LMFDB - Embedded newform 2848.1.bu.a.2063.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2848,1,Mod(271,2848)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2848, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 8]))

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

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

chi := DirichletCharacter("2848.271");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$2848 = 2^{5} \cdot 89$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	2848.bu (of order $22$ , degree $10$ , 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:	$1.42133715598$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 712)
Projective image:	$D_{11}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{11} - \cdots)$

Embedding invariants

Embedding label			2063.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	2848.2063
Dual form			2848.1.bu.a.751.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10181 - 1.27155i) q^{3} +(-0.260554 - 1.81219i) q^{9} +(-1.84125 - 0.540641i) q^{11} +(0.345139 + 0.755750i) q^{17} +(-0.273100 - 1.89945i) q^{19} +(0.841254 - 0.540641i) q^{25} +(-1.17597 - 0.755750i) q^{27} +(-2.71616 + 1.74557i) q^{33} +(-1.30972 - 1.51150i) q^{41} +(0.797176 + 0.234072i) q^{43} +(0.841254 - 0.540641i) q^{49} +(1.34125 + 0.393828i) q^{51} +(-2.71616 - 1.74557i) q^{57} +(0.544078 + 0.627899i) q^{59} +(-0.186393 + 0.215109i) q^{67} +(-0.239446 + 1.66538i) q^{73} +(0.239446 - 1.66538i) q^{75} +(-0.500000 + 0.146813i) q^{81} +(0.544078 + 1.19136i) q^{83} +(0.841254 + 0.540641i) q^{89} +(0.273100 - 0.0801894i) q^{97} +(-0.500000 + 3.47758i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$10 q + 2 q^{3} - 3 q^{9} - 9 q^{11} + 9 q^{17} + 2 q^{19} - q^{25} - 7 q^{27} - 4 q^{33} - 2 q^{41} + 2 q^{43} - q^{49} + 4 q^{51} - 4 q^{57} + 2 q^{59} + 2 q^{67} - 2 q^{73} + 2 q^{75} - 5 q^{81} + 2 q^{83}+ \cdots - 5 q^{99}+O(q^{100})$ 10 * q + 2 * q^3 - 3 * q^9 - 9 * q^11 + 9 * q^17 + 2 * q^19 - q^25 - 7 * q^27 - 4 * q^33 - 2 * q^41 + 2 * q^43 - q^49 + 4 * q^51 - 4 * q^57 + 2 * q^59 + 2 * q^67 - 2 * q^73 + 2 * q^75 - 5 * q^81 + 2 * q^83 - q^89 - 2 * q^97 - 5 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2848\mathbb{Z}\right)^\times$ .

$n$	$357$	$1247$	$1249$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{8}{11}\right)$

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			0
$2$		0			0
$3$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.142315	−	0.989821i	$-0.454545\pi$
$3$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.959493	−	0.281733i	$-0.0909091\pi$
$4$		0			0
$5$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$5$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$6$		0			0
$7$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$7$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$8$		0			0
$9$	−0.260554	−	1.81219i	−0.260554	−	1.81219i
$10$		0			0
$11$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−0.841254	−	0.540641i	$-0.818182\pi$
$11$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−1.00000			$\pi$
$12$		0			0
$13$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$13$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.345139	+	0.755750i	0.345139	+	0.755750i	1.00000			$0$
$17$	0.345139	+	0.755750i	0.345139	+	0.755750i	−0.654861	+	0.755750i	$0.727273\pi$
$18$		0			0
$19$	−0.273100	−	1.89945i	−0.273100	−	1.89945i	−0.415415	−	0.909632i	$-0.636364\pi$
$19$	−0.273100	−	1.89945i	−0.273100	−	1.89945i	0.142315	−	0.989821i	$-0.454545\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$23$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$24$		0			0
$25$	0.841254	−	0.540641i	0.841254	−	0.540641i
$26$		0			0
$27$	−1.17597	−	0.755750i	−1.17597	−	0.755750i
$28$		0			0
$29$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$29$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$30$		0			0
$31$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$31$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$32$		0			0
$33$	−2.71616	+	1.74557i	−2.71616	+	1.74557i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.30972	−	1.51150i	−1.30972	−	1.51150i	−0.654861	−	0.755750i	$-0.727273\pi$
$41$	−1.30972	−	1.51150i	−1.30972	−	1.51150i	−0.654861	−	0.755750i	$-0.727273\pi$
$42$		0			0
$43$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.654861	−	0.755750i	$-0.272727\pi$
$43$	0.797176	+	0.234072i	0.797176	+	0.234072i	0.142315	+	0.989821i	$0.454545\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$47$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$48$		0			0
$49$	0.841254	−	0.540641i	0.841254	−	0.540641i
$50$		0			0
$51$	1.34125	+	0.393828i	1.34125	+	0.393828i
$52$		0			0
$53$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$53$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.71616	−	1.74557i	−2.71616	−	1.74557i
$58$		0			0
$59$	0.544078	+	0.627899i	0.544078	+	0.627899i	0.959493	−	0.281733i	$-0.0909091\pi$
$59$	0.544078	+	0.627899i	0.544078	+	0.627899i	−0.415415	+	0.909632i	$0.636364\pi$
$60$		0			0
