LMFDB - Embedded newform 1805.1.o.b.694.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,1,Mod(299,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("1805.299");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$1805 = 5 \cdot 19^{2}$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	1805.o (of order $18$ , degree $6$ , not 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:	$0.900812347803$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	12.0.101559956668416.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} + 8x^{6} + 64$ x^12 + 8*x^6 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 95)
Projective image:	$D_{4}$
Projective field:	Galois closure of 4.2.475.1
Artin image:	$C_9\times D_8$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{72} - \cdots)$

Embedding invariants

Embedding label			694.1
Root			$0.245576 - 1.39273i$ of defining polynomial
Character	$\chi$	$=$	1805.694
Dual form			1805.1.o.b.1199.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.245576 - 1.39273i) q^{2} +(1.08335 - 0.909039i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-1.53209 - 1.28558i) q^{6} +(0.173648 - 0.984808i) q^{9} +(0.245576 - 1.39273i) q^{10} +(-0.707107 + 1.22474i) q^{12} +(-1.08335 - 0.909039i) q^{13} +(1.32893 - 0.483690i) q^{15} +(-0.766044 + 0.642788i) q^{16} -1.41421 q^{18} -1.00000 q^{20} +(0.766044 + 0.642788i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(-1.00000 - 1.73205i) q^{30} +(1.08335 + 0.909039i) q^{32} +(0.173648 + 0.984808i) q^{36} +1.41421 q^{37} -2.00000 q^{39} +(0.500000 - 0.866025i) q^{45} +(-0.245576 + 1.39273i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.707107 - 1.22474i) q^{50} +(1.32893 + 0.483690i) q^{52} +(-1.32893 + 0.483690i) q^{53} +(-1.08335 + 0.909039i) q^{60} +(0.500000 - 0.866025i) q^{64} +(-0.707107 - 1.22474i) q^{65} +(-0.245576 + 1.39273i) q^{67} +(-0.347296 - 1.96962i) q^{74} +1.41421 q^{75} +(0.491151 + 2.78546i) q^{78} +(-0.939693 + 0.342020i) q^{80} +(0.939693 + 0.342020i) q^{81} +(-1.32893 - 0.483690i) q^{90} +2.00000 q^{96} +(0.245576 + 1.39273i) q^{97} +(-1.08335 + 0.909039i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q - 12 q^{20} - 12 q^{26} - 12 q^{30} - 24 q^{39} + 6 q^{45} - 6 q^{49} + 6 q^{64} + 24 q^{96}+O(q^{100})$ 12 * q - 12 * q^20 - 12 * q^26 - 12 * q^30 - 24 * q^39 + 6 * q^45 - 6 * q^49 + 6 * q^64 + 24 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$ .

$n$	$362$	$1446$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−0.245576	−	1.39273i	−0.245576	−	1.39273i	−0.819152	−	0.573576i	$-0.805556\pi$
$2$	−0.245576	−	1.39273i	−0.245576	−	1.39273i	0.573576	−	0.819152i	$-0.305556\pi$
$3$	1.08335	−	0.909039i	1.08335	−	0.909039i	0.0871557	−	0.996195i	$-0.472222\pi$
$3$	1.08335	−	0.909039i	1.08335	−	0.909039i	0.996195	+	0.0871557i	$0.0277778\pi$
$4$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$5$	0.939693	+	0.342020i	0.939693	+	0.342020i
$5$	0.939693	+	0.342020i	0.939693	+	0.342020i
$6$	−1.53209	−	1.28558i	−1.53209	−	1.28558i
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$		0			0
$9$	0.173648	−	0.984808i	0.173648	−	0.984808i
$10$	0.245576	−	1.39273i	0.245576	−	1.39273i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$13$	−1.08335	−	0.909039i	−1.08335	−	0.909039i	−0.0871557	−	0.996195i	$-0.527778\pi$
$13$	−1.08335	−	0.909039i	−1.08335	−	0.909039i	−0.996195	+	0.0871557i	$0.972222\pi$
$14$		0			0
$15$	1.32893	−	0.483690i	1.32893	−	0.483690i
$16$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$17$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$17$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$18$	−1.41421			−1.41421
$19$		0			0
$19$		0			0
$20$	−1.00000			−1.00000
$21$		0			0
$22$		0			0
$23$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$23$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$24$		0			0
$25$	0.766044	+	0.642788i	0.766044	+	0.642788i
$26$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$27$		0			0
$28$		0			0
$29$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$29$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$30$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	1.08335	+	0.909039i	1.08335	+	0.909039i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.173648	+	0.984808i	0.173648	+	0.984808i
$37$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$37$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$38$		0			0
$39$	−2.00000			−2.00000
$40$		0			0
$41$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$41$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$42$		0			0
$43$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$43$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.500000	−	0.866025i
$46$		0			0
$47$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$47$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$48$	−0.245576	+	1.39273i	−0.245576	+	1.39273i
