LMFDB - Embedded newform 2564.1.d.b.2563.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2564,1,Mod(2563,2564)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2564, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("2564.2563");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2564 = 2^{2} \cdot 641 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2564.d (of order $2$, degree $1$, 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:	yes
Analytic conductor:	$1.27960269239$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{7}$
Projective field:	Galois closure of 7.1.16855982144.1
Artin image:	$D_7$
Artin field:	Galois closure of 7.1.16855982144.1

Embedding invariants

Embedding label			2563.2
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	2564.2563

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.445042 q^{3} +1.00000 q^{4} +1.24698 q^{5} -0.445042 q^{6} +1.00000 q^{8} -0.801938 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.445042 q^{3} +1.00000 q^{4} +1.24698 q^{5} -0.445042 q^{6} +1.00000 q^{8} -0.801938 q^{9} +1.24698 q^{10} -0.445042 q^{12} -0.445042 q^{13} -0.554958 q^{15} +1.00000 q^{16} -0.801938 q^{18} +2.00000 q^{19} +1.24698 q^{20} -1.80194 q^{23} -0.445042 q^{24} +0.554958 q^{25} -0.445042 q^{26} +0.801938 q^{27} -0.554958 q^{30} +1.24698 q^{31} +1.00000 q^{32} -0.801938 q^{36} -1.80194 q^{37} +2.00000 q^{38} +0.198062 q^{39} +1.24698 q^{40} +1.24698 q^{43} -1.00000 q^{45} -1.80194 q^{46} -1.80194 q^{47} -0.445042 q^{48} +1.00000 q^{49} +0.554958 q^{50} -0.445042 q^{52} +0.801938 q^{54} -0.890084 q^{57} -0.554958 q^{60} +1.24698 q^{62} +1.00000 q^{64} -0.554958 q^{65} -1.80194 q^{67} +0.801938 q^{69} -0.801938 q^{72} -1.80194 q^{73} -1.80194 q^{74} -0.246980 q^{75} +2.00000 q^{76} +0.198062 q^{78} +1.24698 q^{80} +0.445042 q^{81} +1.24698 q^{83} +1.24698 q^{86} -1.80194 q^{89} -1.00000 q^{90} -1.80194 q^{92} -0.554958 q^{93} -1.80194 q^{94} +2.49396 q^{95} -0.445042 q^{96} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - q^{3} + 3 q^{4} - q^{5} - q^{6} + 3 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - q^3 + 3 * q^4 - q^5 - q^6 + 3 * q^8 + 2 * q^9	$ 3 q + 3 q^{2} - q^{3} + 3 q^{4} - q^{5} - q^{6} + 3 q^{8} + 2 q^{9} - q^{10} - q^{12} - q^{13} - 2 q^{15} + 3 q^{16} + 2 q^{18} + 6 q^{19} - q^{20} - q^{23} - q^{24} + 2 q^{25} - q^{26} - 2 q^{27} - 2 q^{30} - q^{31} + 3 q^{32} + 2 q^{36} - q^{37} + 6 q^{38} + 5 q^{39} - q^{40} - q^{43} - 3 q^{45} - q^{46} - q^{47} - q^{48} + 3 q^{49} + 2 q^{50} - q^{52} - 2 q^{54} - 2 q^{57} - 2 q^{60} - q^{62} + 3 q^{64} - 2 q^{65} - q^{67} - 2 q^{69} + 2 q^{72} - q^{73} - q^{74} + 4 q^{75} + 6 q^{76} + 5 q^{78} - q^{80} + q^{81} - q^{83} - q^{86} - q^{89} - 3 q^{90} - q^{92} - 2 q^{93} - q^{94} - 2 q^{95} - q^{96} + 3 q^{98}+O(q^{100}) $ 3 * q + 3 * q^2 - q^3 + 3 * q^4 - q^5 - q^6 + 3 * q^8 + 2 * q^9 - q^10 - q^12 - q^13 - 2 * q^15 + 3 * q^16 + 2 * q^18 + 6 * q^19 - q^20 - q^23 - q^24 + 2 * q^25 - q^26 - 2 * q^27 - 2 * q^30 - q^31 + 3 * q^32 + 2 * q^36 - q^37 + 6 * q^38 + 5 * q^39 - q^40 - q^43 - 3 * q^45 - q^46 - q^47 - q^48 + 3 * q^49 + 2 * q^50 - q^52 - 2 * q^54 - 2 * q^57 - 2 * q^60 - q^62 + 3 * q^64 - 2 * q^65 - q^67 - 2 * q^69 + 2 * q^72 - q^73 - q^74 + 4 * q^75 + 6 * q^76 + 5 * q^78 - q^80 + q^81 - q^83 - q^86 - q^89 - 3 * q^90 - q^92 - 2 * q^93 - q^94 - 2 * q^95 - q^96 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2564\mathbb{Z}\right)^\times$.

