LMFDB - Embedded newform 2627.1.x.b.1064.5

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			1064.5
Root			$-0.318487 - 0.947927i$ of defining polynomial
Character	$\chi$	$=$	2627.1064
Dual form			2627.1.x.b.1632.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53991 - 0.271527i) q^{2} +(-0.0940619 + 0.533452i) q^{3} +(1.35790 - 0.494233i) q^{4} +(1.07992 - 1.28699i) q^{5} +0.847006i q^{6} +(0.602663 - 0.347948i) q^{8} +(0.663970 + 0.241665i) q^{9} +O(q^{10})$	\(q+(1.53991 - 0.271527i) q^{2} +(-0.0940619 + 0.533452i) q^{3} +(1.35790 - 0.494233i) q^{4} +(1.07992 - 1.28699i) q^{5} +0.847006i q^{6} +(0.602663 - 0.347948i) q^{8} +(0.663970 + 0.241665i) q^{9} +(1.31352 - 2.27508i) q^{10} +(0.135923 + 0.770860i) q^{12} +(0.584970 + 0.697140i) q^{15} +(-0.273398 + 0.229408i) q^{16} +(1.08807 + 0.191856i) q^{18} +(-1.86705 - 0.329212i) q^{19} +(0.830338 - 2.28133i) q^{20} +(0.128926 + 0.354220i) q^{24} +(-0.316487 - 1.79489i) q^{25} +(-0.462211 + 0.800574i) q^{27} +(-0.975699 + 0.563320i) q^{29} +(1.09009 + 0.914696i) q^{30} +(-0.806030 + 0.960589i) q^{32} +1.02104 q^{36} +(0.318487 + 0.947927i) q^{37} -2.96448 q^{38} +(0.203019 - 1.15138i) q^{40} -1.20761i q^{43} +(1.02805 - 0.593547i) q^{45} +(-0.0966618 - 0.167423i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-0.974720 - 2.67802i) q^{50} +(-0.494385 + 1.35831i) q^{54} +(0.351237 - 0.965016i) q^{57} +(-1.34953 + 1.13239i) q^{58} +(1.13888 + 0.657532i) q^{60} +(-0.801938 + 1.38900i) q^{64} +(-0.173648 + 0.984808i) q^{71} +(0.484237 - 0.0853840i) q^{72} +0.912421 q^{73} +(0.747828 + 1.37324i) q^{74} +0.987254 q^{75} +(-2.69797 + 0.475725i) q^{76} +(1.14400 - 1.36336i) q^{79} +0.599604i q^{80} +(0.157682 + 0.132311i) q^{81} +(-0.686617 - 0.249908i) q^{83} +(-0.327899 - 1.85961i) q^{86} +(-0.208728 - 0.573475i) q^{87} +(-0.920301 - 1.09677i) q^{89} +(1.42194 - 1.19315i) q^{90} +(-2.43995 + 2.04736i) q^{95} +(-0.436611 - 0.520333i) q^{96} +(0.534804 + 1.46936i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.53991	−	0.271527i	1.53991	−	0.271527i	0.661686	−	0.749781i	$-0.269841\pi$
$2$	1.53991	−	0.271527i	1.53991	−	0.271527i	0.878222	+	0.478254i	$0.158730\pi$
$3$	−0.0940619	+	0.533452i	−0.0940619	+	0.533452i	0.900969	+	0.433884i	$0.142857\pi$
$3$	−0.0940619	+	0.533452i	−0.0940619	+	0.533452i	−0.995031	+	0.0995678i	$0.968254\pi$
$4$	1.35790	−	0.494233i	1.35790	−	0.494233i
$5$	1.07992	−	1.28699i	1.07992	−	1.28699i	0.124344	−	0.992239i	$-0.460317\pi$
$5$	1.07992	−	1.28699i	1.07992	−	1.28699i	0.955573	−	0.294755i	$-0.0952381\pi$
$6$			0.847006i			0.847006i
$7$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$7$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$8$	0.602663	−	0.347948i	0.602663	−	0.347948i
$9$	0.663970	+	0.241665i	0.663970	+	0.241665i
$10$	1.31352	−	2.27508i	1.31352	−	2.27508i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	0.135923	+	0.770860i	0.135923	+	0.770860i
$13$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$13$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$14$		0			0
$15$	0.584970	+	0.697140i	0.584970	+	0.697140i
$16$	−0.273398	+	0.229408i	−0.273398	+	0.229408i
$17$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$17$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$18$	1.08807	+	0.191856i	1.08807	+	0.191856i
$19$	−1.86705	−	0.329212i	−1.86705	−	0.329212i	−0.878222	−	0.478254i	$-0.841270\pi$
$19$	−1.86705	−	0.329212i	−1.86705	−	0.329212i	−0.988831	+	0.149042i	$0.952381\pi$
$20$	0.830338	−	2.28133i	0.830338	−	2.28133i
$21$		0			0
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	0.128926	+	0.354220i	0.128926	+	0.354220i
$25$	−0.316487	−	1.79489i	−0.316487	−	1.79489i
$26$		0			0
$27$	−0.462211	+	0.800574i	−0.462211	+	0.800574i
$28$		0			0
$29$	−0.975699	+	0.563320i	−0.975699	+	0.563320i	−0.900969	−	0.433884i	$-0.857143\pi$
$29$	−0.975699	+	0.563320i	−0.975699	+	0.563320i	−0.0747301	+	0.997204i	$0.523810\pi$
$30$	1.09009	+	0.914696i	1.09009	+	0.914696i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−0.806030	+	0.960589i	−0.806030	+	0.960589i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	1.02104			1.02104
$37$	0.318487	+	0.947927i	0.318487	+	0.947927i
$37$	0.318487	+	0.947927i	0.318487	+	0.947927i
$38$	−2.96448			−2.96448
$39$		0			0
$40$	0.203019	−	1.15138i	0.203019	−	1.15138i
$41$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$41$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$42$		0			0
$43$		−	1.20761i		−	1.20761i	−0.797133	−	0.603804i	$-0.793651\pi$
$43$		−	1.20761i		−	1.20761i	0.797133	−	0.603804i	$-0.206349\pi$
$44$		0			0
$45$	1.02805	−	0.593547i	1.02805	−	0.593547i
$46$		0			0
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	−0.0966618	−	0.167423i	−0.0966618	−	0.167423i
$49$	0.173648	+	0.984808i	0.173648	+	0.984808i
$50$	−0.974720	−	2.67802i	−0.974720	−	2.67802i
$51$		0			0
$52$		0			0
$53$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$53$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$54$	−0.494385	+	1.35831i	−0.494385	+	1.35831i
$55$		0			0
$56$		0			0
$57$	0.351237	−	0.965016i	0.351237	−	0.965016i
$58$	−1.34953	+	1.13239i	−1.34953	+	1.13239i
$59$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$59$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$60$	1.13888	+	0.657532i	1.13888	+	0.657532i
$61$		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