$49$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$50$	0.707107	−	1.22474i	0.707107	−	1.22474i
$51$		0			0
$52$	1.32893	+	0.483690i	1.32893	+	0.483690i
$53$	−1.32893	+	0.483690i	−1.32893	+	0.483690i	−0.906308	−	0.422618i	$-0.861111\pi$
$53$	−1.32893	+	0.483690i	−1.32893	+	0.483690i	−0.422618	+	0.906308i	$0.638889\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$59$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$60$	−1.08335	+	0.909039i	−1.08335	+	0.909039i
$61$		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
$64$	0.500000	−	0.866025i	0.500000	−	0.866025i
$65$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$66$		0			0
$67$	−0.245576	+	1.39273i	−0.245576	+	1.39273i	0.573576	+	0.819152i	$0.305556\pi$
$67$	−0.245576	+	1.39273i	−0.245576	+	1.39273i	−0.819152	+	0.573576i	$0.805556\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$71$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$72$		0			0
$73$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$73$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$74$	−0.347296	−	1.96962i	−0.347296	−	1.96962i
$75$	1.41421			1.41421
$76$		0			0
$77$		0			0
$78$	0.491151	+	2.78546i	0.491151	+	2.78546i
$79$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$79$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$80$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$81$	0.939693	+	0.342020i	0.939693	+	0.342020i
$82$		0			0
$83$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$83$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$89$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$90$	−1.32893	−	0.483690i	−1.32893	−	0.483690i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	2.00000			2.00000
$97$	0.245576	+	1.39273i	0.245576	+	1.39273i	0.819152	+	0.573576i	$0.194444\pi$
$97$	0.245576	+	1.39273i	0.245576	+	1.39273i	−0.573576	+	0.819152i	$0.694444\pi$
$98$	−1.08335	+	0.909039i	−1.08335	+	0.909039i
$99$		0			0
$100$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$101$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$101$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$102$		0			0
$103$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$103$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$104$		0			0
$105$		0			0
$106$	1.00000	+	1.73205i	1.00000	+	1.73205i
$107$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$107$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$108$		0			0
$109$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$109$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$110$		0			0
$111$	1.53209	−	1.28558i	1.53209	−	1.28558i
$112$		0			0
$113$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$113$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.08335	+	0.909039i	−1.08335	+	0.909039i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.500000	−	0.866025i	0.500000	−	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.500000	+	0.866025i	0.500000	+	0.866025i
$126$		0			0
$127$	1.08335	+	0.909039i	1.08335	+	0.909039i	0.996195	−	0.0871557i	$-0.0277778\pi$
$127$	1.08335	+	0.909039i	1.08335	+	0.909039i	0.0871557	+	0.996195i	$0.472222\pi$
$128$		0			0
$129$		0			0
$130$	−1.53209	+	1.28558i	−1.53209	+	1.28558i
$131$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$131$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$132$		0			0
$133$		0			0
$134$	2.00000			2.00000
$135$		0			0
$136$		0			0
$137$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$137$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$138$		0			0
$139$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$139$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.500000	+	0.866025i	0.500000	+	0.866025i
$145$		0			0
$146$		0			0
$147$	−1.32893	−	0.483690i	−1.32893	−	0.483690i
$148$	−1.32893	+	0.483690i	−1.32893	+	0.483690i
$149$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$149$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$150$	−0.347296	−	1.96962i	−0.347296	−	1.96962i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	1.87939	−	0.684040i	1.87939	−	0.684040i
$157$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$157$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$158$		0			0
$159$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$160$	0.707107	+	1.22474i	0.707107	+	1.22474i
$161$		0			0
$162$	0.245576	−	1.39273i	0.245576	−	1.39273i
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.32893	+	0.483690i	−1.32893	+	0.483690i	−0.906308	−	0.422618i	$-0.861111\pi$
$167$	−1.32893	+	0.483690i	−1.32893	+	0.483690i	−0.422618	+	0.906308i	$0.638889\pi$
$168$		0			0
$169$	0.173648	+	0.984808i	0.173648	+	0.984808i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.245576	−	1.39273i	−0.245576	−	1.39273i	−0.819152	−	0.573576i	$-0.805556\pi$