$n$	$1283$	$1285$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.00000	1.00000
$2$	1.00000	1.00000
$3$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$3$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$4$	1.00000	1.00000
$5$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$5$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$6$	−0.445042	−0.445042
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	1.00000	1.00000
$9$	−0.801938	−0.801938
$10$	1.24698	1.24698
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	−0.445042	−0.445042
$13$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$13$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$14$	0	0
$15$	−0.554958	−0.554958
$16$	1.00000	1.00000
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	−0.801938	−0.801938
$19$	2.00000	2.00000	1.00000			$0$
$19$	2.00000	2.00000	1.00000			$0$
$20$	1.24698	1.24698
$21$	0	0
$22$	0	0
$23$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$23$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$24$	−0.445042	−0.445042
$25$	0.554958	0.554958
$26$	−0.445042	−0.445042
$27$	0.801938	0.801938
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	−0.554958	−0.554958
$31$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$31$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$32$	1.00000	1.00000
$33$	0	0
$34$	0	0
$35$	0	0
$36$	−0.801938	−0.801938
$37$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$37$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$38$	2.00000	2.00000
$39$	0.198062	0.198062
$40$	1.24698	1.24698
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$43$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$44$	0	0
$45$	−1.00000	−1.00000
$46$	−1.80194	−1.80194
$47$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$47$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$48$	−0.445042	−0.445042
$49$	1.00000	1.00000
$50$	0.554958	0.554958
$51$	0	0
$52$	−0.445042	−0.445042
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0.801938	0.801938
$55$	0	0
$56$	0	0
$57$	−0.890084	−0.890084
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	−0.554958	−0.554958
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	1.24698	1.24698
$63$	0	0
$64$	1.00000	1.00000
$65$	−0.554958	−0.554958
$66$	0	0
$67$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$67$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$68$	0	0
$69$	0.801938	0.801938
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	−0.801938	−0.801938
$73$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$73$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$74$	−1.80194	−1.80194
$75$	−0.246980	−0.246980
$76$	2.00000	2.00000
$77$	0	0
$78$	0.198062	0.198062
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	1.24698	1.24698
$81$	0.445042	0.445042
$82$	0	0
$83$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$83$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$84$	0	0
$85$	0	0
$86$	1.24698	1.24698
$87$	0	0
$88$	0	0
$89$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$89$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$90$	−1.00000	−1.00000
$91$	0	0
$92$	−1.80194	−1.80194
$93$	−0.554958	−0.554958
$94$	−1.80194	−1.80194
$95$	2.49396	2.49396
$96$	−0.445042	−0.445042
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	1.00000	1.00000
$99$	0	0
$100$	0.554958	0.554958
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	−0.445042	−0.445042
$105$	0	0
$106$	0	0
$107$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$107$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$108$	0.801938	0.801938
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0.801938	0.801938
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	−0.890084	−0.890084
$115$	−2.24698	−2.24698
$116$	0	0
$117$	0.356896	0.356896
$118$	0	0
$119$	0	0
$120$	−0.554958	−0.554958
$121$	1.00000	1.00000
$122$	0	0
$123$	0	0
$124$	1.24698	1.24698
$125$	−0.554958	−0.554958
$126$	0	0
$127$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$127$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$128$	1.00000	1.00000
$129$	−0.554958	−0.554958
$130$	−0.554958	−0.554958