$64$	−0.801938	+	1.38900i	−0.801938	+	1.38900i
$65$		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
$72$	0.484237	−	0.0853840i	0.484237	−	0.0853840i
$73$	0.912421			0.912421			0.456211	−	0.889872i	$-0.349206\pi$
$73$	0.912421			0.912421			0.456211	+	0.889872i	$0.349206\pi$
$74$	0.747828	+	1.37324i	0.747828	+	1.37324i
$75$	0.987254			0.987254
$76$	−2.69797	+	0.475725i	−2.69797	+	0.475725i
$77$		0			0
$78$		0			0
$79$	1.14400	−	1.36336i	1.14400	−	1.36336i	0.222521	−	0.974928i	$-0.428571\pi$
$79$	1.14400	−	1.36336i	1.14400	−	1.36336i	0.921476	−	0.388435i	$-0.126984\pi$
$80$			0.599604i			0.599604i
$81$	0.157682	+	0.132311i	0.157682	+	0.132311i
$82$		0			0
$83$	−0.686617	−	0.249908i	−0.686617	−	0.249908i	−0.0249307	−	0.999689i	$-0.507937\pi$
$83$	−0.686617	−	0.249908i	−0.686617	−	0.249908i	−0.661686	+	0.749781i	$0.730159\pi$
$84$		0			0
$85$		0			0
$86$	−0.327899	−	1.85961i	−0.327899	−	1.85961i
$87$	−0.208728	−	0.573475i	−0.208728	−	0.573475i
$88$		0			0
$89$	−0.920301	−	1.09677i	−0.920301	−	1.09677i	−0.995031	−	0.0995678i	$-0.968254\pi$
$89$	−0.920301	−	1.09677i	−0.920301	−	1.09677i	0.0747301	−	0.997204i	$-0.476190\pi$
$90$	1.42194	−	1.19315i	1.42194	−	1.19315i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.43995	+	2.04736i	−2.43995	+	2.04736i
$96$	−0.436611	−	0.520333i	−0.436611	−	0.520333i
$97$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$97$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$98$	0.534804	+	1.46936i	0.534804	+	1.46936i
$99$		0			0
$100$	−1.31685	−	2.28085i	−1.31685	−	2.28085i
$101$	0.878222	−	1.52112i	0.878222	−	1.52112i	0.0249307	−	0.999689i	$-0.492063\pi$
$101$	0.878222	−	1.52112i	0.878222	−	1.52112i	0.853291	−	0.521435i	$-0.174603\pi$
$102$		0			0
$103$	−1.66731	+	0.962624i	−1.66731	+	0.962624i	−0.698237	+	0.715867i	$0.746032\pi$
$103$	−1.66731	+	0.962624i	−1.66731	+	0.962624i	−0.969077	+	0.246757i	$0.920635\pi$
$104$		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	$0.222222\pi$
$108$	−0.231964	+	1.31554i	−0.231964	+	1.31554i
$109$	1.89600	−	0.334316i	1.89600	−	0.334316i	0.900969	−	0.433884i	$-0.142857\pi$
$109$	1.89600	−	0.334316i	1.89600	−	0.334316i	0.995031	+	0.0995678i	$0.0317460\pi$
$110$		0			0
$111$	−0.535631	+	0.0807334i	−0.535631	+	0.0807334i
$112$		0			0
$113$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$113$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$114$	0.278844	−	1.58141i	0.278844	−	1.58141i
$115$		0			0
$116$	−1.04649	+	1.24715i	−1.04649	+	1.24715i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.595108	+	0.216602i	0.595108	+	0.216602i
$121$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.19682	−	0.690984i	−1.19682	−	0.690984i
$126$		0			0
$127$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$127$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$128$	−0.428880	+	1.17834i	−0.428880	+	1.17834i
$129$	0.644201	+	0.113590i	0.644201	+	0.113590i
$130$		0			0
$131$	−0.265705	+	0.730019i	−0.265705	+	0.730019i	0.733052	+	0.680173i	$0.238095\pi$
$131$	−0.265705	+	0.730019i	−0.265705	+	0.730019i	−0.998757	+	0.0498459i	$0.984127\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.531184	+	1.45942i	0.531184	+	1.45942i
$136$		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
$142$			1.56366i			1.56366i
$143$		0			0
$144$	−0.236968	+	0.0862493i	−0.236968	+	0.0862493i
$145$	−0.328684	+	1.86406i	−0.328684	+	1.86406i
$146$	1.40504	−	0.247747i	1.40504	−	0.247747i
$147$	−0.541681			−0.541681
$148$	0.900969	+	1.12978i	0.900969	+	1.12978i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	1.52028	−	0.268066i	1.52028	−	0.268066i
$151$	−0.202732	+	1.14975i	−0.202732	+	1.14975i	0.698237	+	0.715867i	$0.253968\pi$
$151$	−0.202732	+	1.14975i	−0.202732	+	1.14975i	−0.900969	+	0.433884i	$0.857143\pi$
$152$	−1.23975	+	0.451233i	−1.23975	+	0.451233i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.772967	+	0.281337i	0.772967	+	0.281337i	0.698237	−	0.715867i	$-0.253968\pi$
$157$	0.772967	+	0.281337i	0.772967	+	0.281337i	0.0747301	+	0.997204i	$0.476190\pi$
$158$	1.39146	−	2.41008i	1.39146	−	2.41008i
$159$		0			0
$160$	0.365828	+	2.07471i	0.365828	+	2.07471i
$161$		0			0
$162$	0.278742	+	0.160932i	0.278742	+	0.160932i
$163$		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
$166$	−1.12518	−	0.198400i	−1.12518	−	0.198400i
$167$	−0.580554	−	0.102367i	−0.580554	−	0.102367i	−0.124344	−	0.992239i	$-0.539683\pi$
$167$	−0.580554	−	0.102367i	−0.580554	−	0.102367i	−0.456211	+	0.889872i	$0.650794\pi$
$168$		0			0
$169$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$170$		0			0
$171$	−1.16011	−	0.669788i	−1.16011	−	0.669788i
$172$	−0.596841	−	1.63981i	−0.596841	−	1.63981i
$173$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$173$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$174$	−0.477136	−	0.826423i	−0.477136	−	0.826423i
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−1.71498	−	1.43904i	−1.71498	−	1.43904i
$179$		−	1.36035i		−	1.36035i	−0.733052	−	0.680173i	$-0.761905\pi$
$179$		−	1.36035i		−	1.36035i	0.733052	−	0.680173i	$-0.238095\pi$
$180$	1.10264	−	1.31407i	1.10264	−	1.31407i
$181$		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
$185$	1.56392	+	0.613792i	1.56392	+	0.613792i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−3.20139	+	3.81527i	−3.20139	+	3.81527i