$61$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$61$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	−0.841254	−	0.540641i	$-0.818182\pi$
$67$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	0.654861	+	0.755750i	$0.272727\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$71$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$72$		0			0
$73$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$73$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$74$		0			0
$75$	0.239446	−	1.66538i	0.239446	−	1.66538i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$79$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$80$		0			0
$81$	−0.500000	+	0.146813i	−0.500000	+	0.146813i
$82$		0			0
$83$	0.544078	+	1.19136i	0.544078	+	1.19136i	0.959493	+	0.281733i	$0.0909091\pi$
$83$	0.544078	+	1.19136i	0.544078	+	1.19136i	−0.415415	+	0.909632i	$0.636364\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.841254	+	0.540641i	0.841254	+	0.540641i
$89$	0.841254	+	0.540641i	0.841254	+	0.540641i
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	−0.142315	−	0.989821i	$-0.545455\pi$
$97$	0.273100	−	0.0801894i	0.273100	−	0.0801894i	0.415415	+	0.909632i	$0.363636\pi$
$98$		0			0
$99$	−0.500000	+	3.47758i	−0.500000	+	3.47758i
$100$		0			0
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$		0			0
$103$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$103$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.91899	+	0.563465i	1.91899	+	0.563465i	0.959493	+	0.281733i	$0.0909091\pi$
$107$	1.91899	+	0.563465i	1.91899	+	0.563465i	0.959493	+	0.281733i	$0.0909091\pi$
$108$		0			0
$109$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$109$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$113$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	2.25667	+	1.45027i	2.25667	+	1.45027i
$122$		0			0
$123$	−3.36501			−3.36501
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$127$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$128$		0			0
$129$	1.17597	−	0.755750i	1.17597	−	0.755750i
$130$		0			0
$131$	1.10181	+	1.27155i	1.10181	+	1.27155i	0.959493	+	0.281733i	$0.0909091\pi$
$131$	1.10181	+	1.27155i	1.10181	+	1.27155i	0.142315	+	0.989821i	$0.454545\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$137$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$138$		0			0
$139$	−0.273100	−	1.89945i	−0.273100	−	1.89945i	−0.415415	−	0.909632i	$-0.636364\pi$
$139$	−0.273100	−	1.89945i	−0.273100	−	1.89945i	0.142315	−	0.989821i	$-0.454545\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.239446	−	1.66538i	0.239446	−	1.66538i
$148$		0			0
$149$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$149$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$150$		0			0
$151$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$151$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$152$		0			0
$153$	1.27964	−	0.822373i	1.27964	−	0.822373i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$157$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−0.698939	+	1.53046i	−0.698939	+	1.53046i	0.142315	+	0.989821i	$0.454545\pi$
$163$	−0.698939	+	1.53046i	−0.698939	+	1.53046i	−0.841254	+	0.540641i	$0.818182\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$167$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$168$		0			0
$169$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$170$		0			0
$171$	−3.37102	+	0.989821i	−3.37102	+	0.989821i
$172$		0			0
$173$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$173$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.39788			1.39788
$178$		0			0
$179$	0.284630			0.284630			0.142315	−	0.989821i	$-0.454545\pi$
$179$	0.284630			0.284630			0.142315	+	0.989821i	$0.454545\pi$
$180$		0			0
$181$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$181$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.226900	−	1.57812i	−0.226900	−	1.57812i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$191$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$192$		0			0
$193$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$193$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$197$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$198$		0			0
$199$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$199$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$200$		0			0
$201$	0.0681534	+	0.474017i	0.0681534	+	0.474017i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.524075	+	3.64502i	−0.524075	+	3.64502i
$210$		0			0
$211$	−0.698939	+	0.449181i	−0.698939	+	0.449181i	−0.841254	−	0.540641i	$-0.818182\pi$
$211$	−0.698939	+	0.449181i	−0.698939	+	0.449181i	0.142315	+	0.989821i	$0.454545\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$	1.85380	+	2.13940i	1.85380	+	2.13940i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$223$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$224$		0			0
$225$	−1.19894	−	1.38365i	−1.19894	−	1.38365i
$226$		0			0
$227$	−1.41542	+	0.909632i	−1.41542	+	0.909632i	−0.415415	+	0.909632i	$0.636364\pi$