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	−1.80194	−1.80194
$135$	1.00000	1.00000
$136$	0	0
$137$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$137$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$138$	0.801938	0.801938
$139$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$139$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$140$	0	0
$141$	0.801938	0.801938
$142$	0	0
$143$	0	0
$144$	−0.801938	−0.801938
$145$	0	0
$146$	−1.80194	−1.80194
$147$	−0.445042	−0.445042
$148$	−1.80194	−1.80194
$149$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$149$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$150$	−0.246980	−0.246980
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	2.00000	2.00000
$153$	0	0
$154$	0	0
$155$	1.55496	1.55496
$156$	0.198062	0.198062
$157$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$157$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$158$	0	0
$159$	0	0
$160$	1.24698	1.24698
$161$	0	0
$162$	0.445042	0.445042
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	0	0
$166$	1.24698	1.24698
$167$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$167$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$168$	0	0
$169$	−0.801938	−0.801938
$170$	0	0
$171$	−1.60388	−1.60388
$172$	1.24698	1.24698
$173$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$173$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	−1.80194	−1.80194
$179$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$179$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$180$	−1.00000	−1.00000
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	−1.80194	−1.80194
$185$	−2.24698	−2.24698
$186$	−0.554958	−0.554958
$187$	0	0
$188$	−1.80194	−1.80194
$189$	0	0
$190$	2.49396	2.49396
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	−0.445042	−0.445042
$193$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$193$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$194$	0	0
$195$	0.246980	0.246980
$196$	1.00000	1.00000
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$199$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$200$	0.554958	0.554958
$201$	0.801938	0.801938
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	1.44504	1.44504
$208$	−0.445042	−0.445042
$209$	0	0
$210$	0	0
$211$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$211$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$212$	0	0
$213$	0	0
$214$	−0.445042	−0.445042
$215$	1.55496	1.55496
$216$	0.801938	0.801938
$217$	0	0
$218$	0	0
$219$	0.801938	0.801938
$220$	0	0
$221$	0	0
$222$	0.801938	0.801938
$223$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$223$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$224$	0	0
$225$	−0.445042	−0.445042
$226$	0	0
$227$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$227$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$228$	−0.890084	−0.890084
$229$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$229$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$230$	−2.24698	−2.24698
$231$	0	0
$232$	0	0
$233$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$233$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$234$	0.356896	0.356896
$235$	−2.24698	−2.24698
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	−0.554958	−0.554958
$241$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$241$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$242$	1.00000	1.00000
$243$	−1.00000	−1.00000
$244$	0	0
$245$	1.24698	1.24698
$246$	0	0
$247$	−0.890084	−0.890084
$248$	1.24698	1.24698
$249$	−0.554958	−0.554958
$250$	−0.554958	−0.554958
$251$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$251$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$252$	0	0
$253$	0	0
$254$	−0.445042	−0.445042
$255$	0	0
$256$	1.00000	1.00000
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	−0.554958	−0.554958
$259$	0	0
$260$	−0.554958	−0.554958
$261$	0	0
$262$	0	0
$263$	2.00000	2.00000	1.00000			$0$
$263$	2.00000	2.00000	1.00000			$0$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0.801938	0.801938
$268$	−1.80194	−1.80194