$191$			1.82301i			1.82301i	0.411287	+	0.911506i	$0.365079\pi$
$191$			1.82301i			1.82301i	−0.411287	+	0.911506i	$0.634921\pi$
$192$	−0.665531	−	0.558447i	−0.665531	−	0.558447i
$193$		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
$196$	0.722521	+	1.25144i	0.722521	+	1.25144i
$197$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$197$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$198$		0			0
$199$	−1.73151	−	0.999689i	−1.73151	−	0.999689i	−0.878222	−	0.478254i	$-0.841270\pi$
$199$	−1.73151	−	0.999689i	−1.73151	−	0.999689i	−0.853291	−	0.521435i	$-0.825397\pi$
$200$	−0.815261	−	0.971590i	−0.815261	−	0.971590i
$201$		0			0
$202$	0.939353	−	2.58085i	0.939353	−	2.58085i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−2.30613	+	1.93507i	−2.30613	+	1.93507i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$		0			0
$213$	−0.509014	−	0.185266i	−0.509014	−	0.185266i
$214$	1.35417	−	0.781831i	1.35417	−	0.781831i
$215$	−1.55419	−	1.30412i	−1.55419	−	1.30412i
$216$			0.643302i			0.643302i
$217$		0			0
$218$	2.82889	−	1.02963i	2.82889	−	1.02963i
$219$	−0.0858241	+	0.486733i	−0.0858241	+	0.486733i
$220$		0			0
$221$		0			0
$222$	−0.802901	+	0.269760i	−0.802901	+	0.269760i
$223$	1.32337			1.32337			0.661686	−	0.749781i	$-0.269841\pi$
$223$	1.32337			1.32337			0.661686	+	0.749781i	$0.269841\pi$
$224$		0			0
$225$	0.223624	−	1.26823i	0.223624	−	1.26823i
$226$		0			0
$227$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$227$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$228$		−	1.48398i		−	1.48398i
$229$	−1.46402	−	1.22846i	−1.46402	−	1.22846i	−0.921476	−	0.388435i	$-0.873016\pi$
$229$	−1.46402	−	1.22846i	−1.46402	−	1.22846i	−0.542546	−	0.840026i	$-0.682540\pi$
$230$		0			0
$231$		0			0
$232$	−0.392012	+	0.678985i	−0.392012	+	0.678985i
$233$	−0.988831	−	1.71271i	−0.988831	−	1.71271i	−0.623490	−	0.781831i	$-0.714286\pi$
$233$	−0.988831	−	1.71271i	−0.988831	−	1.71271i	−0.365341	−	0.930874i	$-0.619048\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.619681	+	0.738508i	0.619681	+	0.738508i
$238$		0			0
$239$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$239$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$240$	−0.319859	−	0.0563999i	−0.319859	−	0.0563999i
$241$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$241$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$242$	−0.534804	+	1.46936i	−0.534804	+	1.46936i
$243$	−0.793562	+	0.665878i	−0.793562	+	0.665878i
$244$		0			0
$245$	1.45497	+	0.840026i	1.45497	+	0.840026i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	0.197898	−	0.342770i	0.197898	−	0.342770i
$250$	−2.03061	−	0.739082i	−2.03061	−	0.739082i
$251$	1.35417	−	0.781831i	1.35417	−	0.781831i	0.365341	−	0.930874i	$-0.380952\pi$
$251$	1.35417	−	0.781831i	1.35417	−	0.781831i	0.988831	+	0.149042i	$0.0476190\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.0619743	+	0.351474i	−0.0619743	+	0.351474i
$257$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$257$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$258$	1.02285			1.02285
$259$		0			0
$260$		0			0
$261$	−0.783969	+	0.138235i	−0.783969	+	0.138235i
$262$	−0.210941	+	1.19631i	−0.210941	+	1.19631i
$263$	1.01965	−	0.371124i	1.01965	−	0.371124i	0.222521	−	0.974928i	$-0.428571\pi$
$263$	1.01965	−	0.371124i	1.01965	−	0.371124i	0.797133	+	0.603804i	$0.206349\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.671640	−	0.387771i	0.671640	−	0.387771i
$268$		0			0
$269$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$269$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$270$	1.21425	+	2.10313i	1.21425	+	2.10313i
$271$	0.312903	+	1.77456i	0.312903	+	1.77456i	0.583744	+	0.811938i	$0.301587\pi$
$271$	0.312903	+	1.77456i	0.312903	+	1.77456i	−0.270840	+	0.962624i	$0.587302\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−1.83346	−	0.323289i	−1.83346	−	0.323289i	−0.853291	−	0.521435i	$-0.825397\pi$
$277$	−1.83346	−	0.323289i	−1.83346	−	0.323289i	−0.980172	+	0.198146i	$0.936508\pi$
$278$		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	$0.388889\pi$
$284$	0.250929	+	1.42309i	0.250929	+	1.42309i
$285$	−0.862663	−	1.49418i	−0.862663	−	1.49418i
$286$		0			0
$287$		0			0
$288$	−0.767321	+	0.443013i	−0.767321	+	0.443013i
$289$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$290$			2.95972i			2.95972i
$291$		0			0
$292$	1.23897	−	0.450949i	1.23897	−	0.450949i
$293$	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	$-0.222222\pi$
$294$	−0.834138	+	0.147081i	−0.834138	+	0.147081i
$295$		0			0
$296$	0.521769	+	0.460464i	0.521769	+	0.460464i
$297$		0			0
$298$		0			0
$299$		0			0
$300$	1.34059	−	0.487934i	1.34059	−	0.487934i
$301$		0			0
$302$			1.82556i			1.82556i
$303$	0.728839	+	0.611569i	0.728839	+	0.611569i
$304$	0.585972	−	0.338311i	0.585972	−	0.338311i
$305$		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
$309$	−0.356683	−	0.979978i	−0.356683	−	0.979978i
$310$		0			0
$311$	0.254732	+	0.303578i	0.254732	+	0.303578i	0.878222	−	0.478254i	$-0.158730\pi$
$311$	0.254732	+	0.303578i	0.254732	+	0.303578i	−0.623490	+	0.781831i	$0.714286\pi$
$312$		0			0
$313$	−0.135540	+	0.372393i	−0.135540	+	0.372393i	−0.988831	−	0.149042i	$-0.952381\pi$
$313$	−0.135540	+	0.372393i	−0.135540	+	0.372393i	0.853291	+	0.521435i	$0.174603\pi$
$314$	1.26669	+	0.223351i	1.26669	+	0.223351i
$315$		0			0