$173$	−0.245576	−	1.39273i	−0.245576	−	1.39273i	0.573576	−	0.819152i	$-0.305556\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$181$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$181$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.32893	+	0.483690i	1.32893	+	0.483690i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.00000			−2.00000			−1.00000			$\pi$
$191$	−2.00000			−2.00000			−1.00000			$\pi$
$192$	−0.245576	−	1.39273i	−0.245576	−	1.39273i
$193$	1.08335	−	0.909039i	1.08335	−	0.909039i	0.0871557	−	0.996195i	$-0.472222\pi$
$193$	1.08335	−	0.909039i	1.08335	−	0.909039i	0.996195	+	0.0871557i	$0.0277778\pi$
$194$	1.87939	−	0.684040i	1.87939	−	0.684040i
$195$	−1.87939	−	0.684040i	−1.87939	−	0.684040i
$196$	0.766044	+	0.642788i	0.766044	+	0.642788i
$197$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$197$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$198$		0			0
$199$	−0.347296	+	1.96962i	−0.347296	+	1.96962i	−0.173648	+	0.984808i	$0.555556\pi$
$199$	−0.347296	+	1.96962i	−0.347296	+	1.96962i	−0.173648	+	0.984808i	$0.555556\pi$
$200$		0			0
$201$	1.00000	+	1.73205i	1.00000	+	1.73205i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	1.53209	−	1.28558i	1.53209	−	1.28558i
$207$		0			0
$208$	1.41421			1.41421
$209$		0			0
$210$		0			0
$211$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$211$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$212$	1.08335	−	0.909039i	1.08335	−	0.909039i
$213$		0			0
$214$	−1.87939	−	0.684040i	−1.87939	−	0.684040i
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$	−2.16670	−	1.81808i	−2.16670	−	1.81808i
$223$	−1.32893	−	0.483690i	−1.32893	−	0.483690i	−0.422618	−	0.906308i	$-0.638889\pi$
$223$	−1.32893	−	0.483690i	−1.32893	−	0.483690i	−0.906308	+	0.422618i	$0.861111\pi$
$224$		0			0
$225$	0.766044	−	0.642788i	0.766044	−	0.642788i
$226$	0.347296	+	1.96962i	0.347296	+	1.96962i
$227$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$227$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$228$		0			0
$229$		0			0			−	1.00000i	$-0.5\pi$
$229$		0			0				1.00000i	$0.5\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$233$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$234$	1.53209	+	1.28558i	1.53209	+	1.28558i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$239$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$240$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$241$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$241$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$242$	−1.32893	−	0.483690i	−1.32893	−	0.483690i
$243$	1.32893	−	0.483690i	1.32893	−	0.483690i
$244$		0			0
$245$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	1.08335	−	0.909039i	1.08335	−	0.909039i
$251$	1.87939	−	0.684040i	1.87939	−	0.684040i	0.939693	−	0.342020i	$-0.111111\pi$
$251$	1.87939	−	0.684040i	1.87939	−	0.684040i	0.939693	−	0.342020i	$-0.111111\pi$
$252$		0			0
$253$		0			0
$254$	1.00000	−	1.73205i	1.00000	−	1.73205i
$255$		0			0
$256$	0.173648	−	0.984808i	0.173648	−	0.984808i
$257$	0.245576	−	1.39273i	0.245576	−	1.39273i	−0.573576	−	0.819152i	$-0.694444\pi$
$257$	0.245576	−	1.39273i	0.245576	−	1.39273i	0.819152	−	0.573576i	$-0.194444\pi$
$258$		0			0
$259$		0			0
$260$	1.08335	+	0.909039i	1.08335	+	0.909039i
$261$		0			0
$262$	2.65785	−	0.967379i	2.65785	−	0.967379i
$263$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$263$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$264$		0			0
$265$	−1.41421			−1.41421
$266$		0			0
$267$		0			0
$268$	−0.245576	−	1.39273i	−0.245576	−	1.39273i
$269$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$269$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$270$		0			0
$271$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$271$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$281$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$282$		0			0
$283$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$283$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.08335	−	0.909039i	1.08335	−	0.909039i
$289$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$290$		0			0
$291$	1.53209	+	1.28558i	1.53209	+	1.28558i
$292$		0			0
$293$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$293$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$294$	−0.347296	+	1.96962i	−0.347296	+	1.96962i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−1.32893	+	0.483690i	−1.32893	+	0.483690i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−1.08335	+	0.909039i	−1.08335	+	0.909039i	−0.996195	−	0.0871557i	$-0.972222\pi$
$307$	−1.08335	+	0.909039i	−1.08335	+	0.909039i	−0.0871557	+	0.996195i	$0.527778\pi$
$308$		0			0
$309$	1.87939	+	0.684040i	1.87939	+	0.684040i
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$313$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.08335	−	0.909039i	−1.08335	−	0.909039i	−0.0871557	−	0.996195i	$-0.527778\pi$
$317$	−1.08335	−	0.909039i	−1.08335	−	0.909039i	−0.996195	+	0.0871557i	$0.972222\pi$