$269$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$269$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$270$	1.00000	1.00000
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	1.24698	1.24698
$275$	0	0
$276$	0.801938	0.801938
$277$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$277$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$278$	−1.80194	−1.80194
$279$	−1.00000	−1.00000
$280$	0	0
$281$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$281$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$282$	0.801938	0.801938
$283$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$283$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$284$	0	0
$285$	−1.10992	−1.10992
$286$	0	0
$287$	0	0
$288$	−0.801938	−0.801938
$289$	1.00000	1.00000
$290$	0	0
$291$	0	0
$292$	−1.80194	−1.80194
$293$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$293$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$294$	−0.445042	−0.445042
$295$	0	0
$296$	−1.80194	−1.80194
$297$	0	0
$298$	−0.445042	−0.445042
$299$	0.801938	0.801938
$300$	−0.246980	−0.246980
$301$	0	0
$302$	0	0
$303$	0	0
$304$	2.00000	2.00000
$305$	0	0
$306$	0	0
$307$	2.00000	2.00000	1.00000			$0$
$307$	2.00000	2.00000	1.00000			$0$
$308$	0	0
$309$	0	0
$310$	1.55496	1.55496
$311$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$311$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$312$	0.198062	0.198062
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	1.24698	1.24698
$315$	0	0
$316$	0	0
$317$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$317$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$318$	0	0
$319$	0	0
$320$	1.24698	1.24698
$321$	0.198062	0.198062
$322$	0	0
$323$	0	0
$324$	0.445042	0.445042
$325$	−0.246980	−0.246980
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$331$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$332$	1.24698	1.24698
$333$	1.44504	1.44504
$334$	−0.445042	−0.445042
$335$	−2.24698	−2.24698
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	−0.801938	−0.801938
$339$	0	0
$340$	0	0
$341$	0	0
$342$	−1.60388	−1.60388
$343$	0	0
$344$	1.24698	1.24698
$345$	1.00000	1.00000
$346$	1.24698	1.24698
$347$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$347$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$348$	0	0
$349$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$349$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$350$	0	0
$351$	−0.356896	−0.356896
$352$	0	0
$353$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$353$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$354$	0	0
$355$	0	0
$356$	−1.80194	−1.80194
$357$	0	0
$358$	1.24698	1.24698
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	−1.00000	−1.00000
$361$	3.00000	3.00000
$362$	0	0
$363$	−0.445042	−0.445042
$364$	0	0
$365$	−2.24698	−2.24698
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	−1.80194	−1.80194
$369$	0	0
$370$	−2.24698	−2.24698
$371$	0	0
$372$	−0.554958	−0.554958
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	0.246980	0.246980
$376$	−1.80194	−1.80194
$377$	0	0
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	2.49396	2.49396
$381$	0.198062	0.198062
$382$	0	0
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	−0.445042	−0.445042
$385$	0	0
$386$	1.24698	1.24698
$387$	−1.00000	−1.00000
$388$	0	0
$389$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$389$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$390$	0.246980	0.246980
$391$	0	0
$392$	1.00000	1.00000
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	1.24698	1.24698
$399$	0	0
$400$	0.554958	0.554958
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0.801938	0.801938
$403$	−0.554958	−0.554958
$404$	0	0
$405$	0.554958	0.554958
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	−0.554958	−0.554958
$412$	0	0
$413$	0	0
$414$	1.44504	1.44504
$415$	1.55496	1.55496
$416$	−0.445042	−0.445042
$417$	0.801938	0.801938
$418$	0	0
$419$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$419$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$420$	0	0
$421$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$421$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$422$	−0.445042	−0.445042