$316$	0.879609	−	2.41671i	0.879609	−	2.41671i
$317$		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
$320$	0.921605	+	2.53209i	0.921605	+	2.53209i
$321$	0.0940619	+	0.533452i	0.0940619	+	0.533452i
$322$		0			0
$323$		0			0
$324$	0.279509	+	0.101733i	0.279509	+	0.101733i
$325$		0			0
$326$		0			0
$327$			1.04287i			1.04287i
$328$		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	$0.944444\pi$
$332$	−1.05587			−1.05587
$333$	−0.0176156	+	0.706362i	−0.0176156	+	0.706362i
$334$	−0.921795			−0.921795
$335$		0			0
$336$		0			0
$337$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$337$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$338$	−1.00510	+	1.19784i	−1.00510	+	1.19784i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−1.96832	−	0.716411i	−1.96832	−	0.716411i
$343$		0			0
$344$	−0.420185	−	0.727781i	−0.420185	−	0.727781i
$345$		0			0
$346$		0			0
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$	−0.566861	−	0.675559i	−0.566861	−	0.675559i
$349$		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
$355$	1.07992	+	1.28699i	1.07992	+	1.28699i
$356$	−1.79173	−	1.03446i	−1.79173	−	1.03446i
$357$		0			0
$358$	−0.369371	−	2.09481i	−0.369371	−	2.09481i
$359$	−0.797133	−	1.38067i	−0.797133	−	1.38067i	−0.921476	−	0.388435i	$-0.873016\pi$
$359$	−0.797133	−	1.38067i	−0.797133	−	1.38067i	0.124344	−	0.992239i	$-0.460317\pi$
$360$	0.413047	−	0.715418i	0.413047	−	0.715418i
$361$	2.43781	+	0.887291i	2.43781	+	0.887291i
$362$		0			0
$363$	−0.414952	−	0.348186i	−0.414952	−	0.348186i
$364$		0			0
$365$	0.985339	−	1.17428i	0.985339	−	1.17428i
$366$		0			0
$367$	0.320025	−	1.81495i	0.320025	−	1.81495i	−0.222521	−	0.974928i	$-0.571429\pi$
$367$	0.320025	−	1.81495i	0.320025	−	1.81495i	0.542546	−	0.840026i	$-0.317460\pi$
$368$		0			0
$369$		0			0
$370$	2.57495	+	0.520537i	2.57495	+	0.520537i
$371$		0			0
$372$		0			0
$373$	−0.188424	+	1.06861i	−0.188424	+	1.06861i	0.733052	+	0.680173i	$0.238095\pi$
$373$	−0.188424	+	1.06861i	−0.188424	+	1.06861i	−0.921476	+	0.388435i	$0.873016\pi$
$374$		0			0
$375$	0.481181	−	0.573450i	0.481181	−	0.573450i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.09708	+	0.399304i	1.09708	+	0.399304i	0.826239	−	0.563320i	$-0.190476\pi$
$379$	1.09708	+	0.399304i	1.09708	+	0.399304i	0.270840	+	0.962624i	$0.412698\pi$
$380$	−2.30133	+	3.98601i	−2.30133	+	3.98601i
$381$		0			0
$382$	0.494997	+	2.80727i	0.494997	+	2.80727i
$383$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$383$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$384$	−0.588245	−	0.339623i	−0.588245	−	0.339623i
$385$		0			0
$386$		0			0
$387$	0.291837	−	0.801816i	0.291837	−	0.801816i
$388$		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
$392$	0.447313	+	0.533087i	0.447313	+	0.533087i
$393$	−0.364437	−	0.210408i	−0.364437	−	0.210408i
$394$		0			0
$395$	−0.519219	−	2.94464i	−0.519219	−	2.94464i
$396$		0			0
$397$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$397$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$398$	−2.93781	−	1.06928i	−2.93781	−	1.06928i
$399$		0			0
$400$	0.498288	+	0.418114i	0.498288	+	0.418114i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$		0			0
$404$	0.440742	−	2.49957i	0.440742	−	2.49957i
$405$	0.340567	−	0.0600512i	0.340567	−	0.0600512i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	1.96411	−	0.346325i	1.96411	−	0.346325i	0.969077	−	0.246757i	$-0.0793651\pi$
$409$	1.96411	−	0.346325i	1.96411	−	0.346325i	0.995031	−	0.0995678i	$-0.0317460\pi$
$410$		0			0
$411$		0			0
$412$	−1.78828	+	2.13119i	−1.78828	+	2.13119i
$413$		0			0
$414$		0			0
$415$	−1.06312	+	0.613792i	−1.06312	+	0.613792i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.0259535	−	0.147190i	−0.0259535	−	0.147190i	0.969077	−	0.246757i	$-0.0793651\pi$
$419$	−0.0259535	−	0.147190i	−0.0259535	−	0.147190i	−0.995031	+	0.0995678i	$0.968254\pi$
$420$		0			0
$421$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$421$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−0.834138	−	0.147081i	−0.834138	−	0.147081i
$427$		0			0
$428$	1.10697	−	0.928855i	1.10697	−	0.928855i
$429$		0			0
$430$	−2.74741	−	1.58622i	−2.74741	−	1.58622i
$431$	0.327145	+	0.898823i	0.327145	+	0.898823i	0.988831	+	0.149042i	$0.0476190\pi$
$431$	0.327145	+	0.898823i	0.327145	+	0.898823i	−0.661686	+	0.749781i	$0.730159\pi$
$432$	−0.0572905	−	0.324910i	−0.0572905	−	0.324910i
$433$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$433$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$434$		0			0
$435$	−0.963468	−	0.350674i	−0.963468	−	0.350674i
$436$	2.40934	−	1.39103i	2.40934	−	1.39103i
$437$		0			0
$438$			0.772827i			0.772827i
$439$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$439$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$440$		0			0
$441$	−0.122697	+	0.695847i	−0.122697	+	0.695847i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	−0.687429	+	0.374354i	−0.687429	+	0.374354i
$445$	−2.40539			−2.40539
$446$	2.03787	−	0.359331i	2.03787	−	0.359331i
$447$		0			0
$448$		0			0
$449$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$449$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$450$		−	2.01368i		−	2.01368i
$451$		0			0
$452$		0			0
$453$	−0.594267	−	0.216295i	−0.594267	−	0.216295i
$454$		0			0
$455$		0			0
$456$	−0.124097	−	0.703792i	−0.124097	−	0.703792i
