.27919i	−0.698237	+	0.715867i	$0.746032\pi$
$941$	−1.52448	+	1.27919i	−1.52448	+	1.27919i	−0.826239	+	0.563320i	$0.809524\pi$
$942$	−0.945160	+	2.59681i	−0.945160	+	2.59681i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.28518	+	1.53161i	1.28518	+	1.53161i	0.661686	+	0.749781i	$0.269841\pi$
$947$	1.28518	+	1.53161i	1.28518	+	1.53161i	0.623490	+	0.781831i	$0.285714\pi$
$948$	0.169316	+	0.0977544i	0.169316	+	0.0977544i
$949$		0			0
$950$	0.559693	+	3.17418i	0.559693	+	3.17418i
$951$		0			0
$952$		0			0
$953$	−1.24356	−	0.452620i	−1.24356	−	0.452620i	−0.365341	−	0.930874i	$-0.619048\pi$
$953$	−1.24356	−	0.452620i	−1.24356	−	0.452620i	−0.878222	+	0.478254i	$0.841270\pi$
$954$		0			0
$955$	−1.75382	−	1.47163i	−1.75382	−	1.47163i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−4.13939	+	0.729886i	−4.13939	+	0.729886i
$961$	−1.00000			−1.00000
$962$		0			0
$963$	−2.99006			−2.99006
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$967$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$968$			1.08209i			1.08209i
$969$		0			0
$970$		0			0
$971$	0.326352	+	0.118782i	0.326352	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$971$	0.326352	+	0.118782i	0.326352	+	0.118782i	−0.173648	+	0.984808i	$0.555556\pi$
$972$	−0.730236	+	1.26481i	−0.730236	+	1.26481i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.27560	+	1.52020i	1.27560	+	1.52020i	0.733052	+	0.680173i	$0.238095\pi$
$977$	1.27560	+	1.52020i	1.27560	+	1.52020i	0.542546	+	0.840026i	$0.317460\pi$
$978$		0			0
$979$		0			0
$980$	−0.461124	−	0.0813086i	−0.461124	−	0.0813086i
$981$	−0.293556	−	0.0517618i	−0.293556	−	0.0517618i
$982$		0			0
$983$	−1.38036	+	1.15826i	−1.38036	+	1.15826i	−0.411287	+	0.911506i	$0.634921\pi$
$983$	−1.38036	+	1.15826i	−1.38036	+	1.15826i	−0.969077	+	0.246757i	$0.920635\pi$
$984$		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
$995$	3.24773	−	1.18208i	3.24773	−	1.18208i
$996$	0.0128040	−	0.0726153i	0.0128040	−	0.0726153i
$997$	−1.02703	+	0.181093i	−1.02703	+	0.181093i	−0.661686	−	0.749781i	$-0.730159\pi$
$997$	−1.02703	+	0.181093i	−1.02703	+	0.181093i	−0.365341	+	0.930874i	$0.619048\pi$
$998$	−1.54440			−1.54440
$999$	3.85225	−	0.980904i	3.85225	−	0.980904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2627.1.x.b.1064.3	✓	36
37.4	even	18	inner	2627.1.x.b.1632.3	yes	36
71.70	odd	2	CM	2627.1.x.b.1064.3	✓	36
2627.1632	odd	18	inner	2627.1.x.b.1632.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2627.1.x.b.1064.3	✓	36	1.1	even	1	trivial
2627.1.x.b.1064.3	✓	36	71.70	odd	2	CM
2627.1.x.b.1632.3	yes	36	37.4	even	18	inner
2627.1.x.b.1632.3	yes	36	2627.1632	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)

\(f(q)\)	\(=\)	\(q+(-0.854584 + 0.150686i) q^{2} +(0.346865 - 1.96717i) q^{3} +(-0.232085 + 0.0844720i) q^{4} +(1.21863 - 1.45231i) q^{5} +1.73338i q^{6} +(0.937116 - 0.541044i) q^{8} +(-2.80974 - 1.02266i) q^{9} +O(q^{10})\)	\(q+(-0.854584 + 0.150686i) q^{2} +(0.346865 - 1.96717i) q^{3} +(-0.232085 + 0.0844720i) q^{4} +(1.21863 - 1.45231i) q^{5} +1.73338i q^{6} +(0.937116 - 0.541044i) q^{8} +(-2.80974 - 1.02266i) q^{9} +(-0.822581 + 1.42475i) q^{10} +(0.0856685 + 0.485850i) q^{12} +(-2.43423 - 2.90101i) q^{15} +(-0.530119 + 0.444823i) q^{16} +(2.55526 + 0.450561i) q^{18} +(1.40998 + 0.248618i) q^{19} +(-0.160147 + 0.439999i) q^{20} +(-0.739272 - 2.03113i) q^{24} +(-0.450489 - 2.55485i) q^{25} +(-1.98759 + 3.44260i) q^{27} +(-1.17809 + 0.680173i) q^{29} +(2.51740 + 2.11235i) q^{30} +(-0.309550 + 0.368908i) q^{32} +0.738484 q^{36} +(-0.698237 - 0.715867i) q^{37} -1.24241 q^{38} +(0.356236 - 2.02032i) q^{40} -1.99938i q^{43} +(-4.90926 + 2.83436i) q^{45} +(0.691161 + 1.19713i) q^{48} +(0.173648 + 0.984808i) q^{49} +(0.769962 + 2.11545i) q^{50} +(1.17981 - 3.24150i) q^{54} +(0.978146 - 2.68743i) q^{57} +(0.904288 - 0.758787i) q^{58} +(0.810003 + 0.467655i) q^{60} +(0.554958 - 0.961216i) q^{64} +(-0.173648 + 0.984808i) q^{71} +(-3.18636 + 0.561841i) q^{72} +1.96034 q^{73} +(0.704573 + 0.506554i) q^{74} -5.18208 q^{75} +(-0.348237 + 0.0614036i) q^{76} +(0.254732 - 0.303578i) q^{79} +1.31197i q^{80} +(3.79223 + 3.18206i) q^{81} +(-0.140447 - 0.0511184i) q^{83} +(0.301279 + 1.70864i) q^{86} +(0.929374 + 2.55344i) q^{87} +(1.07992 + 1.28699i) q^{89} +(3.76827 - 3.16196i) q^{90} +(2.07932 - 1.74476i) q^{95} +(0.618331 + 0.736898i) q^{96} +(-0.296794 - 0.815435i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{3} + 3 q^{5} - 6 q^{9}+O(q^{10}) \) 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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