LMFDB - Embedded newform 2627.1.x.b.141.5

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			141.5
Root			$-0.0249307 + 0.999689i$ of defining polynomial
Character	$\chi$	$=$	2627.141
Dual form			2627.1.x.b.354.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.534804 + 1.46936i) q^{2} +(1.87005 + 0.680641i) q^{3} +(-1.10697 + 0.928855i) q^{4} +(-1.18926 + 0.209699i) q^{5} +3.11179i q^{6} +(-0.602663 - 0.347948i) q^{8} +(2.26776 + 1.90287i) q^{9} +O(q^{10})$	\(q+(0.534804 + 1.46936i) q^{2} +(1.87005 + 0.680641i) q^{3} +(-1.10697 + 0.928855i) q^{4} +(-1.18926 + 0.209699i) q^{5} +3.11179i q^{6} +(-0.602663 - 0.347948i) q^{8} +(2.26776 + 1.90287i) q^{9} +(-0.944147 - 1.63531i) q^{10} +(-2.70229 + 0.983555i) q^{12} +(-2.36671 - 0.417314i) q^{15} +(-0.0619743 + 0.351474i) q^{16} +(-1.58321 + 4.34982i) q^{18} +(0.683828 - 1.87880i) q^{19} +(1.12169 - 1.33678i) q^{20} +(-0.890180 - 1.06088i) q^{24} +(0.430679 - 0.156754i) q^{25} +(1.95060 + 3.37854i) q^{27} +(-1.72721 - 0.997204i) q^{29} +(-0.652539 - 3.70073i) q^{30} +(-1.23491 + 0.217748i) q^{32} -4.27782 q^{36} +(0.0249307 - 0.999689i) q^{37} +3.12635 q^{38} +(0.789689 + 0.287423i) q^{40} +0.0996918i q^{43} +(-3.09599 - 1.78747i) q^{45} +(-0.355122 + 0.615090i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(0.460658 + 0.548991i) q^{50} +(-3.92112 + 4.67300i) q^{54} +(2.55758 - 3.04800i) q^{57} +(0.541536 - 3.07120i) q^{58} +(3.00749 - 1.73637i) q^{60} +(-0.801938 - 1.38900i) q^{64} +(0.939693 + 0.342020i) q^{71} +(-0.704593 - 1.93585i) q^{72} +1.84295 q^{73} +(1.48224 - 0.498006i) q^{74} +0.912083 q^{75} +(0.988160 + 2.71495i) q^{76} +(0.765067 - 0.134902i) q^{79} -0.430991i q^{80} +(0.834084 + 4.73032i) q^{81} +(-1.51498 - 1.27122i) q^{83} +(-0.146483 + 0.0533156i) q^{86} +(-2.55122 - 3.04043i) q^{87} +(1.79532 + 0.316563i) q^{89} +(0.970693 - 5.50507i) q^{90} +(-0.419268 + 2.37779i) q^{95} +(-2.45755 - 0.433332i) q^{96} +(-1.00510 - 1.19784i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2627\mathbb{Z}\right)^\times$.

$n$	$149$	$853$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.534804	+	1.46936i	0.534804	+	1.46936i	0.853291	+	0.521435i	$0.174603\pi$
$2$	0.534804	+	1.46936i	0.534804	+	1.46936i	−0.318487	+	0.947927i	$0.603175\pi$
$3$	1.87005	+	0.680641i	1.87005	+	0.680641i	0.969077	+	0.246757i	$0.0793651\pi$
$3$	1.87005	+	0.680641i	1.87005	+	0.680641i	0.900969	+	0.433884i	$0.142857\pi$
$4$	−1.10697	+	0.928855i	−1.10697	+	0.928855i
$5$	−1.18926	+	0.209699i	−1.18926	+	0.209699i	−0.733052	−	0.680173i	$-0.761905\pi$
$5$	−1.18926	+	0.209699i	−1.18926	+	0.209699i	−0.456211	+	0.889872i	$0.650794\pi$
$6$			3.11179i			3.11179i
$7$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$7$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$8$	−0.602663	−	0.347948i	−0.602663	−	0.347948i
$9$	2.26776	+	1.90287i	2.26776	+	1.90287i
$10$	−0.944147	−	1.63531i	−0.944147	−	1.63531i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	−2.70229	+	0.983555i	−2.70229	+	0.983555i
$13$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$13$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$14$		0			0
$15$	−2.36671	−	0.417314i	−2.36671	−	0.417314i
$16$	−0.0619743	+	0.351474i	−0.0619743	+	0.351474i
$17$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$17$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$18$	−1.58321	+	4.34982i	−1.58321	+	4.34982i
$19$	0.683828	−	1.87880i	0.683828	−	1.87880i	0.318487	−	0.947927i	$-0.396825\pi$
$19$	0.683828	−	1.87880i	0.683828	−	1.87880i	0.365341	−	0.930874i	$-0.380952\pi$
$20$	1.12169	−	1.33678i	1.12169	−	1.33678i
$21$		0			0
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	−0.890180	−	1.06088i	−0.890180	−	1.06088i
$25$	0.430679	−	0.156754i	0.430679	−	0.156754i
$26$		0			0
$27$	1.95060	+	3.37854i	1.95060	+	3.37854i
$28$		0			0
$29$	−1.72721	−	0.997204i	−1.72721	−	0.997204i	−0.900969	−	0.433884i	$-0.857143\pi$
$29$	−1.72721	−	0.997204i	−1.72721	−	0.997204i	−0.826239	−	0.563320i	$-0.809524\pi$
$30$	−0.652539	−	3.70073i	−0.652539	−	3.70073i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−1.23491	+	0.217748i	−1.23491	+	0.217748i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−4.27782			−4.27782
$37$	0.0249307	−	0.999689i	0.0249307	−	0.999689i
$37$	0.0249307	−	0.999689i	0.0249307	−	0.999689i
$38$	3.12635			3.12635
$39$		0			0
$40$	0.789689	+	0.287423i	0.789689	+	0.287423i
$41$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$41$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$42$		0			0
$43$			0.0996918i			0.0996918i	0.998757	+	0.0498459i	$0.0158730\pi$
$43$			0.0996918i			0.0996918i	−0.998757	+	0.0498459i	$0.984127\pi$
$44$		0			0
$45$	−3.09599	−	1.78747i	−3.09599	−	1.78747i
$46$		0			0
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$	−0.355122	+	0.615090i	−0.355122	+	0.615090i
$49$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$50$	0.460658	+	0.548991i	0.460658	+	0.548991i
$51$		0			0
$52$		0			0
$53$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$53$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$54$	−3.92112	+	4.67300i	−3.92112	+	4.67300i
$55$		0			0
$56$		0			0
$57$	2.55758	−	3.04800i	2.55758	−	3.04800i
$58$	0.541536	−	3.07120i	0.541536	−	3.07120i
$59$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$59$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$60$	3.00749	−	1.73637i	3.00749	−	1.73637i
$61$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$61$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$62$		0			0
$63$		0			0
$64$	−0.801938	−	1.38900i	−0.801938	−	1.38900i
$65$		0			0
$66$		0			0
$67$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$67$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$68$		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