$457$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$457$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$458$	−2.58802	−	1.49419i	−2.58802	−	1.49419i
$459$		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
$463$	−0.293556	−	0.0517618i	−0.293556	−	0.0517618i	0.0249307	−	0.999689i	$-0.492063\pi$
$463$	−0.293556	−	0.0517618i	−0.293556	−	0.0517618i	−0.318487	+	0.947927i	$0.603175\pi$
$464$	0.137524	−	0.377844i	0.137524	−	0.377844i
$465$		0			0
$466$	−1.98775	−	2.36891i	−1.98775	−	2.36891i
$467$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$467$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.222786	+	0.385877i	−0.222786	+	0.385877i
$472$		0			0
$473$		0			0
$474$	1.15478	+	0.968973i	1.15478	+	0.968973i
$475$			3.45534i			3.45534i
$476$		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	$0.944444\pi$
$480$	−1.14117			−1.14117
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.250929	+	1.42309i	−0.250929	+	1.42309i
$485$		0			0
$486$	−1.04121	+	1.24086i	−1.04121	+	1.24086i
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$		0			0
$489$		0			0
$490$	2.46861	+	0.898499i	2.46861	+	0.898499i
$491$		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
$498$	0.211674	−	0.581569i	0.211674	−	0.581569i
$499$	0.486017	+	0.0856979i	0.486017	+	0.0856979i	0.411287	−	0.911506i	$-0.365079\pi$
$499$	0.486017	+	0.0856979i	0.486017	+	0.0856979i	0.0747301	+	0.997204i	$0.476190\pi$
$500$	−1.96666	−	0.346776i	−1.96666	−	0.346776i
$501$	0.109216	−	0.300069i	0.109216	−	0.300069i
$502$	1.87301	−	1.57164i	1.87301	−	1.57164i
$503$	−1.28198	−	1.52780i	−1.28198	−	1.52780i	−0.698237	−	0.715867i	$-0.746032\pi$
$503$	−1.28198	−	1.52780i	−1.28198	−	1.52780i	−0.583744	−	0.811938i	$-0.698413\pi$
$504$		0			0
$505$	−1.00927	−	2.77295i	−1.00927	−	2.77295i
$506$		0			0
$507$	−0.270840	−	0.469109i	−0.270840	−	0.469109i
$508$		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
$512$		−	0.695895i		−	0.695895i
$513$	1.12653	−	1.34255i	1.12653	−	1.34255i
$514$		0			0
$515$	−0.561668	+	3.18538i	−0.561668	+	3.18538i
$516$	0.930897	−	0.164142i	0.930897	−	0.164142i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.254586	+	1.44383i	−0.254586	+	1.44383i	0.542546	+	0.840026i	$0.317460\pi$
$521$	−0.254586	+	1.44383i	−0.254586	+	1.44383i	−0.797133	+	0.603804i	$0.793651\pi$
$522$	−1.16971	+	0.425738i	−1.16971	+	0.425738i
$523$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$523$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$524$			1.12261i			1.12261i
$525$		0			0
$526$	1.46940	−	0.848359i	1.46940	−	0.848359i
$527$		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
$534$	0.928973	−	0.779501i	0.928973	−	0.779501i
$535$	0.574612	−	1.57873i	0.574612	−	1.57873i
$536$		0			0
$537$	0.725678	+	0.127957i	0.725678	+	0.127957i
$538$		0			0
$539$		0			0
$540$	1.44258	+	1.71921i	1.44258	+	1.71921i
$541$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$541$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$542$	0.963684	+	2.64770i	0.963684	+	2.64770i
$543$		0			0
$544$		0			0
$545$	1.61726	−	2.80117i	1.61726	−	2.80117i
$546$		0			0
$547$	−0.903152	+	0.521435i	−0.903152	+	0.521435i	−0.878222	−	0.478254i	$-0.841270\pi$
$547$	−0.903152	+	0.521435i	−0.903152	+	0.521435i	−0.0249307	+	0.999689i	$0.507937\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.00713	−	0.730537i	2.00713	−	0.730537i
$552$		0			0
$553$		0			0
$554$	−2.91115			−2.91115
$555$	−0.474533	+	0.776539i	−0.474533	+	0.776539i
$556$		0			0
$557$	−1.59921	+	0.281983i	−1.59921	+	0.281983i	−0.900969	−	0.433884i	$-0.857143\pi$
$557$	−1.59921	+	0.281983i	−1.59921	+	0.281983i	−0.698237	+	0.715867i	$0.746032\pi$
$558$		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
$568$	0.238010	+	0.653928i	0.238010	+	0.653928i
$569$	1.68862	+	0.974928i	1.68862	+	0.974928i	0.955573	+	0.294755i	$0.0952381\pi$
$569$	1.68862	+	0.974928i	1.68862	+	0.974928i	0.733052	+	0.680173i	$0.238095\pi$
$570$	−1.73413	−	2.06666i	−1.73413	−	2.06666i
$571$	0.0381960	−	0.0320503i	0.0381960	−	0.0320503i	−0.623490	−	0.781831i	$-0.714286\pi$
$571$	0.0381960	−	0.0320503i	0.0381960	−	0.0320503i	0.661686	+	0.749781i	$0.269841\pi$
$572$		0			0
$573$	−0.972488	−	0.171476i	−0.972488	−	0.171476i
$574$		0			0
$575$		0			0
$576$	−0.868135	+	0.728451i	−0.868135	+	0.728451i
$577$	0.874413	+	1.04209i	0.874413	+	1.04209i	0.998757	+	0.0498459i	$0.0158730\pi$
$577$	0.874413	+	1.04209i	0.874413	+	1.04209i	−0.124344	+	0.992239i	$0.539683\pi$
$578$	−1.35417	−	0.781831i	−1.35417	−	0.781831i
$579$		0			0
$580$	0.474962	+	2.69364i	0.474962	+	2.69364i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.549883	−	0.317475i	0.549883	−	0.317475i
$585$		0			0
$586$		−	2.39567i		−	2.39567i
$587$	1.28198	−	1.52780i	1.28198	−	1.52780i	0.583744	−	0.811938i	$-0.301587\pi$
$587$	1.28198	−	1.52780i	1.28198	−	1.52780i	0.698237	−	0.715867i	$-0.253968\pi$
$588$	−0.735546	+	0.267717i	−0.735546	+	0.267717i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.304536	−	0.186098i	−0.304536	−	0.186098i
$593$	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
$597$	0.696155	−	0.829645i	0.696155	−	0.829645i
$598$		0			0
$599$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$599$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$600$	0.594981	−	0.343513i	0.594981	−	0.343513i
$601$		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