$227$	−1.41542	+	0.909632i	−1.41542	+	0.909632i	−1.00000			$\pi$
$228$		0			0
$229$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$229$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$233$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$239$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$240$		0			0
$241$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$241$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$242$		0			0
$243$	0.216476	−	0.474017i	0.216476	−	0.474017i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	2.11435	+	0.620830i	2.11435	+	0.620830i
$250$		0			0
$251$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	0.654861	+	0.755750i	$0.272727\pi$
$251$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	−0.841254	+	0.540641i	$0.818182\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$257$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$263$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.61435	−	0.474017i	1.61435	−	0.474017i
$268$		0			0
$269$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$269$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$270$		0			0
$271$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$271$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$276$		0			0
$277$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$277$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$281$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$282$		0			0
$283$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	0.654861	+	0.755750i	$0.272727\pi$
$283$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	−0.841254	+	0.540641i	$0.818182\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.202824	−	0.234072i	0.202824	−	0.234072i
$290$		0			0
$291$	0.198939	−	0.435615i	0.198939	−	0.435615i
$292$		0			0
$293$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$293$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.75667	+	2.02730i	1.75667	+	2.02730i
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.10181	−	0.708089i	1.10181	−	0.708089i	0.142315	−	0.989821i	$-0.454545\pi$
$307$	1.10181	−	0.708089i	1.10181	−	0.708089i	0.959493	+	0.281733i	$0.0909091\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$311$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$312$		0			0
$313$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	0.415415	−	0.909632i	$-0.363636\pi$
$313$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	−0.142315	+	0.989821i	$0.545455\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$317$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	2.83083	−	1.81926i	2.83083	−	1.81926i
$322$		0			0
$323$	1.34125	−	0.861971i	1.34125	−	0.861971i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.61435	−	1.03748i	1.61435	−	1.03748i	0.654861	−	0.755750i	$-0.272727\pi$
$331$	1.61435	−	1.03748i	1.61435	−	1.03748i	0.959493	−	0.281733i	$-0.0909091\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$337$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$338$		0			0
$339$	0.915415	+	2.00448i	0.915415	+	2.00448i
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.186393	−	1.29639i	−0.186393	−	1.29639i	−0.841254	−	0.540641i	$-0.818182\pi$
$347$	−0.186393	−	1.29639i	−0.186393	−	1.29639i	0.654861	−	0.755750i	$-0.272727\pi$
$348$		0			0
$349$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$349$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$353$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$359$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$360$		0			0
$361$	−2.57385	+	0.755750i	−2.57385	+	0.755750i
$362$		0			0
$363$	4.33052	−	1.27155i	4.33052	−	1.27155i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$367$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$368$		0			0
$369$	−2.39788	+	2.76730i	−2.39788	+	2.76730i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$373$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i	0.959493	−	0.281733i	$-0.0909091\pi$
$379$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i	−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$383$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.216476	−	1.50563i	0.216476	−	1.50563i
$388$		0			0
$389$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$389$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	2.83083			2.83083
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$397$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$401$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$409$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$410$		0			0
$411$	−1.39788			−1.39788
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.71616	−	1.74557i	−2.71616	−	1.74557i
$418$		0			0
$419$	0.118239	+	0.258908i	0.118239	+	0.258908i	0.959493	−	0.281733i	$-0.0909091\pi$
$419$	0.118239	+	0.258908i	0.118239	+	0.258908i	−0.841254	+	0.540641i	$0.818182\pi$
$420$		0			0
$421$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$421$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.698939	+	0.449181i	0.698939	+	0.449181i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$431$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$432$		0			0