$72$	−0.704593	−	1.93585i	−0.704593	−	1.93585i
$73$	1.84295			1.84295			0.921476	−	0.388435i	$-0.126984\pi$
$73$	1.84295			1.84295			0.921476	+	0.388435i	$0.126984\pi$
$74$	1.48224	−	0.498006i	1.48224	−	0.498006i
$75$	0.912083			0.912083
$76$	0.988160	+	2.71495i	0.988160	+	2.71495i
$77$		0			0
$78$		0			0
$79$	0.765067	−	0.134902i	0.765067	−	0.134902i	0.222521	−	0.974928i	$-0.428571\pi$
$79$	0.765067	−	0.134902i	0.765067	−	0.134902i	0.542546	+	0.840026i	$0.317460\pi$
$80$		−	0.430991i		−	0.430991i
$81$	0.834084	+	4.73032i	0.834084	+	4.73032i
$82$		0			0
$83$	−1.51498	−	1.27122i	−1.51498	−	1.27122i	−0.853291	−	0.521435i	$-0.825397\pi$
$83$	−1.51498	−	1.27122i	−1.51498	−	1.27122i	−0.661686	−	0.749781i	$-0.730159\pi$
$84$		0			0
$85$		0			0
$86$	−0.146483	+	0.0533156i	−0.146483	+	0.0533156i
$87$	−2.55122	−	3.04043i	−2.55122	−	3.04043i
$88$		0			0
$89$	1.79532	+	0.316563i	1.79532	+	0.316563i	0.969077	−	0.246757i	$-0.0793651\pi$
$89$	1.79532	+	0.316563i	1.79532	+	0.316563i	0.826239	+	0.563320i	$0.190476\pi$
$90$	0.970693	−	5.50507i	0.970693	−	5.50507i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.419268	+	2.37779i	−0.419268	+	2.37779i
$96$	−2.45755	−	0.433332i	−2.45755	−	0.433332i
$97$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$97$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$98$	−1.00510	−	1.19784i	−1.00510	−	1.19784i
$99$		0			0
$100$	−0.331145	+	0.573560i	−0.331145	+	0.573560i
$101$	−0.318487	−	0.551635i	−0.318487	−	0.551635i	0.661686	−	0.749781i	$-0.269841\pi$
$101$	−0.318487	−	0.551635i	−0.318487	−	0.551635i	−0.980172	+	0.198146i	$0.936508\pi$
$102$		0			0
$103$	−0.172457	−	0.0995678i	−0.172457	−	0.0995678i	0.411287	−	0.911506i	$-0.365079\pi$
$103$	−0.172457	−	0.0995678i	−0.172457	−	0.0995678i	−0.583744	+	0.811938i	$0.698413\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$107$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$108$	−5.29743	−	1.92811i	−5.29743	−	1.92811i
$109$	−0.0681084	−	0.187126i	−0.0681084	−	0.187126i	0.900969	−	0.433884i	$-0.142857\pi$
$109$	−0.0681084	−	0.187126i	−0.0681084	−	0.187126i	−0.969077	+	0.246757i	$0.920635\pi$
$110$		0			0
$111$	0.727051	−	1.85250i	0.727051	−	1.85250i
$112$		0			0
$113$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$113$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$114$	5.84643	+	2.12793i	5.84643	+	2.12793i
$115$		0			0
$116$	2.83822	−	0.500454i	2.83822	−	0.500454i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	1.28112	+	1.07499i	1.28112	+	1.07499i
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.566501	−	0.327069i	0.566501	−	0.327069i
$126$		0			0
$127$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$127$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$128$	0.806030	−	0.960589i	0.806030	−	0.960589i
$129$	−0.0678543	+	0.186428i	−0.0678543	+	0.186428i
$130$		0			0
$131$	−1.07992	+	1.28699i	−1.07992	+	1.28699i	−0.124344	+	0.992239i	$0.539683\pi$
$131$	−1.07992	+	1.28699i	−1.07992	+	1.28699i	−0.955573	+	0.294755i	$0.904762\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−3.02826	−	3.60894i	−3.02826	−	3.60894i
$136$		0			0
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$139$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$140$		0			0
$141$		0			0
$142$			1.56366i			1.56366i
$143$		0			0
$144$	−0.809353	+	0.679128i	−0.809353	+	0.679128i
$145$	2.26322	+	0.823743i	2.26322	+	0.823743i
$146$	0.985619	+	2.70797i	0.985619	+	2.70797i
$147$	−1.99006			−1.99006
$148$	0.900969	+	1.12978i	0.900969	+	1.12978i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	0.487786	+	1.34018i	0.487786	+	1.34018i
$151$	−1.31226	−	0.477622i	−1.31226	−	0.477622i	−0.411287	−	0.911506i	$-0.634921\pi$
$151$	−1.31226	−	0.477622i	−1.31226	−	0.477622i	−0.900969	+	0.433884i	$0.857143\pi$
$152$	−1.06584	+	0.894348i	−1.06584	+	0.894348i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.414952	+	0.348186i	0.414952	+	0.348186i	0.826239	−	0.563320i	$-0.190476\pi$
$157$	0.414952	+	0.348186i	0.414952	+	0.348186i	−0.411287	+	0.911506i	$0.634921\pi$
$158$	0.607381	+	1.05201i	0.607381	+	1.05201i
$159$		0			0
$160$	1.42297	−	0.517919i	1.42297	−	0.517919i
$161$		0			0
$162$	−6.50449	+	3.75537i	−6.50449	+	3.75537i
$163$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$163$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$164$		0			0
$165$		0			0
$166$	1.05766	−	2.90590i	1.05766	−	2.90590i
$167$	−0.465266	+	1.27831i	−0.465266	+	1.27831i	0.456211	+	0.889872i	$0.349206\pi$
$167$	−0.465266	+	1.27831i	−0.465266	+	1.27831i	−0.921476	+	0.388435i	$0.873016\pi$
$168$		0			0
$169$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$170$		0			0
$171$	5.12587	−	2.95942i	5.12587	−	2.95942i
$172$	−0.0925992	−	0.110355i	−0.0925992	−	0.110355i
$173$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$173$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$174$	3.10308	−	5.37470i	3.10308	−	5.37470i
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.494997	+	2.80727i	0.494997	+	2.80727i
$179$		−	0.589510i		−	0.589510i	−0.955573	−	0.294755i	$-0.904762\pi$
$179$		−	0.589510i		−	0.589510i	0.955573	−	0.294755i	$-0.0952381\pi$
$180$	5.08745	−	0.897055i	5.08745	−	0.897055i
$181$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$181$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.179985	+	1.19412i	0.179985	+	1.19412i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−3.71806	+	0.655594i	−3.71806	+	0.655594i
$191$			1.92525i			1.92525i	0.270840	+	0.962624i	$0.412698\pi$
$191$			1.92525i			1.92525i	−0.270840	+	0.962624i	$0.587302\pi$
$192$	−0.554252	−	3.14332i	−0.554252	−	3.14332i