$604$	0.292956	+	1.66144i	0.292956	+	1.66144i
$605$	0.574612	+	1.57873i	0.574612	+	1.57873i
$606$	1.28840	+	0.743859i	1.28840	+	0.743859i
$607$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$607$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$608$	1.82114	−	1.52812i	1.82114	−	1.52812i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.114493	+	0.0960712i	−0.114493	+	0.0960712i	−0.698237	−	0.715867i	$-0.746032\pi$
$613$	−0.114493	+	0.0960712i	−0.114493	+	0.0960712i	0.583744	+	0.811938i	$0.301587\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.0431841	+	0.244909i	0.0431841	+	0.244909i	0.998757	−	0.0498459i	$-0.0158730\pi$
$617$	0.0431841	+	0.244909i	0.0431841	+	0.244909i	−0.955573	+	0.294755i	$0.904762\pi$
$618$	−0.815349	−	1.41223i	−0.815349	−	1.41223i
$619$		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
$622$	0.474693	+	0.398315i	0.474693	+	0.398315i
$623$		0			0
$624$		0			0
$625$	−0.469097	+	0.170737i	−0.469097	+	0.170737i
$626$	−0.107604	+	0.610253i	−0.107604	+	0.610253i
$627$		0			0
$628$	1.18865			1.18865
$629$		0			0
$630$		0			0
$631$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$631$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$632$	0.215066	−	1.21970i	0.215066	−	1.21970i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−0.353291	+	0.611918i	−0.353291	+	0.611918i
$640$	1.05336	+	1.82447i	1.05336	+	1.82447i
$641$	0.340410	+	1.93056i	0.340410	+	1.93056i	0.365341	+	0.930874i	$0.380952\pi$
$641$	0.340410	+	1.93056i	0.340410	+	1.93056i	−0.0249307	+	0.999689i	$0.507937\pi$
$642$	0.289693	+	0.795926i	0.289693	+	0.795926i
$643$	−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
$645$	0.841873	−	0.706415i	0.841873	−	0.706415i
$646$		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	$0.222222\pi$
$648$	0.141067	+	0.0248739i	0.141067	+	0.0248739i
$649$		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	$0.388889\pi$
$654$	0.283168	+	1.60592i	0.283168	+	1.60592i
$655$	0.652591	+	1.13032i	0.652591	+	1.13032i
$656$		0			0
$657$	0.605820	+	0.220500i	0.605820	+	0.220500i
$658$		0			0
$659$	1.26587	+	1.06219i	1.26587	+	1.06219i	0.995031	+	0.0995678i	$0.0317460\pi$
$659$	1.26587	+	1.06219i	1.26587	+	1.06219i	0.270840	+	0.962624i	$0.412698\pi$
$660$		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
$664$	−0.500753	+	0.0882963i	−0.500753	+	0.0882963i
$665$		0			0
$666$	0.164670	+	1.09252i	0.164670	+	1.09252i
$667$		0			0
$668$	−0.838925	+	0.147925i	−0.838925	+	0.147925i
$669$	−0.124479	+	0.705955i	−0.124479	+	0.705955i
$670$		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
$675$	1.58322	+	0.576246i	1.58322	+	0.576246i
$676$	−0.722521	+	1.25144i	−0.722521	+	1.25144i
$677$	−0.698237	−	1.20938i	−0.698237	−	1.20938i	−0.969077	−	0.246757i	$-0.920635\pi$
$677$	−0.698237	−	1.20938i	−0.698237	−	1.20938i	0.270840	−	0.962624i	$-0.412698\pi$
$678$		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	$0.611111\pi$
$684$	−1.90634	−	0.336138i	−1.90634	−	0.336138i
$685$		0			0
$686$		0			0
$687$	0.793033	−	0.665434i	0.793033	−	0.665434i
$688$	0.277035	+	0.330158i	0.277035	+	0.330158i
$689$		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
$696$	−0.325332	−	0.272986i	−0.325332	−	0.272986i
$697$		0			0
$698$		0			0
$699$	1.00666	−	0.366393i	1.00666	−	0.366393i
$700$		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
$703$	−0.282562	−	1.87468i	−0.282562	−	1.87468i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0			−	1.00000i	$-0.5\pi$
$709$		0			0				1.00000i	$0.5\pi$
$710$	2.01243	+	1.68863i	2.01243	+	1.68863i
$711$	1.08906	−	0.628767i	1.08906	−	0.628767i
$712$	−0.936251	−	0.340767i	−0.936251	−	0.340767i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.672328	−	1.84721i	−0.672328	−	1.84721i
$717$		0			0
$718$	−1.60240	−	1.90967i	−1.60240	−	1.90967i
$719$	−0.0381960	+	0.0320503i	−0.0381960	+	0.0320503i	−0.661686	−	0.749781i	$-0.730159\pi$
$719$	−0.0381960	+	0.0320503i	−0.0381960	+	0.0320503i	0.623490	+	0.781831i	$0.285714\pi$
$720$	−0.144903	+	0.398119i	−0.144903	+	0.398119i
$721$		0			0
$722$	3.99493	+	0.704414i	3.99493	+	0.704414i
$723$		0			0
$724$		0			0
$725$	1.31989	+	1.57298i	1.31989	+	1.57298i
$726$	−0.733529	−	0.423503i	−0.733529	−	0.423503i
$727$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$727$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$728$		0			0
$729$	−0.177650	−	0.307699i	−0.177650	−	0.307699i
$730$	1.19848	−	2.07583i	1.19848	−	2.07583i
$731$		0			0
$732$		0			0
$733$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$733$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$734$		−	2.88176i		−	2.88176i
$735$	−0.584970	+	0.697140i	−0.584970	+	0.697140i
$736$		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	$0.111111\pi$
$740$	2.42699	+	0.0605254i	2.42699	+	0.0605254i
$741$		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
$746$			1.69672i			1.69672i
$747$	−0.395498	−	0.331863i	−0.395498	−	0.331863i
$748$		0			0
$749$		0			0
$750$	0.585268	−	1.01371i	0.585268	−	1.01371i
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$		0			0
$753$	0.289693	+	0.795926i	0.289693	+	0.795926i
$754$		0			0
$755$	1.26079	+	1.50255i	1.26079	+	1.50255i
$756$		0			0
$757$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$757$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$758$	1.79782	+	0.317005i	1.79782	+	0.317005i
$759$		0			0