$433$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$433$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$439$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$440$		0			0
$441$	−1.19894	−	1.38365i	−1.19894	−	1.38365i
$442$		0			0
$443$	0.544078	−	1.19136i	0.544078	−	1.19136i	−0.415415	−	0.909632i	$-0.636364\pi$
$443$	0.544078	−	1.19136i	0.544078	−	1.19136i	0.959493	−	0.281733i	$-0.0909091\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.857685	+	0.989821i	0.857685	+	0.989821i	1.00000			$0$
$449$	0.857685	+	0.989821i	0.857685	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$450$		0			0
$451$	1.59435	+	3.49114i	1.59435	+	3.49114i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$457$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$458$		0			0
$459$	0.165284	−	1.14958i	0.165284	−	1.14958i
$460$		0			0
$461$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$461$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$462$		0			0
$463$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$463$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.544078	−	0.627899i	0.544078	−	0.627899i	−0.415415	−	0.909632i	$-0.636364\pi$
$467$	0.544078	−	0.627899i	0.544078	−	0.627899i	0.959493	+	0.281733i	$0.0909091\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.34125	−	0.861971i	−1.34125	−	0.861971i
$474$		0			0
$475$	−1.25667	−	1.45027i	−1.25667	−	1.45027i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		1.00000			$0$
$479$		0			0		−1.00000			$\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$487$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$488$		0			0
$489$	1.17597	+	2.57501i	1.17597	+	2.57501i
$490$		0			0
$491$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−0.841254	−	0.540641i	$-0.818182\pi$
$491$	−1.84125	−	0.540641i	−1.84125	−	0.540641i	−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.10181	−	0.708089i	1.10181	−	0.708089i	0.142315	−	0.989821i	$-0.454545\pi$
$499$	1.10181	−	0.708089i	1.10181	−	0.708089i	0.959493	+	0.281733i	$0.0909091\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$503$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$508$		0			0
$509$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$509$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−1.11435	+	2.44009i	−1.11435	+	2.44009i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$521$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$522$		0			0
$523$	1.61435	+	0.474017i	1.61435	+	0.474017i	0.959493	−	0.281733i	$-0.0909091\pi$
$523$	1.61435	+	0.474017i	1.61435	+	0.474017i	0.654861	+	0.755750i	$0.272727\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$530$		0			0
$531$	0.996114	−	1.14958i	0.996114	−	1.14958i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.313607	−	0.361922i	0.313607	−	0.361922i
$538$		0			0
$539$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$540$		0			0
$541$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$541$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.415415	+	0.909632i	$0.636364\pi$
$547$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.841254	+	0.540641i	$0.818182\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$557$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−2.25667	−	1.45027i	−2.25667	−	1.45027i
$562$		0			0
$563$	−1.84125	+	0.540641i	−1.84125	+	0.540641i	−0.841254	+	0.540641i	$0.818182\pi$
$563$	−1.84125	+	0.540641i	−1.84125	+	0.540641i	−1.00000			$1.00000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$569$	−0.239446	+	0.153882i	−0.239446	+	0.153882i	0.415415	+	0.909632i	$0.363636\pi$
$570$		0			0
$571$	−2.00000			−2.00000			−1.00000			$\pi$
$571$	−2.00000			−2.00000			−1.00000			$\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$577$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$578$		0			0
$579$	0.198939	+	0.435615i	0.198939	+	0.435615i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.415415	+	0.909632i	$0.636364\pi$
$587$	−1.25667	+	1.45027i	−1.25667	+	1.45027i	−0.841254	+	0.540641i	$0.818182\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$593$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$599$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$600$		0			0
$601$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$601$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$602$		0			0
$603$	0.438384	+	0.281733i	0.438384	+	0.281733i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$607$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$613$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.698939	+	1.53046i	0.698939	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$617$	0.698939	+	1.53046i	0.698939	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$618$		0			0
$619$	1.10181	+	1.27155i	1.10181	+	1.27155i	0.959493	+	0.281733i	$0.0909091\pi$
$619$	1.10181	+	1.27155i	1.10181	+	1.27155i	0.142315	+	0.989821i	$0.454545\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.415415	−	0.909632i	0.415415	−	0.909632i