$193$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$193$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$194$		0			0
$195$		0			0
$196$	0.722521	−	1.25144i	0.722521	−	1.25144i
$197$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$197$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$198$		0			0
$199$	1.29866	−	0.749781i	1.29866	−	0.749781i	0.318487	−	0.947927i	$-0.396825\pi$
$199$	1.29866	−	0.749781i	1.29866	−	0.749781i	0.980172	+	0.198146i	$0.0634921\pi$
$200$	−0.314097	−	0.0553837i	−0.314097	−	0.0553837i
$201$		0			0
$202$	0.640224	−	0.762989i	0.640224	−	0.762989i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	0.0540708	−	0.306651i	0.0540708	−	0.306651i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$	1.52448	+	1.27919i	1.52448	+	1.27919i
$214$	−1.35417	−	0.781831i	−1.35417	−	0.781831i
$215$	−0.0209053	−	0.118560i	−0.0209053	−	0.118560i
$216$		−	2.71483i		−	2.71483i
$217$		0			0
$218$	0.238532	−	0.200152i	0.238532	−	0.200152i
$219$	3.44641	+	1.25439i	3.44641	+	1.25439i
$220$		0			0
$221$		0			0
$222$	3.11082	+	0.0775790i	3.11082	+	0.0775790i
$223$	1.70658			1.70658			0.853291	−	0.521435i	$-0.174603\pi$
$223$	1.70658			1.70658			0.853291	+	0.521435i	$0.174603\pi$
$224$		0			0
$225$	1.27496	+	0.464047i	1.27496	+	0.464047i
$226$		0			0
$227$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$227$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$228$			5.74966i			5.74966i
$229$	0.254586	+	1.44383i	0.254586	+	1.44383i	0.797133	+	0.603804i	$0.206349\pi$
$229$	0.254586	+	1.44383i	0.254586	+	1.44383i	−0.542546	+	0.840026i	$0.682540\pi$
$230$		0			0
$231$		0			0
$232$	0.693950	+	1.20196i	0.693950	+	1.20196i
$233$	0.365341	−	0.632789i	0.365341	−	0.632789i	−0.623490	−	0.781831i	$-0.714286\pi$
$233$	0.365341	−	0.632789i	0.365341	−	0.632789i	0.988831	+	0.149042i	$0.0476190\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.52253	+	0.268463i	1.52253	+	0.268463i
$238$		0			0
$239$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$239$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$240$	0.293350	−	0.805972i	0.293350	−	0.805972i
$241$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$241$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$242$	1.00510	−	1.19784i	1.00510	−	1.19784i
$243$	−0.982441	+	5.57170i	−0.982441	+	5.57170i
$244$		0			0
$245$	1.04582	−	0.603804i	1.04582	−	0.603804i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−1.96783	−	3.40839i	−1.96783	−	3.40839i
$250$	0.783550	+	0.657477i	0.783550	+	0.657477i
$251$	−1.35417	−	0.781831i	−1.35417	−	0.781831i	−0.365341	−	0.930874i	$-0.619048\pi$
$251$	−1.35417	−	0.781831i	−1.35417	−	0.781831i	−0.988831	+	0.149042i	$0.952381\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.335372	+	0.122066i	0.335372	+	0.122066i
$257$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$257$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$258$	−0.310219			−0.310219
$259$		0			0
$260$		0			0
$261$	−2.01933	−	5.54807i	−2.01933	−	5.54807i
$262$	−2.46861	−	0.898499i	−2.46861	−	0.898499i
$263$	1.22128	−	1.02477i	1.22128	−	1.02477i	0.222521	−	0.974928i	$-0.428571\pi$
$263$	1.22128	−	1.02477i	1.22128	−	1.02477i	0.998757	−	0.0498459i	$-0.0158730\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	3.14186	+	1.81395i	3.14186	+	1.81395i
$268$		0			0
$269$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$269$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$270$	3.68331	−	6.37968i	3.68331	−	6.37968i
$271$	−1.69327	+	0.616299i	−1.69327	+	0.616299i	−0.995031	−	0.0995678i	$-0.968254\pi$
$271$	−1.69327	+	0.616299i	−1.69327	+	0.616299i	−0.698237	+	0.715867i	$0.746032\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	0.101951	−	0.280108i	0.101951	−	0.280108i	−0.878222	−	0.478254i	$-0.841270\pi$
$277$	0.101951	−	0.280108i	0.101951	−	0.280108i	0.980172	+	0.198146i	$0.0634921\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$281$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$282$		0			0
$283$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$283$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$284$	−1.35790	+	0.494233i	−1.35790	+	0.494233i
$285$	−2.40247	+	4.16120i	−2.40247	+	4.16120i
$286$		0			0
$287$		0			0
$288$	−3.21482	−	1.85608i	−3.21482	−	1.85608i
$289$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$290$			3.76603i			3.76603i
$291$		0			0
$292$	−2.04009	+	1.71184i	−2.04009	+	1.71184i
$293$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$293$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$294$	−1.06429	−	2.92412i	−1.06429	−	2.92412i
$295$		0			0
$296$	−0.362864	+	0.593801i	−0.362864	+	0.593801i
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−1.00965	+	0.847193i	−1.00965	+	0.847193i
$301$		0			0
$302$		−	2.18361i		−	2.18361i
$303$	−0.220119	−	1.24836i	−0.220119	−	1.24836i
$304$	0.617970	+	0.356785i	0.617970	+	0.356785i
$305$		0			0
$306$		0			0
$307$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$307$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$308$		0			0
$309$	−0.254732	−	0.303578i	−0.254732	−	0.303578i
$310$		0			0
$311$	−0.941976	−	0.166096i	−0.941976	−	0.166096i	−0.318487	−	0.947927i	$-0.603175\pi$
$311$	−0.941976	−	0.166096i	−0.941976	−	0.166096i	−0.623490	+	0.781831i	$0.714286\pi$
$312$		0			0
$313$	−0.614831	+	0.732728i	−0.614831	+	0.732728i	−0.980172	−	0.198146i	$-0.936508\pi$
$313$	−0.614831	+	0.732728i	−0.614831	+	0.732728i	0.365341	+	0.930874i	$0.380952\pi$
$314$	−0.289693	+	0.795926i	−0.289693	+	0.795926i
$315$		0			0
$316$	−0.721599	+	0.859968i	−0.721599	+	0.859968i
$317$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$317$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$318$		0			0