$760$	−0.758095	+	2.08285i	−0.758095	+	2.08285i
$761$		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
$764$	0.900993	+	2.47546i	0.900993	+	2.47546i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.181665	−	0.0661206i	−0.181665	−	0.0661206i
$769$		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	$0.888889\pi$
$774$	0.231687	−	1.31396i	0.231687	−	1.31396i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		−	1.04149i		−	1.04149i
$784$	−0.273398	−	0.229408i	−0.273398	−	0.229408i
$785$	1.19682	−	0.690984i	1.19682	−	0.690984i
$786$	−0.618330	−	0.225054i	−0.618330	−	0.225054i
$787$	0.698237	−	1.20938i	0.698237	−	1.20938i	−0.270840	−	0.962624i	$-0.587302\pi$
$787$	0.698237	−	1.20938i	0.698237	−	1.20938i	0.969077	−	0.246757i	$-0.0793651\pi$
$788$		0			0
$789$	0.102066	+	0.578844i	0.102066	+	0.578844i
$790$	−1.59910	−	4.39348i	−1.59910	−	4.39348i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−2.84529	−	0.501702i	−2.84529	−	0.501702i
$797$	0.327145	−	0.898823i	0.327145	−	0.898823i	−0.661686	−	0.749781i	$-0.730159\pi$
$797$	0.327145	−	0.898823i	0.327145	−	0.898823i	0.988831	−	0.149042i	$-0.0476190\pi$
$798$		0			0
$799$		0			0
$800$	1.97925	+	1.14272i	1.97925	+	1.14272i
$801$	−0.346000	−	0.950628i	−0.346000	−	0.950628i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		−	1.22230i		−	1.22230i
$809$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$809$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$810$	0.508137	−	0.184947i	0.508137	−	0.184947i
$811$	−0.346865	+	1.96717i	−0.346865	+	1.96717i	−0.124344	+	0.992239i	$0.539683\pi$
$811$	−0.346865	+	1.96717i	−0.346865	+	1.96717i	−0.222521	+	0.974928i	$0.571429\pi$
$812$		0			0
$813$	−0.976075			−0.976075
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−0.397559	+	2.25467i	−0.397559	+	2.25467i
$818$	2.93051	−	1.06662i	2.93051	−	1.06662i
$819$		0			0
$820$		0			0
$821$	0.487950	+	0.409439i	0.487950	+	0.409439i	0.853291	−	0.521435i	$-0.174603\pi$
$821$	0.487950	+	0.409439i	0.487950	+	0.409439i	−0.365341	+	0.930874i	$0.619048\pi$
$822$		0			0
$823$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$823$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$824$	−0.669886	+	1.16028i	−0.669886	+	1.16028i
$825$		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
$829$	−0.614831	−	0.732728i	−0.614831	−	0.732728i	0.365341	−	0.930874i	$-0.380952\pi$
$829$	−0.614831	−	0.732728i	−0.614831	−	0.732728i	−0.980172	+	0.198146i	$0.936508\pi$
$830$	−1.47044	+	1.23385i	−1.47044	+	1.23385i
$831$	0.344918	−	0.947655i	0.344918	−	0.947655i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.758697	+	0.636622i	−0.758697	+	0.636622i
$836$		0			0
$837$		0			0
$838$	−0.0799319	−	0.219611i	−0.0799319	−	0.219611i
$839$	0.126882	+	0.719581i	0.126882	+	0.719581i	0.980172	+	0.198146i	$0.0634921\pi$
$839$	0.126882	+	0.719581i	0.126882	+	0.719581i	−0.853291	+	0.521435i	$0.825397\pi$
$840$		0			0
$841$	0.134659	−	0.233236i	0.134659	−	0.233236i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			1.68005i			1.68005i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	−0.782752			−0.782752
$853$	0.486017	−	0.0856979i	0.486017	−	0.0856979i	0.0747301	−	0.997204i	$-0.476190\pi$
$853$	0.486017	−	0.0856979i	0.486017	−	0.0856979i	0.411287	+	0.911506i	$0.365079\pi$
$854$		0			0
$855$	−2.11483	+	0.769736i	−2.11483	+	0.769736i
$856$	0.447313	−	0.533087i	0.447313	−	0.533087i
$857$			0.493515i			0.493515i	0.969077	+	0.246757i	$0.0793651\pi$
$857$			0.493515i			0.493515i	−0.969077	+	0.246757i	$0.920635\pi$
$858$		0			0
$859$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$859$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$860$	−2.75496	−	1.00272i	−2.75496	−	1.00272i
$861$		0			0
$862$	0.747828	+	1.29528i	0.747828	+	1.29528i
$863$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$863$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$864$	−0.396466	−	1.08928i	−0.396466	−	1.08928i
$865$		0			0
$866$		0			0
$867$	0.414952	−	0.348186i	0.414952	−	0.348186i
$868$		0			0
$869$		0			0
$870$	−1.57887	−	0.278397i	−1.57887	−	0.278397i
$871$		0			0
$872$	1.02632	−	0.861189i	1.02632	−	0.861189i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	0.124019	+	0.703349i	0.124019	+	0.703349i
$877$	−0.733052	−	1.26968i	−0.733052	−	1.26968i	−0.955573	−	0.294755i	$-0.904762\pi$
$877$	−0.733052	−	1.26968i	−0.733052	−	1.26968i	0.222521	−	0.974928i	$-0.428571\pi$
$878$		0			0
$879$	0.779854	+	0.283844i	0.779854	+	0.283844i
$880$		0			0
$881$	0.340922	+	0.286067i	0.340922	+	0.286067i	0.797133	−	0.603804i	$-0.206349\pi$
$881$	0.340922	+	0.286067i	0.340922	+	0.286067i	−0.456211	+	0.889872i	$0.650794\pi$
$882$			1.10486i			1.10486i
$883$		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			$\pi$
$888$	−0.294714	+	0.235027i	−0.294714	+	0.235027i
$889$		0			0
$890$	−3.70407	+	0.653128i	−3.70407	+	0.653128i
$891$		0			0
$892$	1.79700	−	0.654055i	1.79700	−	0.654055i
$893$		0			0
$894$		0			0
$895$	−1.75076	−	1.46906i	−1.75076	−	1.46906i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.323146	−	1.83265i	−0.323146	−	1.83265i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−0.973846	−	0.171715i	−0.973846	−	0.171715i
$907$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$907$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$908$		0			0
$909$	0.950715	−	0.797745i	0.950715	−	0.797745i