$423$	1.44504	1.44504
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	−0.445042	−0.445042
$429$	0	0
$430$	1.55496	1.55496
$431$	2.00000	2.00000	1.00000			$0$
$431$	2.00000	2.00000	1.00000			$0$
$432$	0.801938	0.801938
$433$	2.00000	2.00000	1.00000			$0$
$433$	2.00000	2.00000	1.00000			$0$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−3.60388	−3.60388
$438$	0.801938	0.801938
$439$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$439$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$440$	0	0
$441$	−0.801938	−0.801938
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0.801938	0.801938
$445$	−2.24698	−2.24698
$446$	−1.80194	−1.80194
$447$	0.198062	0.198062
$448$	0	0
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	−0.445042	−0.445042
$451$	0	0
$452$	0	0
$453$	0	0
$454$	−1.80194	−1.80194
$455$	0	0
$456$	−0.890084	−0.890084
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	−1.80194	−1.80194
$459$	0	0
$460$	−2.24698	−2.24698
$461$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$461$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	−0.692021	−0.692021
$466$	−0.445042	−0.445042
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0.356896	0.356896
$469$	0	0
$470$	−2.24698	−2.24698
$471$	−0.554958	−0.554958
$472$	0	0
$473$	0	0
$474$	0	0
$475$	1.10992	1.10992
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	−0.554958	−0.554958
$481$	0.801938	0.801938
$482$	−0.445042	−0.445042
$483$	0	0
$484$	1.00000	1.00000
$485$	0	0
$486$	−1.00000	−1.00000
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	1.24698	1.24698
$491$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$491$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$492$	0	0
$493$	0	0
$494$	−0.890084	−0.890084
$495$	0	0
$496$	1.24698	1.24698
$497$	0	0
$498$	−0.554958	−0.554958
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	−0.554958	−0.554958
$501$	0.198062	0.198062
$502$	−1.80194	−1.80194
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0.356896	0.356896
$508$	−0.445042	−0.445042
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	1.00000
$513$	1.60388	1.60388
$514$	0	0
$515$	0	0
$516$	−0.554958	−0.554958
$517$	0	0
$518$	0	0
$519$	−0.554958	−0.554958
$520$	−0.554958	−0.554958
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	2.00000	2.00000
$527$	0	0
$528$	0	0
$529$	2.24698	2.24698
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0.801938	0.801938
$535$	−0.554958	−0.554958
$536$	−1.80194	−1.80194
$537$	−0.554958	−0.554958
$538$	−0.445042	−0.445042
$539$	0	0
$540$	1.00000	1.00000
$541$	2.00000	2.00000	1.00000			$0$
$541$	2.00000	2.00000	1.00000			$0$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	2.00000	2.00000	1.00000			$0$
$547$	2.00000	2.00000	1.00000			$0$
$548$	1.24698	1.24698
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0.801938	0.801938
$553$	0	0
$554$	−0.445042	−0.445042
$555$	1.00000	1.00000
$556$	−1.80194	−1.80194
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	−1.00000	−1.00000
$559$	−0.554958	−0.554958
$560$	0	0
$561$	0	0
$562$	−0.445042	−0.445042
$563$	2.00000	2.00000	1.00000			$0$
$563$	2.00000	2.00000	1.00000			$0$
$564$	0.801938	0.801938
$565$	0	0
$566$	1.24698	1.24698
$567$	0	0
$568$	0	0
$569$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$569$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$570$	−1.10992	−1.10992
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	−1.00000	−1.00000
$576$	−0.801938	−0.801938
$577$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$577$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$578$	1.00000	1.00000
$579$	−0.554958	−0.554958
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	−1.80194	−1.80194
$585$	0.445042	0.445042
$586$	−0.445042	−0.445042
$587$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$587$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$588$	−0.445042	−0.445042
$589$	2.49396	2.49396
$590$	0	0
$591$	0	0
$592$	−1.80194	−1.80194
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	−0.445042	−0.445042
$597$	−0.554958	−0.554958
$598$	0.801938	0.801938