$318$	2.65785	+	0.967379i	2.65785	+	0.967379i
$319$		0			0
$320$	0.766044	−	0.642788i	0.766044	−	0.642788i
$321$	−0.347296	−	1.96962i	−0.347296	−	1.96962i
$322$		0			0
$323$		0			0
$324$	−1.00000			−1.00000
$325$	−0.245576	−	1.39273i	−0.245576	−	1.39273i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$		0			0
$333$	0.245576	−	1.39273i	0.245576	−	1.39273i
$334$	1.00000	+	1.73205i	1.00000	+	1.73205i
$335$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$336$		0			0
$337$	1.32893	+	0.483690i	1.32893	+	0.483690i	0.906308	−	0.422618i	$-0.138889\pi$
$337$	1.32893	+	0.483690i	1.32893	+	0.483690i	0.422618	+	0.906308i	$0.361111\pi$
$338$	1.32893	−	0.483690i	1.32893	−	0.483690i
$339$	−1.53209	+	1.28558i	−1.53209	+	1.28558i
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−1.87939	+	0.684040i	−1.87939	+	0.684040i
$347$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$347$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$348$		0			0
$349$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$349$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$353$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$359$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$	−0.245576	−	1.39273i	−0.245576	−	1.39273i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$367$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$368$		0			0
$369$		0			0
$370$	0.347296	−	1.96962i	0.347296	−	1.96962i
$371$		0			0
$372$		0			0
$373$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$373$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$374$		0			0
$375$	1.32893	+	0.483690i	1.32893	+	0.483690i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	2.00000			2.00000
$382$	0.491151	+	2.78546i	0.491151	+	2.78546i
$383$	−1.08335	+	0.909039i	−1.08335	+	0.909039i	−0.996195	−	0.0871557i	$-0.972222\pi$
$383$	−1.08335	+	0.909039i	−1.08335	+	0.909039i	−0.0871557	+	0.996195i	$0.527778\pi$
$384$		0			0
$385$		0			0
$386$	−1.53209	−	1.28558i	−1.53209	−	1.28558i
$387$		0			0
$388$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$389$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$389$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$390$	−0.491151	+	2.78546i	−0.491151	+	2.78546i
$391$		0			0
$392$		0			0
$393$	2.16670	+	1.81808i	2.16670	+	1.81808i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$397$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$398$	2.82843			2.82843
$399$		0			0
$400$	−1.00000			−1.00000
$401$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$401$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$402$	2.16670	−	1.81808i	2.16670	−	1.81808i
$403$		0			0
$404$		0			0
$405$	0.766044	+	0.642788i	0.766044	+	0.642788i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$409$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$410$		0			0
$411$		0			0
$412$	−1.08335	−	0.909039i	−1.08335	−	0.909039i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.347296	−	1.96962i	−0.347296	−	1.96962i
$417$		0			0
$418$		0			0
$419$	2.00000			2.00000			1.00000			$0$
$419$	2.00000			2.00000			1.00000			$0$
$420$		0			0
$421$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$421$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.245576	+	1.39273i	−0.245576	+	1.39273i
$429$		0			0
$430$		0			0
$431$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$431$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$432$		0			0
$433$	1.32893	−	0.483690i	1.32893	−	0.483690i	0.422618	−	0.906308i	$-0.361111\pi$
$433$	1.32893	−	0.483690i	1.32893	−	0.483690i	0.906308	+	0.422618i	$0.138889\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$439$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$440$		0			0
$441$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$442$		0			0
$443$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$443$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$444$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$445$		0			0
$446$	−0.347296	+	1.96962i	−0.347296	+	1.96962i
$447$		0			0
$448$		0			0
$449$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$449$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$450$	−1.08335	−	0.909039i	−1.08335	−	0.909039i
$451$		0			0
$452$	1.32893	−	0.483690i	1.32893	−	0.483690i
$453$		0			0
$454$	0.347296	+	1.96962i	0.347296	+	1.96962i
$455$		0			0
$456$		0			0
$457$		0			0		1.00000			$0$
$457$		0			0		−1.00000			$\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.87939	−	0.684040i	−1.87939	−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$461$	−1.87939	−	0.684040i	−1.87939	−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$462$		0			0
$463$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$463$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$467$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$468$	0.707107	−	1.22474i	0.707107	−	1.22474i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.245576	+	1.39273i	0.245576	+	1.39273i