$319$		0			0
$320$	1.24499	+	1.48372i	1.24499	+	1.48372i
$321$	−1.87005	+	0.680641i	−1.87005	+	0.680641i
$322$		0			0
$323$		0			0
$324$	−5.31709	−	4.46157i	−5.31709	−	4.46157i
$325$		0			0
$326$		0			0
$327$		−	0.396292i		−	0.396292i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$331$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$332$	2.85780			2.85780
$333$	1.95882	−	2.21961i	1.95882	−	2.21961i
$334$	−2.12712			−2.12712
$335$		0			0
$336$		0			0
$337$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$337$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$338$	−1.53991	+	0.271527i	−1.53991	+	0.271527i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	7.08981	+	5.94905i	7.08981	+	5.94905i
$343$		0			0
$344$	0.0346875	−	0.0600806i	0.0346875	−	0.0600806i
$345$		0			0
$346$		0			0
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$	5.64823	+	0.995935i	5.64823	+	0.995935i
$349$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$349$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$353$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$354$		0			0
$355$	−1.18926	−	0.209699i	−1.18926	−	0.209699i
$356$	−2.28140	+	1.31716i	−2.28140	+	1.31716i
$357$		0			0
$358$	0.866204	−	0.315273i	0.866204	−	0.315273i
$359$	−0.998757	+	1.72990i	−0.998757	+	1.72990i	−0.456211	+	0.889872i	$0.650794\pi$
$359$	−0.998757	+	1.72990i	−0.998757	+	1.72990i	−0.542546	+	0.840026i	$0.682540\pi$
$360$	1.24389	+	2.15448i	1.24389	+	2.15448i
$361$	−2.29623	−	1.92676i	−2.29623	−	1.92676i
$362$		0			0
$363$	−0.345571	−	1.95983i	−0.345571	−	1.95983i
$364$		0			0
$365$	−2.19175	+	0.386465i	−2.19175	+	0.386465i
$366$		0			0
$367$	−1.01965	−	0.371124i	−1.01965	−	0.371124i	−0.222521	−	0.974928i	$-0.571429\pi$
$367$	−1.01965	−	0.371124i	−1.01965	−	0.371124i	−0.797133	+	0.603804i	$0.793651\pi$
$368$		0			0
$369$		0			0
$370$	−1.65834	+	0.903084i	−1.65834	+	0.903084i
$371$		0			0
$372$		0			0
$373$	−1.49812	−	0.545271i	−1.49812	−	0.545271i	−0.542546	−	0.840026i	$-0.682540\pi$
$373$	−1.49812	−	0.545271i	−1.49812	−	0.545271i	−0.955573	+	0.294755i	$0.904762\pi$
$374$		0			0
$375$	1.28200	−	0.226051i	1.28200	−	0.226051i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.06976	+	0.897636i	1.06976	+	0.897636i	0.995031	−	0.0995678i	$-0.0317460\pi$
$379$	1.06976	+	0.897636i	1.06976	+	0.897636i	0.0747301	+	0.997204i	$0.476190\pi$
$380$	−1.74450	−	3.02157i	−1.74450	−	3.02157i
$381$		0			0
$382$	−2.82889	+	1.02963i	−2.82889	+	1.02963i
$383$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$383$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$384$	2.16113	−	1.24773i	2.16113	−	1.24773i
$385$		0			0
$386$		0			0
$387$	−0.189701	+	0.226077i	−0.189701	+	0.226077i
$388$		0			0
$389$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$389$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$390$		0			0
$391$		0			0
$392$	0.685323	+	0.120841i	0.685323	+	0.120841i
$393$	−2.89548	+	1.67170i	−2.89548	+	1.67170i
$394$		0			0
$395$	−0.881577	+	0.320868i	−0.881577	+	0.320868i
$396$		0			0
$397$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$397$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$398$	1.79623	+	1.50721i	1.79623	+	1.50721i
$399$		0			0
$400$	0.0284040	+	0.161087i	0.0284040	+	0.161087i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$		0			0
$404$	0.864943	+	0.314813i	0.864943	+	0.314813i
$405$	−1.98389	−	5.45069i	−1.98389	−	5.45069i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.385334	−	1.05870i	−0.385334	−	1.05870i	−0.969077	−	0.246757i	$-0.920635\pi$
$409$	−0.385334	−	1.05870i	−0.385334	−	1.05870i	0.583744	−	0.811938i	$-0.301587\pi$
$410$		0			0
$411$		0			0
$412$	0.283388	−	0.0499689i	0.283388	−	0.0499689i
$413$		0			0
$414$		0			0
$415$	2.06828	+	1.19412i	2.06828	+	1.19412i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.55282	−	0.565181i	1.55282	−	0.565181i	0.583744	−	0.811938i	$-0.301587\pi$
$419$	1.55282	−	0.565181i	1.55282	−	0.565181i	0.969077	+	0.246757i	$0.0793651\pi$
$420$		0			0
$421$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$421$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−1.06429	+	2.92412i	−1.06429	+	2.92412i
$427$		0			0
$428$	0.250929	−	1.42309i	0.250929	−	1.42309i
$429$		0			0
$430$	0.163027	−	0.0941236i	0.163027	−	0.0941236i
$431$	−1.21863	−	1.45231i	−1.21863	−	1.45231i	−0.853291	−	0.521435i	$-0.825397\pi$
$431$	−1.21863	−	1.45231i	−1.21863	−	1.45231i	−0.365341	−	0.930874i	$-0.619048\pi$
$432$	−1.30836	+	0.476203i	−1.30836	+	0.476203i
$433$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$433$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$434$		0			0
$435$	3.67164	+	3.08088i	3.67164	+	3.08088i
$436$	0.249207	+	0.143880i	0.249207	+	0.143880i
$437$		0			0
$438$			5.73487i			5.73487i
$439$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$439$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$440$		0			0
$441$	−2.78181	−	1.01250i	−2.78181	−	1.01250i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	0.915879	+	2.72598i	0.915879	+	2.72598i
$445$	−2.20149			−2.20149
$446$	0.912687	+	2.50759i	0.912687	+	2.50759i
$447$		0			0
$448$		0			0
$449$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$449$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$450$			2.12155i			2.12155i
$451$		0			0
$452$		0			0
$453$	−2.12889	−	1.78635i	−2.12889	−	1.78635i
$454$		0			0
$455$		0			0
$456$	−2.60190	+	0.947016i	−2.60190	+	0.947016i
$457$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$457$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$458$	−1.98536	+	1.14625i	−1.98536	+	1.14625i
$459$		0			0
$460$		0			0
$461$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$461$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$462$		0			0