$626$		0			0
$627$	4.05742	+	4.68251i	4.05742	+	4.68251i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$631$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$632$		0			0
$633$	−0.198939	+	1.38365i	−0.198939	+	1.38365i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$641$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$642$		0			0
$643$	0.239446	+	0.153882i	0.239446	+	0.153882i	0.654861	−	0.755750i	$-0.272727\pi$
$643$	0.239446	+	0.153882i	0.239446	+	0.153882i	−0.415415	+	0.909632i	$0.636364\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$647$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$648$		0			0
$649$	−0.662317	−	1.45027i	−0.662317	−	1.45027i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$653$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	3.08038			3.08038
$658$		0			0
$659$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.142315	−	0.989821i	$-0.454545\pi$
$659$	1.10181	−	1.27155i	1.10181	−	1.27155i	0.959493	−	0.281733i	$-0.0909091\pi$
$660$		0			0
$661$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$661$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.284630	−	1.97964i	−0.284630	−	1.97964i	−0.142315	−	0.989821i	$-0.545455\pi$
$673$	−0.284630	−	1.97964i	−0.284630	−	1.97964i	−0.142315	−	0.989821i	$-0.545455\pi$
$674$		0			0
$675$	−1.39788			−1.39788
$676$		0			0
$677$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$677$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.402869	+	2.80202i	−0.402869	+	2.80202i
$682$		0			0
$683$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.654861	−	0.755750i	$-0.272727\pi$
$683$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.959493	+	0.281733i	$0.0909091\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.544078	−	1.19136i	0.544078	−	1.19136i	−0.415415	−	0.909632i	$-0.636364\pi$
$691$	0.544078	−	1.19136i	0.544078	−	1.19136i	0.959493	−	0.281733i	$-0.0909091\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.690279	−	1.51150i	0.690279	−	1.51150i
$698$		0			0
$699$	−1.44306	+	1.66538i	−1.44306	+	1.66538i
$700$		0			0
$701$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$701$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$709$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$719$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−2.11435	−	0.620830i	−2.11435	−	0.620830i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$727$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$728$		0			0
$729$	−0.580699	−	1.27155i	−0.580699	−	1.27155i
$730$		0			0
$731$	0.0982369	+	0.683252i	0.0982369	+	0.683252i
$732$		0			0
$733$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$733$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.459493	−	0.295298i	0.459493	−	0.295298i
$738$		0			0
$739$	0.239446	+	0.153882i	0.239446	+	0.153882i	0.654861	−	0.755750i	$-0.272727\pi$
$739$	0.239446	+	0.153882i	0.239446	+	0.153882i	−0.415415	+	0.909632i	$0.636364\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$743$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.01722	−	1.29639i	2.01722	−	1.29639i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$751$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$752$		0			0
$753$	1.44306	+	1.66538i	1.44306	+	1.66538i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$757$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$761$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$769$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$770$		0			0
$771$	−2.11435	−	2.44009i	−2.11435	−	2.44009i
$772$		0			0
$773$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$773$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.51334	+	2.90055i	−2.51334	+	2.90055i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	0.654861	+	0.755750i	$0.272727\pi$
$787$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	−0.841254	+	0.540641i	$0.818182\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$797$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	0.760554	−	1.66538i	0.760554	−	1.66538i
$802$		0			0
$803$	1.34125	−	2.93694i	1.34125	−	2.93694i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$809$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$810$		0			0
$811$	0.284630	−	1.97964i	0.284630	−	1.97964i	0.142315	−	0.989821i	$-0.454545\pi$
$811$	0.284630	−	1.97964i	0.284630	−	1.97964i	0.142315	−	0.989821i	$-0.454545\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.226900	−	1.57812i	0.226900	−	1.57812i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$821$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$822$		0			0
$823$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$823$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$824$		0			0
$825$	−1.34125	+	2.93694i	−1.34125	+	2.93694i
$826$		0			0
$827$	0.544078	+	1.19136i	0.544078	+	1.19136i	0.959493	+	0.281733i	$0.0909091\pi$
$827$	0.544078	+	1.19136i	0.544078	+	1.19136i	−0.415415	+	0.909632i	$0.636364\pi$
$828$		0			0