$478$	−2.16670	+	1.81808i	−2.16670	+	1.81808i
$479$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$479$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$480$	1.87939	+	0.684040i	1.87939	+	0.684040i
$481$	−1.53209	−	1.28558i	−1.53209	−	1.28558i
$482$		0			0
$483$		0			0
$484$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$485$	−0.245576	+	1.39273i	−0.245576	+	1.39273i
$486$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$487$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$487$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$488$		0			0
$489$		0			0
$490$	−1.32893	+	0.483690i	−1.32893	+	0.483690i
$491$	−1.53209	+	1.28558i	−1.53209	+	1.28558i	−0.766044	+	0.642788i	$0.777778\pi$
$491$	−1.53209	+	1.28558i	−1.53209	+	1.28558i	−0.766044	+	0.642788i	$0.777778\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$499$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$500$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$501$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$502$	−1.41421	−	2.44949i	−1.41421	−	2.44949i
$503$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$503$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.08335	+	0.909039i	1.08335	+	0.909039i
$508$	−1.32893	−	0.483690i	−1.32893	−	0.483690i
$509$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$509$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$510$		0			0
$511$		0			0
$512$	−1.41421			−1.41421
$513$		0			0
$514$	−2.00000			−2.00000
$515$	0.245576	+	1.39273i	0.245576	+	1.39273i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.53209	−	1.28558i	−1.53209	−	1.28558i
$520$		0			0
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$		0			0
$523$	0.245576	−	1.39273i	0.245576	−	1.39273i	−0.573576	−	0.819152i	$-0.694444\pi$
$523$	0.245576	−	1.39273i	0.245576	−	1.39273i	0.819152	−	0.573576i	$-0.194444\pi$
$524$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.766044	−	0.642788i	0.766044	−	0.642788i
$530$	0.347296	+	1.96962i	0.347296	+	1.96962i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.08335	−	0.909039i	1.08335	−	0.909039i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$541$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.32893	+	0.483690i	−1.32893	+	0.483690i	−0.906308	−	0.422618i	$-0.861111\pi$
$547$	−1.32893	+	0.483690i	−1.32893	+	0.483690i	−0.422618	+	0.906308i	$0.638889\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.87939	−	0.684040i	1.87939	−	0.684040i
$556$		0			0
$557$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$557$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$563$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$564$		0			0
$565$	−1.32893	−	0.483690i	−1.32893	−	0.483690i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$	−2.16670	+	1.81808i	−2.16670	+	1.81808i
$574$		0			0
$575$		0			0
$576$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	0.707107	+	1.22474i	0.707107	+	1.22474i
$579$	0.347296	−	1.96962i	0.347296	−	1.96962i
$580$		0			0
$581$		0			0
$582$	1.41421	−	2.44949i	1.41421	−	2.44949i
$583$		0			0
$584$		0			0
$585$	−1.32893	+	0.483690i	−1.32893	+	0.483690i
$586$	−1.53209	+	1.28558i	−1.53209	+	1.28558i
$587$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$587$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$588$	1.41421			1.41421
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.08335	+	0.909039i	−1.08335	+	0.909039i
$593$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$593$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.41421	+	2.44949i	1.41421	+	2.44949i
$598$		0			0
$599$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$599$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$600$		0			0
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$	1.32893	+	0.483690i	1.32893	+	0.483690i
$604$		0			0
$605$	0.766044	−	0.642788i	0.766044	−	0.642788i
$606$		0			0
$607$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$607$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$613$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$614$	1.53209	+	1.28558i	1.53209	+	1.28558i
$615$		0			0
$616$		0			0
$617$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$617$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$618$	0.491151	−	2.78546i	0.491151	−	2.78546i
$619$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$619$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	1.53209	−	1.28558i	1.53209	−	1.28558i
$625$	0.173648	+	0.984808i	0.173648	+	0.984808i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		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			0
$633$		0			0
$634$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$635$	0.707107	+	1.22474i	0.707107	+	1.22474i
$636$	0.347296	−	1.96962i	0.347296	−	1.96962i