$463$	0.636755	−	1.74947i	0.636755	−	1.74947i	−0.0249307	−	0.999689i	$-0.507937\pi$
$463$	0.636755	−	1.74947i	0.636755	−	1.74947i	0.661686	−	0.749781i	$-0.269841\pi$
$464$	0.457534	−	0.545267i	0.457534	−	0.545267i
$465$		0			0
$466$	1.12518	+	0.198400i	1.12518	+	0.198400i
$467$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$467$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.538989	+	0.933557i	0.538989	+	0.933557i
$472$		0			0
$473$		0			0
$474$	0.419786	+	2.38073i	0.419786	+	2.38073i
$475$		−	0.916353i		−	0.916353i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$479$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$480$	3.01354			3.01354
$481$		0			0
$482$		0			0
$483$		0			0
$484$	1.35790	+	0.494233i	1.35790	+	0.494233i
$485$		0			0
$486$	−8.71226	+	1.53621i	−8.71226	+	1.53621i
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$		0			0
$489$		0			0
$490$	1.44652	+	1.21377i	1.44652	+	1.21377i
$491$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$491$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	3.95575	−	4.71428i	3.95575	−	4.71428i
$499$	0.555398	−	1.52594i	0.555398	−	1.52594i	−0.270840	−	0.962624i	$-0.587302\pi$
$499$	0.555398	−	1.52594i	0.555398	−	1.52594i	0.826239	−	0.563320i	$-0.190476\pi$
$500$	−0.323297	+	0.888252i	−0.323297	+	0.888252i
$501$	−1.74014	+	2.07381i	−1.74014	+	2.07381i
$502$	0.424577	−	2.40790i	0.424577	−	2.40790i
$503$	1.10952	+	0.195639i	1.10952	+	0.195639i	0.698237	−	0.715867i	$-0.253968\pi$
$503$	1.10952	+	0.195639i	1.10952	+	0.195639i	0.411287	+	0.911506i	$0.365079\pi$
$504$		0			0
$505$	0.494442	+	0.589253i	0.494442	+	0.589253i
$506$		0			0
$507$	−0.995031	+	1.72344i	−0.995031	+	1.72344i
$508$		0			0
$509$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.939693	+	0.342020i	$0.111111\pi$
$509$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.500000	+	0.866025i	$0.333333\pi$
$510$		0			0
$511$		0			0
$512$		−	0.695895i		−	0.695895i
$513$	7.68149	−	1.35445i	7.68149	−	1.35445i
$514$		0			0
$515$	0.225975	+	0.0822483i	0.225975	+	0.0822483i
$516$	−0.0980523	−	0.269397i	−0.0980523	−	0.269397i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.79589	−	0.653650i	−1.79589	−	0.653650i	−0.998757	−	0.0498459i	$-0.984127\pi$
$521$	−1.79589	−	0.653650i	−1.79589	−	0.653650i	−0.797133	−	0.603804i	$-0.793651\pi$
$522$	7.07218	−	5.93426i	7.07218	−	5.93426i
$523$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$523$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$524$		−	2.42775i		−	2.42775i
$525$		0			0
$526$	2.15891	+	1.24645i	2.15891	+	1.24645i
$527$		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
$534$	−0.985075	+	5.58664i	−0.985075	+	5.58664i
$535$	0.776236	−	0.925082i	0.776236	−	0.925082i
$536$		0			0
$537$	0.401245	−	1.10241i	0.401245	−	1.10241i
$538$		0			0
$539$		0			0
$540$	6.70436	+	1.18216i	6.70436	+	1.18216i
$541$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$541$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$542$	−1.81113	−	2.15842i	−1.81113	−	2.15842i
$543$		0			0
$544$		0			0
$545$	0.120239	+	0.208260i	0.120239	+	0.208260i
$546$		0			0
$547$	−0.343199	−	0.198146i	−0.343199	−	0.198146i	0.318487	−	0.947927i	$-0.396825\pi$
$547$	−0.343199	−	0.198146i	−0.343199	−	0.198146i	−0.661686	+	0.749781i	$0.730159\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3.05466	+	2.56316i	−3.05466	+	2.56316i
$552$		0			0
$553$		0			0
$554$	0.466104			0.466104
$555$	−0.476188	+	2.35557i	−0.476188	+	2.35557i
$556$		0			0
$557$	−0.489682	−	1.34539i	−0.489682	−	1.34539i	−0.900969	−	0.433884i	$-0.857143\pi$
$557$	−0.489682	−	1.34539i	−0.489682	−	1.34539i	0.411287	−	0.911506i	$-0.365079\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−0.447313	−	0.533087i	−0.447313	−	0.533087i
$569$	−1.68862	+	0.974928i	−1.68862	+	0.974928i	−0.733052	+	0.680173i	$0.761905\pi$
$569$	−1.68862	+	0.974928i	−1.68862	+	0.974928i	−0.955573	+	0.294755i	$0.904762\pi$
$570$	−7.39916	−	1.30467i	−7.39916	−	1.30467i
$571$	0.229801	−	1.30327i	0.229801	−	1.30327i	−0.623490	−	0.781831i	$-0.714286\pi$
$571$	0.229801	−	1.30327i	0.229801	−	1.30327i	0.853291	−	0.521435i	$-0.174603\pi$
$572$		0			0
$573$	−1.31040	+	3.60030i	−1.31040	+	3.60030i
$574$		0			0
$575$		0			0
$576$	0.824486	−	4.67589i	0.824486	−	4.67589i
$577$	0.580554	+	0.102367i	0.580554	+	0.102367i	0.456211	−	0.889872i	$-0.349206\pi$
$577$	0.580554	+	0.102367i	0.580554	+	0.102367i	0.124344	+	0.992239i	$0.460317\pi$
$578$	1.35417	−	0.781831i	1.35417	−	0.781831i
$579$		0			0
$580$	−3.27044	+	1.19034i	−3.27044	+	1.19034i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−1.11068	−	0.641251i	−1.11068	−	0.641251i
$585$		0			0
$586$		−	0.543054i		−	0.543054i
$587$	−1.10952	+	0.195639i	−1.10952	+	0.195639i	−0.698237	−	0.715867i	$-0.746032\pi$
$587$	−1.10952	+	0.195639i	−1.10952	+	0.195639i	−0.411287	+	0.911506i	$0.634921\pi$
$588$	2.20293	−	1.84848i	2.20293	−	1.84848i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.349820	+	0.0707175i	0.349820	+	0.0707175i
$593$	1.80194			1.80194			0.900969	−	0.433884i	$-0.142857\pi$
$593$	1.80194			1.80194			0.900969	+	0.433884i	$0.142857\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.93888	−	0.518205i	2.93888	−	0.518205i
$598$		0			0
$599$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$599$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$600$	−0.549679	−	0.317357i	−0.549679	−	0.317357i
$601$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$601$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$602$		0			0
$603$		0			0
$604$	1.89626	−	0.690184i	1.89626	−	0.690184i
$605$	0.776236	+	0.925082i	0.776236	+	0.925082i