$829$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$829$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.698939	+	0.449181i	0.698939	+	0.449181i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$839$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$840$		0			0
$841$	0.841254	−	0.540641i	0.841254	−	0.540641i
$842$		0			0
$843$	−2.11435	−	2.44009i	−2.11435	−	2.44009i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.44306	+	1.66538i	1.44306	+	1.66538i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$857$	−1.61435	+	1.03748i	−1.61435	+	1.03748i	−0.959493	+	0.281733i	$0.909091\pi$
$858$		0			0
$859$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	0.654861	+	0.755750i	$0.272727\pi$
$859$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	−0.841254	+	0.540641i	$0.818182\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$863$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−0.0741615	−	0.515804i	−0.0741615	−	0.515804i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.216476	−	0.474017i	−0.216476	−	0.474017i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$877$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	−0.959493	−	0.281733i	$-0.909091\pi$
$881$	−0.118239	−	0.822373i	−0.118239	−	0.822373i	0.841254	−	0.540641i	$-0.181818\pi$
$882$		0			0
$883$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.841254	−	0.540641i	$-0.818182\pi$
$883$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.415415	+	0.909632i	$0.636364\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$887$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.00000			1.00000
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	0.654861	−	0.755750i	$-0.272727\pi$
$907$	−0.345139	−	0.755750i	−0.345139	−	0.755750i	−1.00000			$\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$911$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$912$		0			0
$913$	−0.357685	−	2.48775i	−0.357685	−	2.48775i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$919$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$920$		0			0
$921$	0.313607	−	2.18119i	0.313607	−	2.18119i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$929$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$930$		0			0
$931$	−1.25667	−	1.45027i	−1.25667	−	1.45027i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	0.415415	−	0.909632i	$-0.363636\pi$
$937$	−0.544078	−	0.627899i	−0.544078	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$938$		0			0
$939$	0.402869	−	0.258908i	0.402869	−	0.258908i
$940$		0			0
$941$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$941$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.239446	+	0.153882i	0.239446	+	0.153882i	0.654861	−	0.755750i	$-0.272727\pi$
$947$	0.239446	+	0.153882i	0.239446	+	0.153882i	−0.415415	+	0.909632i	$0.636364\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.698939	+	1.53046i	0.698939	+	1.53046i	0.841254	+	0.540641i	$0.181818\pi$
$953$	0.698939	+	1.53046i	0.698939	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$962$		0			0
$963$	0.521109	−	3.62439i	0.521109	−	3.62439i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$		0			0
$969$	0.381761	−	2.65520i	0.381761	−	2.65520i
$970$		0			0
$971$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	−0.415415	−	0.909632i	$-0.636364\pi$
$971$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	0.142315	+	0.989821i	$0.454545\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$977$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$978$		0			0
$979$	−1.25667	−	1.45027i	−1.25667	−	1.45027i
$980$		0			0
$981$		0			0
$982$		0			0
$983$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$983$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$	0.459493	−	3.19584i	0.459493	−	3.19584i
$994$		0			0
$995$		0			0
$996$		0			0
$997$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$997$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$998$		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	2848.1.bu.a.2063.1		10
4.3	odd	2		712.1.s.a.283.1	✓	10
8.3	odd	2	CM	2848.1.bu.a.2063.1		10
8.5	even	2		712.1.s.a.283.1	✓	10
89.39	even	11	inner	2848.1.bu.a.751.1		10
356.39	odd	22		712.1.s.a.395.1	yes	10
712.395	odd	22	inner	2848.1.bu.a.751.1		10
712.573	even	22		712.1.s.a.395.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
712.1.s.a.283.1	✓	10	4.3	odd	2
712.1.s.a.283.1	✓	10	8.5	even	2
712.1.s.a.395.1	yes	10	356.39	odd	22
712.1.s.a.395.1	yes	10	712.573	even	22
2848.1.bu.a.751.1		10	89.39	even	11	inner
2848.1.bu.a.751.1		10	712.395	odd	22	inner
2848.1.bu.a.2063.1		10	1.1	even	1	trivial
2848.1.bu.a.2063.1		10	8.3	odd	2	CM

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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

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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	2848.1.bu.a.2063.1

Level	$2848$
Weight	$1$
Character	2848.2063
Analytic conductor	$1.421$
Analytic rank	$0$
Dimension	$10$
Projective image	$D_{11}$
CM discriminant	-8
Inner twists	$4$