$637$	−0.245576	+	1.39273i	−0.245576	+	1.39273i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$641$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$642$	−2.65785	+	0.967379i	−2.65785	+	0.967379i
$643$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$643$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$		0			0
$649$		0			0
$650$	−1.87939	+	0.684040i	−1.87939	+	0.684040i
$651$		0			0
$652$		0			0
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$		0			0
$655$	−0.347296	+	1.96962i	−0.347296	+	1.96962i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$659$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$660$		0			0
$661$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$661$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−2.00000			−2.00000
$667$		0			0
$668$	1.08335	−	0.909039i	1.08335	−	0.909039i
$669$	−1.87939	+	0.684040i	−1.87939	+	0.684040i
$670$	1.87939	+	0.684040i	1.87939	+	0.684040i
$671$		0			0
$672$		0			0
$673$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$673$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$674$	0.347296	−	1.96962i	0.347296	−	1.96962i
$675$		0			0
$676$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$677$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$677$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$678$	2.16670	+	1.81808i	2.16670	+	1.81808i
$679$		0			0
$680$		0			0
$681$	−1.53209	+	1.28558i	−1.53209	+	1.28558i
$682$		0			0
$683$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$683$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.87939	+	0.684040i	1.87939	+	0.684040i
$690$		0			0
$691$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$691$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$692$	0.707107	+	1.22474i	0.707107	+	1.22474i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−2.65785	−	0.967379i	−2.65785	−	0.967379i
$699$		0			0
$700$		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			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.53209	−	1.28558i	−1.53209	−	1.28558i	−0.766044	−	0.642788i	$-0.777778\pi$
$709$	−1.53209	−	1.28558i	−1.53209	−	1.28558i	−0.766044	−	0.642788i	$-0.777778\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−2.65785	−	0.967379i	−2.65785	−	0.967379i
$718$		0			0
$719$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$719$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$720$	0.173648	+	0.984808i	0.173648	+	0.984808i
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−1.87939	+	0.684040i	−1.87939	+	0.684040i
$727$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$727$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$728$		0			0
$729$	0.500000	−	0.866025i	0.500000	−	0.866025i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$733$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$734$		0			0
$735$	−1.08335	−	0.909039i	−1.08335	−	0.909039i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−0.347296	−	1.96962i	−0.347296	−	1.96962i	−0.173648	−	0.984808i	$-0.555556\pi$
$739$	−0.347296	−	1.96962i	−0.347296	−	1.96962i	−0.173648	−	0.984808i	$-0.555556\pi$
$740$	−1.41421			−1.41421
$741$		0			0
$742$		0			0
$743$	0.245576	+	1.39273i	0.245576	+	1.39273i	0.819152	+	0.573576i	$0.194444\pi$
$743$	0.245576	+	1.39273i	0.245576	+	1.39273i	−0.573576	+	0.819152i	$0.694444\pi$
$744$		0			0
$745$		0			0
$746$	1.87939	+	0.684040i	1.87939	+	0.684040i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	0.347296	−	1.96962i	0.347296	−	1.96962i
$751$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$751$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$752$		0			0
$753$	1.41421	−	2.44949i	1.41421	−	2.44949i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$757$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0			−	1.00000i	$-0.5\pi$
$761$		0			0				1.00000i	$0.5\pi$
$762$	−0.491151	−	2.78546i	−0.491151	−	2.78546i
$763$		0			0
$764$	1.87939	−	0.684040i	1.87939	−	0.684040i
$765$		0			0
$766$	1.53209	+	1.28558i	1.53209	+	1.28558i
$767$		0			0
$768$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$769$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$769$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$770$		0			0
$771$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$772$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$773$	−1.08335	−	0.909039i	−1.08335	−	0.909039i	−0.0871557	−	0.996195i	$-0.527778\pi$
$773$	−1.08335	−	0.909039i	−1.08335	−	0.909039i	−0.996195	+	0.0871557i	$0.972222\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−2.82843			−2.82843
$779$		0			0
$780$	2.00000			2.00000
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.939693	+	0.342020i	0.939693	+	0.342020i
$785$		0			0
$786$	2.00000	−	3.46410i	2.00000	−	3.46410i
$787$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$787$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−1.53209	+	1.28558i	−1.53209	+	1.28558i
$796$	−0.347296	−	1.96962i	−0.347296	−	1.96962i