$606$	1.71657	−	0.991062i	1.71657	−	0.991062i
$607$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$607$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$608$	−0.435360	+	2.46905i	−0.435360	+	2.46905i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.286950	+	1.62737i	−0.286950	+	1.62737i	0.411287	+	0.911506i	$0.365079\pi$
$613$	−0.286950	+	1.62737i	−0.286950	+	1.62737i	−0.698237	+	0.715867i	$0.746032\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.857396	−	0.312066i	0.857396	−	0.312066i	0.124344	−	0.992239i	$-0.460317\pi$
$617$	0.857396	−	0.312066i	0.857396	−	0.312066i	0.733052	+	0.680173i	$0.238095\pi$
$618$	0.309834	−	0.536648i	0.309834	−	0.536648i
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$		0			0
$622$	−0.259718	−	1.47293i	−0.259718	−	1.47293i
$623$		0			0
$624$		0			0
$625$	−0.956225	+	0.802368i	−0.956225	+	0.802368i
$626$	−1.40546	−	0.511545i	−1.40546	−	0.511545i
$627$		0			0
$628$	−0.782752			−0.782752
$629$		0			0
$630$		0			0
$631$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$631$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$632$	−0.508017	−	0.184903i	−0.508017	−	0.184903i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.48017	+	2.56373i	1.48017	+	2.56373i
$640$	−0.757147	+	1.31142i	−0.757147	+	1.31142i
$641$	−1.65052	+	0.600739i	−1.65052	+	0.600739i	−0.988831	−	0.149042i	$-0.952381\pi$
$641$	−1.65052	+	0.600739i	−1.65052	+	0.600739i	−0.661686	+	0.749781i	$0.730159\pi$
$642$	−2.00022	−	2.38377i	−2.00022	−	2.38377i
$643$	−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
$645$	0.0416028	−	0.235941i	0.0416028	−	0.235941i
$646$		0			0
$647$	−0.592396	+	1.62760i	−0.592396	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$647$	−0.592396	+	1.62760i	−0.592396	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$648$	1.14323	−	3.14101i	1.14323	−	3.14101i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$653$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$654$	0.582297	−	0.211939i	0.582297	−	0.211939i
$655$	1.01442	−	1.75703i	1.01442	−	1.75703i
$656$		0			0
$657$	4.17937	+	3.50690i	4.17937	+	3.50690i
$658$		0			0
$659$	0.0259535	+	0.147190i	0.0259535	+	0.147190i	0.995031	−	0.0995678i	$-0.0317460\pi$
$659$	0.0259535	+	0.147190i	0.0259535	+	0.147190i	−0.969077	+	0.246757i	$0.920635\pi$
$660$		0			0
$661$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$661$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$662$		0			0
$663$		0			0
$664$	0.470704	+	1.29325i	0.470704	+	1.29325i
$665$		0			0
$666$	4.30900	+	1.69116i	4.30900	+	1.69116i
$667$		0			0
$668$	−0.672328	−	1.84721i	−0.672328	−	1.84721i
$669$	3.19139	+	1.16157i	3.19139	+	1.16157i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$673$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$674$		0			0
$675$	1.36969	+	1.14930i	1.36969	+	1.14930i
$676$	−0.722521	−	1.25144i	−0.722521	−	1.25144i
$677$	0.411287	−	0.712370i	0.411287	−	0.712370i	−0.583744	−	0.811938i	$-0.698413\pi$
$677$	0.411287	−	0.712370i	0.411287	−	0.712370i	0.995031	+	0.0995678i	$0.0317460\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$683$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$684$	−2.92529	+	8.03718i	−2.92529	+	8.03718i
$685$		0			0
$686$		0			0
$687$	−0.506642	+	2.87331i	−0.506642	+	2.87331i
$688$	−0.0350390	−	0.00617833i	−0.0350390	−	0.00617833i
$689$		0			0
$690$		0			0
$691$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$691$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	0.479617	+	2.72004i	0.479617	+	2.72004i
$697$		0			0
$698$		0			0
$699$	1.11391	−	0.934679i	1.11391	−	0.934679i
$700$		0			0
$701$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$701$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$702$		0			0
$703$	−1.86117	−	0.730455i	−1.86117	−	0.730455i
$704$		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	$0.5\pi$
$710$	−0.327899	−	1.85961i	−0.327899	−	1.85961i
$711$	1.99169	+	1.14990i	1.99169	+	1.14990i
$712$	−0.971824	−	0.815457i	−0.971824	−	0.815457i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.547570	+	0.652568i	0.547570	+	0.652568i
$717$		0			0
$718$	−3.07599	−	0.542379i	−3.07599	−	0.542379i
$719$	−0.229801	+	1.30327i	−0.229801	+	1.30327i	0.623490	+	0.781831i	$0.285714\pi$
$719$	−0.229801	+	1.30327i	−0.229801	+	1.30327i	−0.853291	+	0.521435i	$0.825397\pi$
$720$	0.820120	−	0.977381i	0.820120	−	0.977381i
$721$		0			0
$722$	1.60308	−	4.40443i	1.60308	−	4.40443i
$723$		0			0
$724$		0			0
$725$	−0.900188	−	0.158727i	−0.900188	−	0.158727i
$726$	2.69489	−	1.55589i	2.69489	−	1.55589i
$727$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$727$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$728$		0			0
$729$	−3.22789	+	5.59087i	−3.22789	+	5.59087i
$730$	−1.74002	−	3.01380i	−1.74002	−	3.01380i
$731$		0			0
$732$		0			0
$733$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$733$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$734$		−	1.69672i		−	1.69672i
$735$	2.36671	−	0.417314i	2.36671	−	0.417314i
$736$		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	$0.777778\pi$
$740$	−1.30840	−	1.15467i	−1.30840	−	1.15467i
$741$		0			0
$742$		0			0
$743$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$743$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$744$		0			0
$745$		0			0
$746$		−	2.49289i		−	2.49289i
$747$	−1.01663	−	5.76562i	−1.01663	−	5.76562i
$748$		0			0
$749$		0			0
$750$	1.01777	+	1.76283i	1.01777	+	1.76283i
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$	−2.00022	−	2.38377i	−2.00022	−	2.38377i
$754$		0			0
$755$	1.66077	+	0.292839i	1.66077	+	0.292839i
$756$		0			0
$757$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$757$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$758$	−0.746840	+	2.05193i	−0.746840	+	2.05193i