$599$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$599$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$600$	−0.246980	−0.246980
$601$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$601$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$602$	0	0
$603$	1.44504	1.44504
$604$	0	0
$605$	1.24698	1.24698
$606$	0	0
$607$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$607$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$608$	2.00000	2.00000
$609$	0	0
$610$	0	0
$611$	0.801938	0.801938
$612$	0	0
$613$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$613$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$614$	2.00000	2.00000
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	1.55496	1.55496
$621$	−1.44504	−1.44504
$622$	−0.445042	−0.445042
$623$	0	0
$624$	0.198062	0.198062
$625$	−1.24698	−1.24698
$626$	0	0
$627$	0	0
$628$	1.24698	1.24698
$629$	0	0
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0.198062	0.198062
$634$	−1.80194	−1.80194
$635$	−0.554958	−0.554958
$636$	0	0
$637$	−0.445042	−0.445042
$638$	0	0
$639$	0	0
$640$	1.24698	1.24698
$641$	1.00000	1.00000
$641$	1.00000	1.00000
$642$	0.198062	0.198062
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	−0.692021	−0.692021
$646$	0	0
$647$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$647$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$648$	0.445042	0.445042
$649$	0	0
$650$	−0.246980	−0.246980
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	1.44504	1.44504
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$661$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$662$	1.24698	1.24698
$663$	0	0
$664$	1.24698	1.24698
$665$	0	0
$666$	1.44504	1.44504
$667$	0	0
$668$	−0.445042	−0.445042
$669$	0.801938	0.801938
$670$	−2.24698	−2.24698
$671$	0	0
$672$	0	0
$673$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$673$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$674$	0	0
$675$	0.445042	0.445042
$676$	−0.801938	−0.801938
$677$	2.00000	2.00000	1.00000			$0$
$677$	2.00000	2.00000	1.00000			$0$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0.801938	0.801938
$682$	0	0
$683$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$683$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$684$	−1.60388	−1.60388
$685$	1.55496	1.55496
$686$	0	0
$687$	0.801938	0.801938
$688$	1.24698	1.24698
$689$	0	0
$690$	1.00000	1.00000
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	1.24698	1.24698
$693$	0	0
$694$	−0.445042	−0.445042
$695$	−2.24698	−2.24698
$696$	0	0
$697$	0	0
$698$	−1.80194	−1.80194
$699$	0.198062	0.198062
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	−0.356896	−0.356896
$703$	−3.60388	−3.60388
$704$	0	0
$705$	1.00000	1.00000
$706$	−0.445042	−0.445042
$707$	0	0
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	−1.80194	−1.80194
$713$	−2.24698	−2.24698
$714$	0	0
$715$	0	0
$716$	1.24698	1.24698
$717$	0	0
$718$	0	0
$719$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$719$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$720$	−1.00000	−1.00000
$721$	0	0
$722$	3.00000	3.00000
$723$	0.198062	0.198062
$724$	0	0
$725$	0	0
$726$	−0.445042	−0.445042
$727$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$727$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$728$	0	0
$729$	0	0
$730$	−2.24698	−2.24698
$731$	0	0
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	−0.554958	−0.554958
$736$	−1.80194	−1.80194
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	−2.24698	−2.24698
$741$	0.396125	0.396125
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	−0.554958	−0.554958
$745$	−0.554958	−0.554958
$746$	0	0
$747$	−1.00000	−1.00000
$748$	0	0
$749$	0	0
$750$	0.246980	0.246980
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	−1.80194	−1.80194
$753$	0.801938	0.801938
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	2.49396	2.49396
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0.198062	0.198062
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	−0.445042	−0.445042
$769$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$769$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$770$	0	0
$771$	0	0
$772$	1.24698	1.24698