$797$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$797$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$798$		0			0
$799$		0			0
$800$	0.245576	+	1.39273i	0.245576	+	1.39273i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−1.53209	−	1.28558i	−1.53209	−	1.28558i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$809$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$810$	0.707107	−	1.22474i	0.707107	−	1.22474i
$811$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$811$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.87939	+	0.684040i	−1.87939	+	0.684040i	−0.939693	+	0.342020i	$0.888889\pi$
$821$	−1.87939	+	0.684040i	−1.87939	+	0.684040i	−0.939693	+	0.342020i	$0.888889\pi$
$822$		0			0
$823$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$823$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.245576	−	1.39273i	0.245576	−	1.39273i	−0.573576	−	0.819152i	$-0.694444\pi$
$827$	0.245576	−	1.39273i	0.245576	−	1.39273i	0.819152	−	0.573576i	$-0.194444\pi$
$828$		0			0
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$		0			0
$832$	−1.32893	+	0.483690i	−1.32893	+	0.483690i
$833$		0			0
$834$		0			0
$835$	−1.41421			−1.41421
$836$		0			0
$837$		0			0
$838$	−0.491151	−	2.78546i	−0.491151	−	2.78546i
$839$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$839$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$840$		0			0
$841$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$846$		0			0
$847$		0			0
$848$	0.707107	−	1.22474i	0.707107	−	1.22474i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$853$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.245576	+	1.39273i	0.245576	+	1.39273i	0.819152	+	0.573576i	$0.194444\pi$
$857$	0.245576	+	1.39273i	0.245576	+	1.39273i	−0.573576	+	0.819152i	$0.694444\pi$
$858$		0			0
$859$	−1.87939	+	0.684040i	−1.87939	+	0.684040i	−0.939693	+	0.342020i	$0.888889\pi$
$859$	−1.87939	+	0.684040i	−1.87939	+	0.684040i	−0.939693	+	0.342020i	$0.888889\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$863$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$864$		0			0
$865$	0.245576	−	1.39273i	0.245576	−	1.39273i
$866$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$867$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	1.53209	−	1.28558i	1.53209	−	1.28558i
$872$		0			0
$873$	1.41421			1.41421
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.08335	−	0.909039i	1.08335	−	0.909039i	0.0871557	−	0.996195i	$-0.472222\pi$
$877$	1.08335	−	0.909039i	1.08335	−	0.909039i	0.996195	+	0.0871557i	$0.0277778\pi$
$878$		0			0
$879$	−1.87939	−	0.684040i	−1.87939	−	0.684040i
$880$		0			0
$881$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$881$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$882$	0.707107	+	1.22474i	0.707107	+	1.22474i
$883$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$883$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.08335	−	0.909039i	−1.08335	−	0.909039i	−0.0871557	−	0.996195i	$-0.527778\pi$
$887$	−1.08335	−	0.909039i	−1.08335	−	0.909039i	−0.996195	+	0.0871557i	$0.972222\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	1.41421			1.41421
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.32893	+	0.483690i	1.32893	+	0.483690i	0.906308	−	0.422618i	$-0.138889\pi$
$907$	1.32893	+	0.483690i	1.32893	+	0.483690i	0.422618	+	0.906308i	$0.361111\pi$
$908$	1.32893	−	0.483690i	1.32893	−	0.483690i
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$919$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$920$		0			0
$921$	−0.347296	+	1.96962i	−0.347296	+	1.96962i
$922$	−0.491151	+	2.78546i	−0.491151	+	2.78546i
$923$		0			0
$924$		0			0
$925$	1.08335	+	0.909039i	1.08335	+	0.909039i
$926$		0			0
$927$	1.32893	−	0.483690i	1.32893	−	0.483690i
$928$		0			0
$929$	−0.347296	−	1.96962i	−0.347296	−	1.96962i	−0.173648	−	0.984808i	$-0.555556\pi$
$929$	−0.347296	−	1.96962i	−0.347296	−	1.96962i	−0.173648	−	0.984808i	$-0.555556\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$937$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$941$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$947$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−2.00000			−2.00000
$952$		0			0
$953$	1.08335	−	0.909039i	1.08335	−	0.909039i	0.0871557	−	0.996195i	$-0.472222\pi$
$953$	1.08335	−	0.909039i	1.08335	−	0.909039i	0.996195	+	0.0871557i	$0.0277778\pi$
$954$	1.87939	−	0.684040i	1.87939	−	0.684040i
$955$	−1.87939	−	0.684040i	−1.87939	−	0.684040i
$956$	1.53209	+	1.28558i	1.53209	+	1.28558i
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.245576	−	1.39273i	0.245576	−	1.39273i
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$	−1.41421	+	2.44949i	−1.41421	+	2.44949i
$963$	−1.08335	−	0.909039i	−1.08335	−	0.909039i
$964$		0			0
$965$	1.32893	−	0.483690i	1.32893	−	0.483690i
$966$		0			0
$967$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$967$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$968$		0			0