$759$		0			0
$760$	1.08002	−	1.28712i	1.08002	−	1.28712i
$761$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$761$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$762$		0			0
$763$		0			0
$764$	−1.78828	−	2.13119i	−1.78828	−	2.13119i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.544079	+	0.456537i	0.544079	+	0.456537i
$769$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$769$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$773$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$774$	−0.433641	−	0.157833i	−0.433641	−	0.157833i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		−	7.78060i		−	7.78060i
$784$	−0.0619743	−	0.351474i	−0.0619743	−	0.351474i
$785$	−0.566501	−	0.327069i	−0.566501	−	0.327069i
$786$	−4.00485	−	3.36047i	−4.00485	−	3.36047i
$787$	−0.411287	−	0.712370i	−0.411287	−	0.712370i	0.583744	−	0.811938i	$-0.301587\pi$
$787$	−0.411287	−	0.712370i	−0.411287	−	0.712370i	−0.995031	+	0.0995678i	$0.968254\pi$
$788$		0			0
$789$	2.98135	−	1.08512i	2.98135	−	1.08512i
$790$	−0.942942	−	1.12375i	−0.942942	−	1.12375i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.741134	+	2.03625i	−0.741134	+	2.03625i
$797$	−1.21863	+	1.45231i	−1.21863	+	1.45231i	−0.365341	+	0.930874i	$0.619048\pi$
$797$	−1.21863	+	1.45231i	−1.21863	+	1.45231i	−0.853291	+	0.521435i	$0.825397\pi$
$798$		0			0
$799$		0			0
$800$	−0.497717	+	0.287357i	−0.497717	+	0.287357i
$801$	3.46896	+	4.13415i	3.46896	+	4.13415i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$			0.443267i			0.443267i
$809$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$809$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$810$	6.94805	−	5.83011i	6.94805	−	5.83011i
$811$	0.233690	+	0.0850561i	0.233690	+	0.0850561i	0.456211	−	0.889872i	$-0.349206\pi$
$811$	0.233690	+	0.0850561i	0.233690	+	0.0850561i	−0.222521	+	0.974928i	$0.571429\pi$
$812$		0			0
$813$	−3.58597			−3.58597
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.187301	+	0.0681720i	0.187301	+	0.0681720i
$818$	1.34953	−	1.13239i	1.34953	−	1.13239i
$819$		0			0
$820$		0			0
$821$	0.00865834	+	0.0491039i	0.00865834	+	0.0491039i	0.988831	−	0.149042i	$-0.0476190\pi$
$821$	0.00865834	+	0.0491039i	0.00865834	+	0.0491039i	−0.980172	+	0.198146i	$0.936508\pi$
$822$		0			0
$823$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$823$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$824$	0.0692888	+	0.120012i	0.0692888	+	0.120012i
$825$		0			0
$826$		0			0
$827$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$827$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$828$		0			0
$829$	−1.86705	−	0.329212i	−1.86705	−	0.329212i	−0.878222	−	0.478254i	$-0.841270\pi$
$829$	−1.86705	−	0.329212i	−1.86705	−	0.329212i	−0.988831	+	0.149042i	$0.952381\pi$
$830$	−0.648473	+	3.67767i	−0.648473	+	3.67767i
$831$	0.381306	−	0.454423i	0.381306	−	0.454423i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.285263	−	1.61781i	0.285263	−	1.61781i
$836$		0			0
$837$		0			0
$838$	1.66091	+	1.97940i	1.66091	+	1.97940i
$839$	1.85839	−	0.676400i	1.85839	−	0.676400i	0.878222	−	0.478254i	$-0.158730\pi$
$839$	1.85839	−	0.676400i	1.85839	−	0.676400i	0.980172	−	0.198146i	$-0.0634921\pi$
$840$		0			0
$841$	1.48883	+	2.57873i	1.48883	+	2.57873i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	1.20761i		−	1.20761i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	−2.87572			−2.87572
$853$	0.555398	+	1.52594i	0.555398	+	1.52594i	0.826239	+	0.563320i	$0.190476\pi$
$853$	0.555398	+	1.52594i	0.555398	+	1.52594i	−0.270840	+	0.962624i	$0.587302\pi$
$854$		0			0
$855$	−5.47542	+	4.59442i	−5.47542	+	4.59442i
$856$	0.685323	−	0.120841i	0.685323	−	0.120841i
$857$			1.62388i			1.62388i	0.583744	+	0.811938i	$0.301587\pi$
$857$			1.62388i			1.62388i	−0.583744	+	0.811938i	$0.698413\pi$
$858$		0			0
$859$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$859$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$860$	0.133266	+	0.111824i	0.133266	+	0.111824i
$861$		0			0
$862$	1.48224	−	2.56731i	1.48224	−	2.56731i
$863$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$863$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$864$	−3.14449	−	3.74746i	−3.14449	−	3.74746i
$865$		0			0
$866$		0			0
$867$	0.345571	−	1.95983i	0.345571	−	1.95983i
$868$		0			0
$869$		0			0
$870$	−2.56331	+	7.04264i	−2.56331	+	7.04264i
$871$		0			0
$872$	−0.0240638	+	0.136472i	−0.0240638	+	0.136472i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−4.98020	+	1.81264i	−4.98020	+	1.81264i
$877$	0.955573	−	1.65510i	0.955573	−	1.65510i	0.222521	−	0.974928i	$-0.428571\pi$
$877$	0.955573	−	1.65510i	0.955573	−	1.65510i	0.733052	−	0.680173i	$-0.238095\pi$
$878$		0			0
$879$	−0.529445	−	0.444257i	−0.529445	−	0.444257i
$880$		0			0
$881$	0.0772807	+	0.438281i	0.0772807	+	0.438281i	0.998757	+	0.0498459i	$0.0158730\pi$
$881$	0.0772807	+	0.438281i	0.0772807	+	0.438281i	−0.921476	+	0.388435i	$0.873016\pi$
$882$		−	4.62898i		−	4.62898i
$883$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$883$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$	−1.08274	+	0.863455i	−1.08274	+	0.863455i
$889$		0			0
$890$	−1.17736	−	3.23478i	−1.17736	−	3.23478i
$891$		0			0
$892$	−1.88913	+	1.58517i	−1.88913	+	1.58517i
$893$		0			0
$894$		0			0
$895$	0.123620	+	0.701083i	0.123620	+	0.701083i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−1.84237	+	0.670567i	−1.84237	+	0.670567i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	1.48626	−	4.08346i	1.48626	−	4.08346i
$907$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$907$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$908$		0			0