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	−1.00000	−1.00000
$775$	0.692021	0.692021
$776$	0	0
$777$	0	0
$778$	1.24698	1.24698
$779$	0	0
$780$	0.246980	0.246980
$781$	0	0
$782$	0	0
$783$	0	0
$784$	1.00000	1.00000
$785$	1.55496	1.55496
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	0	0
$789$	−0.890084	−0.890084
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	1.24698	1.24698
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	0.554958	0.554958
$801$	1.44504	1.44504
$802$	0	0
$803$	0	0
$804$	0.801938	0.801938
$805$	0	0
$806$	−0.554958	−0.554958
$807$	0.198062	0.198062
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0.554958	0.554958
$811$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$811$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	2.49396	2.49396
$818$	0	0
$819$	0	0
$820$	0	0
$821$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$821$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$822$	−0.554958	−0.554958
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	1.44504	1.44504
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	1.55496	1.55496
$831$	0.198062	0.198062
$832$	−0.445042	−0.445042
$833$	0	0
$834$	0.801938	0.801938
$835$	−0.554958	−0.554958
$836$	0	0
$837$	1.00000	1.00000
$838$	−1.80194	−1.80194
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	1.00000	1.00000
$842$	−1.80194	−1.80194
$843$	0.198062	0.198062
$844$	−0.445042	−0.445042
$845$	−1.00000	−1.00000
$846$	1.44504	1.44504
$847$	0	0
$848$	0	0
$849$	−0.554958	−0.554958
$850$	0	0
$851$	3.24698	3.24698
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	−2.00000	−2.00000
$856$	−0.445042	−0.445042
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$859$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$860$	1.55496	1.55496
$861$	0	0
$862$	2.00000	2.00000
$863$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$863$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$864$	0.801938	0.801938
$865$	1.55496	1.55496
$866$	2.00000	2.00000
$867$	−0.445042	−0.445042
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0.801938	0.801938
$872$	0	0
$873$	0	0
$874$	−3.60388	−3.60388
$875$	0	0
$876$	0.801938	0.801938
$877$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$877$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$878$	−0.445042	−0.445042
$879$	0.198062	0.198062
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	−0.801938	−0.801938
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0.801938	0.801938
$889$	0	0
$890$	−2.24698	−2.24698
$891$	0	0
$892$	−1.80194	−1.80194
$893$	−3.60388	−3.60388
$894$	0.198062	0.198062
$895$	1.55496	1.55496
$896$	0	0
$897$	−0.356896	−0.356896
$898$	0	0
$899$	0	0
$900$	−0.445042	−0.445042
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$907$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$908$	−1.80194	−1.80194
$909$	0	0
$910$	0	0
$911$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$911$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$912$	−0.890084	−0.890084
$913$	0	0
$914$	0	0
$915$	0	0
$916$	−1.80194	−1.80194
$917$	0	0
$918$	0	0
$919$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$919$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$920$	−2.24698	−2.24698
$921$	−0.890084	−0.890084
$922$	1.24698	1.24698
$923$	0	0
$924$	0	0
$925$	−1.00000	−1.00000
$926$	0	0
$927$	0	0
$928$	0	0
$929$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$929$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$930$	−0.692021	−0.692021
$931$	2.00000	2.00000
$932$	−0.445042	−0.445042
$933$	0.198062	0.198062
$934$	0	0
$935$	0	0
$936$	0.356896	0.356896
$937$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$937$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$938$	0	0
$939$	0	0
$940$	−2.24698	−2.24698
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	−0.554958	−0.554958
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$947$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$948$	0	0
$949$	0.801938	0.801938
$950$	1.10992	1.10992
$951$	0.801938	0.801938
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	−0.554958	−0.554958
$961$	0.554958	0.554958