$910$		0			0
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$	0.125355	+	0.344410i	0.125355	+	0.344410i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−2.59514	−	0.944552i	−2.59514	−	0.944552i
$917$		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
$925$	1.60062	−	0.871653i	1.60062	−	0.871653i
$926$	−0.466104			−0.466104
$927$	−1.33968	+	0.236222i	−1.33968	+	0.236222i
$928$	0.245324	−	1.39130i	0.245324	−	1.39130i
$929$	−1.17178	+	0.426492i	−1.17178	+	0.426492i	−0.853291	−	0.521435i	$-0.825397\pi$
$929$	−1.17178	+	0.426492i	−1.17178	+	0.426492i	−0.318487	+	0.947927i	$0.603175\pi$
$930$		0			0
$931$		−	1.89585i		−	1.89585i
$932$	−2.18920	−	1.83696i	−2.18920	−	1.83696i
$933$	−0.185904	+	0.107332i	−0.185904	+	0.107332i
$934$		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
$939$	−0.185904	−	0.107332i	−0.185904	−	0.107332i
$940$		0			0
$941$	1.30732	−	1.09697i	1.30732	−	1.09697i	0.318487	−	0.947927i	$-0.396825\pi$
$941$	1.30732	−	1.09697i	1.30732	−	1.09697i	0.988831	−	0.149042i	$-0.0476190\pi$
$942$	−0.238294	+	0.654708i	−0.238294	+	0.654708i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.776236	+	0.925082i	0.776236	+	0.925082i	0.998757	−	0.0498459i	$-0.0158730\pi$
$947$	0.776236	+	0.925082i	0.776236	+	0.925082i	−0.222521	+	0.974928i	$0.571429\pi$
$948$	1.20646	+	0.696549i	1.20646	+	0.696549i
$949$		0			0
$950$	0.938218	+	5.32090i	0.938218	+	5.32090i
$951$		0			0
$952$		0			0
$953$	−1.87705	−	0.683190i	−1.87705	−	0.683190i	−0.955573	−	0.294755i	$-0.904762\pi$
$953$	−1.87705	−	0.683190i	−1.87705	−	0.683190i	−0.921476	−	0.388435i	$-0.873016\pi$
$954$		0			0
$955$	2.34621	+	1.96870i	2.34621	+	1.96870i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−1.43744	+	0.253459i	−1.43744	+	0.253459i
$961$	−1.00000			−1.00000
$962$		0			0
$963$	0.706582			0.706582
$964$		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	$0.722222\pi$
$968$			0.695895i			0.695895i
$969$		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	$0.555556\pi$
$972$	−0.748475	+	1.29640i	−0.748475	+	1.29640i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.128002	−	0.152547i	−0.128002	−	0.152547i	0.698237	−	0.715867i	$-0.253968\pi$
$977$	−0.128002	−	0.152547i	−0.128002	−	0.152547i	−0.826239	+	0.563320i	$0.809524\pi$
$978$		0			0
$979$		0			0
$980$	2.39086	+	0.421574i	2.39086	+	0.421574i
$981$	1.33968	+	0.236222i	1.33968	+	0.236222i
$982$		0			0
$983$	0.955242	−	0.801543i	0.955242	−	0.801543i	−0.0249307	−	0.999689i	$-0.507937\pi$
$983$	0.955242	−	0.801543i	0.955242	−	0.801543i	0.980172	+	0.198146i	$0.0634921\pi$
$984$		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
$995$	−3.15648	+	1.14887i	−3.15648	+	1.14887i
$996$	0.0993168	−	0.563253i	0.0993168	−	0.563253i
$997$	−1.95433	+	0.344601i	−1.95433	+	0.344601i	−0.955573	+	0.294755i	$0.904762\pi$
$997$	−1.95433	+	0.344601i	−1.95433	+	0.344601i	−0.998757	+	0.0498459i	$0.984127\pi$
$998$	0.771691			0.771691
$999$	−0.906094	−	0.183171i	−0.906094	−	0.183171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2627.1.x.b.1064.5	✓	36
37.4	even	18	inner	2627.1.x.b.1632.5	yes	36
71.70	odd	2	CM	2627.1.x.b.1064.5	✓	36
2627.1632	odd	18	inner	2627.1.x.b.1632.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2627.1.x.b.1064.5	✓	36	1.1	even	1	trivial
2627.1.x.b.1064.5	✓	36	71.70	odd	2	CM
2627.1.x.b.1632.5	yes	36	37.4	even	18	inner
2627.1.x.b.1632.5	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)

\(f(q)\)	\(=\)	\(q+(1.53991 - 0.271527i) q^{2} +(-0.0940619 + 0.533452i) q^{3} +(1.35790 - 0.494233i) q^{4} +(1.07992 - 1.28699i) q^{5} +0.847006i q^{6} +(0.602663 - 0.347948i) q^{8} +(0.663970 + 0.241665i) q^{9} +O(q^{10})\)	\(q+(1.53991 - 0.271527i) q^{2} +(-0.0940619 + 0.533452i) q^{3} +(1.35790 - 0.494233i) q^{4} +(1.07992 - 1.28699i) q^{5} +0.847006i q^{6} +(0.602663 - 0.347948i) q^{8} +(0.663970 + 0.241665i) q^{9} +(1.31352 - 2.27508i) q^{10} +(0.135923 + 0.770860i) q^{12} +(0.584970 + 0.697140i) q^{15} +(-0.273398 + 0.229408i) q^{16} +(1.08807 + 0.191856i) q^{18} +(-1.86705 - 0.329212i) q^{19} +(0.830338 - 2.28133i) q^{20} +(0.128926 + 0.354220i) q^{24} +(-0.316487 - 1.79489i) q^{25} +(-0.462211 + 0.800574i) q^{27} +(-0.975699 + 0.563320i) q^{29} +(1.09009 + 0.914696i) q^{30} +(-0.806030 + 0.960589i) q^{32} +1.02104 q^{36} +(0.318487 + 0.947927i) q^{37} -2.96448 q^{38} +(0.203019 - 1.15138i) q^{40} -1.20761i q^{43} +(1.02805 - 0.593547i) q^{45} +(-0.0966618 - 0.167423i) q^{48} +(0.173648 + 0.984808i) q^{49} +(-0.974720 - 2.67802i) q^{50} +(-0.494385 + 1.35831i) q^{54} +(0.351237 - 0.965016i) q^{57} +(-1.34953 + 1.13239i) q^{58} +(1.13888 + 0.657532i) q^{60} +(-0.801938 + 1.38900i) q^{64} +(-0.173648 + 0.984808i) q^{71} +(0.484237 - 0.0853840i) q^{72} +0.912421 q^{73} +(0.747828 + 1.37324i) q^{74} +0.987254 q^{75} +(-2.69797 + 0.475725i) q^{76} +(1.14400 - 1.36336i) q^{79} +0.599604i q^{80} +(0.157682 + 0.132311i) q^{81} +(-0.686617 - 0.249908i) q^{83} +(-0.327899 - 1.85961i) q^{86} +(-0.208728 - 0.573475i) q^{87} +(-0.920301 - 1.09677i) q^{89} +(1.42194 - 1.19315i) q^{90} +(-2.43995 + 2.04736i) q^{95} +(-0.436611 - 0.520333i) q^{96} +(0.534804 + 1.46936i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{3} + 3 q^{5} - 6 q^{9}+O(q^{10}) \) 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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