$909$	0.327442	−	1.85701i	0.327442	−	1.85701i
$910$		0			0
$911$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$911$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$912$	0.912789	+	1.08782i	0.912789	+	1.08782i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−1.62293	−	1.36180i	−1.62293	−	1.36180i
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.145969	−	0.434453i	−0.145969	−	0.434453i
$926$	2.91115			2.91115
$927$	−0.201624	−	0.553959i	−0.201624	−	0.553959i
$928$	2.35008	+	0.855361i	2.35008	+	0.855361i
$929$	0.955242	−	0.801543i	0.955242	−	0.801543i	−0.0249307	−	0.999689i	$-0.507937\pi$
$929$	0.955242	−	0.801543i	0.955242	−	0.801543i	0.980172	+	0.198146i	$0.0634921\pi$
$930$		0			0
$931$			1.99938i			1.99938i
$932$	0.183349	+	1.03983i	0.183349	+	1.03983i
$933$	−1.64849	−	0.951755i	−1.64849	−	0.951755i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$937$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$938$		0			0
$939$	−1.64849	+	0.951755i	−1.64849	+	0.951755i
$940$		0			0
$941$	−0.340410	+	1.93056i	−0.340410	+	1.93056i	0.0249307	+	0.999689i	$0.492063\pi$
$941$	−0.340410	+	1.93056i	−0.340410	+	1.93056i	−0.365341	+	0.930874i	$0.619048\pi$
$942$	−1.08348	+	1.29124i	−1.08348	+	1.29124i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.0981772	−	0.0173113i	−0.0981772	−	0.0173113i	0.124344	−	0.992239i	$-0.460317\pi$
$947$	−0.0981772	−	0.0173113i	−0.0981772	−	0.0173113i	−0.222521	+	0.974928i	$0.571429\pi$
$948$	−1.93475	+	1.11703i	−1.93475	+	1.11703i
$949$		0			0
$950$	1.34646	−	0.490070i	1.34646	−	0.490070i
$951$		0			0
$952$		0			0
$953$	0.190506	+	0.159853i	0.190506	+	0.159853i	0.733052	−	0.680173i	$-0.238095\pi$
$953$	0.190506	+	0.159853i	0.190506	+	0.159853i	−0.542546	+	0.840026i	$0.682540\pi$
$954$		0			0
$955$	−0.403723	−	2.28963i	−0.403723	−	2.28963i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	1.31830	+	3.62201i	1.31830	+	3.62201i
$961$	−1.00000			−1.00000
$962$		0			0
$963$	−2.96034			−2.96034
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$967$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$968$			0.695895i			0.695895i
$969$		0			0
$970$		0			0
$971$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.939693	+	0.342020i	$0.111111\pi$
$971$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.500000	+	0.866025i	$0.333333\pi$
$972$	−4.08777	−	7.08023i	−4.08777	−	7.08023i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.486017	−	0.0856979i	−0.486017	−	0.0856979i	−0.0747301	−	0.997204i	$-0.523810\pi$
$977$	−0.486017	−	0.0856979i	−0.486017	−	0.0856979i	−0.411287	+	0.911506i	$0.634921\pi$
$978$		0			0
$979$		0			0
$980$	−0.596841	+	1.63981i	−0.596841	+	1.63981i
$981$	0.201624	−	0.553959i	0.201624	−	0.553959i
$982$		0			0
$983$	0.216536	−	1.22804i	0.216536	−	1.22804i	−0.661686	−	0.749781i	$-0.730159\pi$
$983$	0.216536	−	1.22804i	0.216536	−	1.22804i	0.878222	−	0.478254i	$-0.158730\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$991$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.38722	+	1.16401i	−1.38722	+	1.16401i
$996$	5.34423	+	1.94514i	5.34423	+	1.94514i
$997$	0.608708	+	1.67241i	0.608708	+	1.67241i	0.733052	+	0.680173i	$0.238095\pi$
$997$	0.608708	+	1.67241i	0.608708	+	1.67241i	−0.124344	+	0.992239i	$0.539683\pi$
$998$	2.53919			2.53919
$999$	3.42612	−	1.86577i	3.42612	−	1.86577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2627.1.x.b.141.5	✓	36
37.21	even	18	inner	2627.1.x.b.354.5	yes	36
71.70	odd	2	CM	2627.1.x.b.141.5	✓	36
2627.354	odd	18	inner	2627.1.x.b.354.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2627.1.x.b.141.5	✓	36	1.1	even	1	trivial
2627.1.x.b.141.5	✓	36	71.70	odd	2	CM
2627.1.x.b.354.5	yes	36	37.21	even	18	inner
2627.1.x.b.354.5	yes	36	2627.354	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)

\(f(q)\)	\(=\)	\(q+(0.534804 + 1.46936i) q^{2} +(1.87005 + 0.680641i) q^{3} +(-1.10697 + 0.928855i) q^{4} +(-1.18926 + 0.209699i) q^{5} +3.11179i q^{6} +(-0.602663 - 0.347948i) q^{8} +(2.26776 + 1.90287i) q^{9} +O(q^{10})\)	\(q+(0.534804 + 1.46936i) q^{2} +(1.87005 + 0.680641i) q^{3} +(-1.10697 + 0.928855i) q^{4} +(-1.18926 + 0.209699i) q^{5} +3.11179i q^{6} +(-0.602663 - 0.347948i) q^{8} +(2.26776 + 1.90287i) q^{9} +(-0.944147 - 1.63531i) q^{10} +(-2.70229 + 0.983555i) q^{12} +(-2.36671 - 0.417314i) q^{15} +(-0.0619743 + 0.351474i) q^{16} +(-1.58321 + 4.34982i) q^{18} +(0.683828 - 1.87880i) q^{19} +(1.12169 - 1.33678i) q^{20} +(-0.890180 - 1.06088i) q^{24} +(0.430679 - 0.156754i) q^{25} +(1.95060 + 3.37854i) q^{27} +(-1.72721 - 0.997204i) q^{29} +(-0.652539 - 3.70073i) q^{30} +(-1.23491 + 0.217748i) q^{32} -4.27782 q^{36} +(0.0249307 - 0.999689i) q^{37} +3.12635 q^{38} +(0.789689 + 0.287423i) q^{40} +0.0996918i q^{43} +(-3.09599 - 1.78747i) q^{45} +(-0.355122 + 0.615090i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(0.460658 + 0.548991i) q^{50} +(-3.92112 + 4.67300i) q^{54} +(2.55758 - 3.04800i) q^{57} +(0.541536 - 3.07120i) q^{58} +(3.00749 - 1.73637i) q^{60} +(-0.801938 - 1.38900i) q^{64} +(0.939693 + 0.342020i) q^{71} +(-0.704593 - 1.93585i) q^{72} +1.84295 q^{73} +(1.48224 - 0.498006i) q^{74} +0.912083 q^{75} +(0.988160 + 2.71495i) q^{76} +(0.765067 - 0.134902i) q^{79} -0.430991i q^{80} +(0.834084 + 4.73032i) q^{81} +(-1.51498 - 1.27122i) q^{83} +(-0.146483 + 0.0533156i) q^{86} +(-2.55122 - 3.04043i) q^{87} +(1.79532 + 0.316563i) q^{89} +(0.970693 - 5.50507i) q^{90} +(-0.419268 + 2.37779i) q^{95} +(-2.45755 - 0.433332i) q^{96} +(-1.00510 - 1.19784i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{3} + 3 q^{5} - 6 q^{9}+O(q^{10}) \) 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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