$962$	0.801938	0.801938
$963$	0.356896	0.356896
$964$	−0.445042	−0.445042
$965$	1.55496	1.55496
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	1.00000	1.00000
$969$	0	0
$970$	0	0
$971$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$971$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$972$	−1.00000	−1.00000
$973$	0	0
$974$	0	0
$975$	0.109916	0.109916
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	1.24698	1.24698
$981$	0	0
$982$	−1.80194	−1.80194
$983$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$983$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	−0.890084	−0.890084
$989$	−2.24698	−2.24698
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	1.24698	1.24698
$993$	−0.554958	−0.554958
$994$	0	0
$995$	1.55496	1.55496
$996$	−0.554958	−0.554958
$997$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$997$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$998$	0	0
$999$	−1.44504	−1.44504

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2564.1.d.b.2563.2	✓	3
4.3	odd	2		2564.1.d.c.2563.2	yes	3
641.640	even	2		2564.1.d.c.2563.2	yes	3
2564.2563	odd	2	CM	2564.1.d.b.2563.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2564.1.d.b.2563.2	✓	3	1.1	even	1	trivial
2564.1.d.b.2563.2	✓	3	2564.2563	odd	2	CM
2564.1.d.c.2563.2	yes	3	4.3	odd	2
2564.1.d.c.2563.2	yes	3	641.640	even	2

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:	\( N \)	\(=\)	\( 2564 = 2^{2} \cdot 641 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2564.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.445042 q^{3} +1.00000 q^{4} +1.24698 q^{5} -0.445042 q^{6} +1.00000 q^{8} -0.801938 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.445042 q^{3} +1.00000 q^{4} +1.24698 q^{5} -0.445042 q^{6} +1.00000 q^{8} -0.801938 q^{9} +1.24698 q^{10} -0.445042 q^{12} -0.445042 q^{13} -0.554958 q^{15} +1.00000 q^{16} -0.801938 q^{18} +2.00000 q^{19} +1.24698 q^{20} -1.80194 q^{23} -0.445042 q^{24} +0.554958 q^{25} -0.445042 q^{26} +0.801938 q^{27} -0.554958 q^{30} +1.24698 q^{31} +1.00000 q^{32} -0.801938 q^{36} -1.80194 q^{37} +2.00000 q^{38} +0.198062 q^{39} +1.24698 q^{40} +1.24698 q^{43} -1.00000 q^{45} -1.80194 q^{46} -1.80194 q^{47} -0.445042 q^{48} +1.00000 q^{49} +0.554958 q^{50} -0.445042 q^{52} +0.801938 q^{54} -0.890084 q^{57} -0.554958 q^{60} +1.24698 q^{62} +1.00000 q^{64} -0.554958 q^{65} -1.80194 q^{67} +0.801938 q^{69} -0.801938 q^{72} -1.80194 q^{73} -1.80194 q^{74} -0.246980 q^{75} +2.00000 q^{76} +0.198062 q^{78} +1.24698 q^{80} +0.445042 q^{81} +1.24698 q^{83} +1.24698 q^{86} -1.80194 q^{89} -1.00000 q^{90} -1.80194 q^{92} -0.554958 q^{93} -1.80194 q^{94} +2.49396 q^{95} -0.445042 q^{96} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} - q^{5} - q^{6} + 3 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - q^3 + 3 * q^4 - q^5 - q^6 + 3 * q^8 + 2 * q^9	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} - q^{5} - q^{6} + 3 q^{8} + 2 q^{9} - q^{10} - q^{12} - q^{13} - 2 q^{15} + 3 q^{16} + 2 q^{18} + 6 q^{19} - q^{20} - q^{23} - q^{24} + 2 q^{25} - q^{26} - 2 q^{27} - 2 q^{30} - q^{31} + 3 q^{32} + 2 q^{36} - q^{37} + 6 q^{38} + 5 q^{39} - q^{40} - q^{43} - 3 q^{45} - q^{46} - q^{47} - q^{48} + 3 q^{49} + 2 q^{50} - q^{52} - 2 q^{54} - 2 q^{57} - 2 q^{60} - q^{62} + 3 q^{64} - 2 q^{65} - q^{67} - 2 q^{69} + 2 q^{72} - q^{73} - q^{74} + 4 q^{75} + 6 q^{76} + 5 q^{78} - q^{80} + q^{81} - q^{83} - q^{86} - q^{89} - 3 q^{90} - q^{92} - 2 q^{93} - q^{94} - 2 q^{95} - q^{96} + 3 q^{98}+O(q^{100}) \) 3 * q + 3 * q^2 - q^3 + 3 * q^4 - q^5 - q^6 + 3 * q^8 + 2 * q^9 - q^10 - q^12 - q^13 - 2 * q^15 + 3 * q^16 + 2 * q^18 + 6 * q^19 - q^20 - q^23 - q^24 + 2 * q^25 - q^26 - 2 * q^27 - 2 * q^30 - q^31 + 3 * q^32 + 2 * q^36 - q^37 + 6 * q^38 + 5 * q^39 - q^40 - q^43 - 3 * q^45 - q^46 - q^47 - q^48 + 3 * q^49 + 2 * q^50 - q^52 - 2 * q^54 - 2 * q^57 - 2 * q^60 - q^62 + 3 * q^64 - 2 * q^65 - q^67 - 2 * q^69 + 2 * q^72 - q^73 - q^74 + 4 * q^75 + 6 * q^76 + 5 * q^78 - q^80 + q^81 - q^83 - q^86 - q^89 - 3 * q^90 - q^92 - 2 * q^93 - q^94 - 2 * q^95 - q^96 + 3 * q^98

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