$969$		0			0
$970$	2.00000			2.00000
$971$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$971$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$972$	−1.08335	+	0.909039i	−1.08335	+	0.909039i
$973$		0			0
$974$	−1.87939	−	0.684040i	−1.87939	−	0.684040i
$975$	−1.53209	−	1.28558i	−1.53209	−	1.28558i
$976$		0			0
$977$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$977$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$978$		0			0
$979$		0			0
$980$	0.500000	+	0.866025i	0.500000	+	0.866025i
$981$		0			0
$982$	2.16670	+	1.81808i	2.16670	+	1.81808i
$983$	1.32893	+	0.483690i	1.32893	+	0.483690i	0.906308	−	0.422618i	$-0.138889\pi$
$983$	1.32893	+	0.483690i	1.32893	+	0.483690i	0.422618	+	0.906308i	$0.361111\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$991$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$996$		0			0
$997$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$997$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$998$		0			0
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.1.o.b.694.1		12
5.4	even	2	inner	1805.1.o.b.694.2		12
19.2	odd	18	inner	1805.1.o.b.1199.2		12
19.3	odd	18	inner	1805.1.o.b.299.1		12
19.4	even	9		1805.1.h.b.654.2		4
19.5	even	9	inner	1805.1.o.b.1029.1		12
19.6	even	9		95.1.d.b.94.1	✓	2
19.7	even	3	inner	1805.1.o.b.984.2		12
19.8	odd	6	inner	1805.1.o.b.849.2		12
19.9	even	9		1805.1.h.b.69.2		4
19.10	odd	18		1805.1.h.b.69.1		4
19.11	even	3	inner	1805.1.o.b.849.1		12
19.12	odd	6	inner	1805.1.o.b.984.1		12
19.13	odd	18		95.1.d.b.94.2	yes	2
19.14	odd	18	inner	1805.1.o.b.1029.2		12
19.15	odd	18		1805.1.h.b.654.1		4
19.16	even	9	inner	1805.1.o.b.299.2		12
19.17	even	9	inner	1805.1.o.b.1199.1		12
19.18	odd	2	inner	1805.1.o.b.694.2		12
57.32	even	18		855.1.g.c.379.1		2
57.44	odd	18		855.1.g.c.379.2		2
76.51	even	18		1520.1.m.b.1329.2		2
76.63	odd	18		1520.1.m.b.1329.1		2
95.4	even	18		1805.1.h.b.654.1		4
95.9	even	18		1805.1.h.b.69.1		4
95.13	even	36		475.1.c.b.151.1		2
95.14	odd	18	inner	1805.1.o.b.1029.1		12
95.24	even	18	inner	1805.1.o.b.1029.2		12
95.29	odd	18		1805.1.h.b.69.2		4
95.32	even	36		475.1.c.b.151.2		2
95.34	odd	18		1805.1.h.b.654.2		4
95.44	even	18		95.1.d.b.94.2	yes	2
95.49	even	6	inner	1805.1.o.b.849.2		12
95.54	even	18	inner	1805.1.o.b.299.1		12
95.59	odd	18	inner	1805.1.o.b.1199.1		12
95.63	odd	36		475.1.c.b.151.2		2
95.64	even	6	inner	1805.1.o.b.984.1		12
95.69	odd	6	inner	1805.1.o.b.984.2		12
95.74	even	18	inner	1805.1.o.b.1199.2		12
95.79	odd	18	inner	1805.1.o.b.299.2		12
95.82	odd	36		475.1.c.b.151.1		2
95.84	odd	6	inner	1805.1.o.b.849.1		12
95.89	odd	18		95.1.d.b.94.1	✓	2
95.94	odd	2	CM	1805.1.o.b.694.1		12
285.44	odd	18		855.1.g.c.379.1		2
285.89	even	18		855.1.g.c.379.2		2
380.139	odd	18		1520.1.m.b.1329.2		2
380.279	even	18		1520.1.m.b.1329.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.1.d.b.94.1	✓	2	19.6	even	9
95.1.d.b.94.1	✓	2	95.89	odd	18
95.1.d.b.94.2	yes	2	19.13	odd	18
95.1.d.b.94.2	yes	2	95.44	even	18
475.1.c.b.151.1		2	95.13	even	36
475.1.c.b.151.1		2	95.82	odd	36
475.1.c.b.151.2		2	95.32	even	36
475.1.c.b.151.2		2	95.63	odd	36
855.1.g.c.379.1		2	57.32	even	18
855.1.g.c.379.1		2	285.44	odd	18
855.1.g.c.379.2		2	57.44	odd	18
855.1.g.c.379.2		2	285.89	even	18
1520.1.m.b.1329.1		2	76.63	odd	18
1520.1.m.b.1329.1		2	380.279	even	18
1520.1.m.b.1329.2		2	76.51	even	18
1520.1.m.b.1329.2		2	380.139	odd	18
1805.1.h.b.69.1		4	19.10	odd	18
1805.1.h.b.69.1		4	95.9	even	18
1805.1.h.b.69.2		4	19.9	even	9
1805.1.h.b.69.2		4	95.29	odd	18
1805.1.h.b.654.1		4	19.15	odd	18
1805.1.h.b.654.1		4	95.4	even	18
1805.1.h.b.654.2		4	19.4	even	9
1805.1.h.b.654.2		4	95.34	odd	18
1805.1.o.b.299.1		12	19.3	odd	18	inner
1805.1.o.b.299.1		12	95.54	even	18	inner
1805.1.o.b.299.2		12	19.16	even	9	inner
1805.1.o.b.299.2		12	95.79	odd	18	inner
1805.1.o.b.694.1		12	1.1	even	1	trivial
1805.1.o.b.694.1		12	95.94	odd	2	CM
1805.1.o.b.694.2		12	5.4	even	2	inner
1805.1.o.b.694.2		12	19.18	odd	2	inner
1805.1.o.b.849.1		12	19.11	even	3	inner
1805.1.o.b.849.1		12	95.84	odd	6	inner
1805.1.o.b.849.2		12	19.8	odd	6	inner
1805.1.o.b.849.2		12	95.49	even	6	inner
1805.1.o.b.984.1		12	19.12	odd	6	inner
1805.1.o.b.984.1		12	95.64	even	6	inner
1805.1.o.b.984.2		12	19.7	even	3	inner
1805.1.o.b.984.2		12	95.69	odd	6	inner
1805.1.o.b.1029.1		12	19.5	even	9	inner
1805.1.o.b.1029.1		12	95.14	odd	18	inner
1805.1.o.b.1029.2		12	19.14	odd	18	inner
1805.1.o.b.1029.2		12	95.24	even	18	inner
1805.1.o.b.1199.1		12	19.17	even	9	inner
1805.1.o.b.1199.1		12	95.59	odd	18	inner
1805.1.o.b.1199.2		12	19.2	odd	18	inner
1805.1.o.b.1199.2		12	95.74	even	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1805.1.o.b.694.1

Level	$1805$
Weight	$1$
Character	1805.694
Analytic conductor	$0.901$
Analytic rank	$0$
Dimension	$12$
Projective image	$D_{4}$
CM discriminant	-95
Inner twists	$24$