LMFDB - Embedded newform 3143.1.d.c.3142.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3143,1,Mod(3142,3143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3143, 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("3143.3142");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3143 = 7 \cdot 449 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3143.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:	$1.56856133471$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{7}$
Projective field:	Galois closure of 7.1.31047965207.1
Artin image:	$D_7$
Artin field:	Galois closure of 7.1.31047965207.1

Embedding invariants

Embedding label			3142.1
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	3143.3142

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.80194 q^{2} -0.445042 q^{3} +2.24698 q^{4} +0.801938 q^{6} +1.00000 q^{7} -2.24698 q^{8} -0.801938 q^{9} +O(q^{10})$	\(q-1.80194 q^{2} -0.445042 q^{3} +2.24698 q^{4} +0.801938 q^{6} +1.00000 q^{7} -2.24698 q^{8} -0.801938 q^{9} +1.24698 q^{11} -1.00000 q^{12} -1.80194 q^{13} -1.80194 q^{14} +1.80194 q^{16} -1.80194 q^{17} +1.44504 q^{18} -0.445042 q^{19} -0.445042 q^{21} -2.24698 q^{22} -0.445042 q^{23} +1.00000 q^{24} +1.00000 q^{25} +3.24698 q^{26} +0.801938 q^{27} +2.24698 q^{28} +2.00000 q^{31} -1.00000 q^{32} -0.554958 q^{33} +3.24698 q^{34} -1.80194 q^{36} +0.801938 q^{38} +0.801938 q^{39} +0.801938 q^{42} +2.80194 q^{44} +0.801938 q^{46} +2.00000 q^{47} -0.801938 q^{48} +1.00000 q^{49} -1.80194 q^{50} +0.801938 q^{51} -4.04892 q^{52} -1.80194 q^{53} -1.44504 q^{54} -2.24698 q^{56} +0.198062 q^{57} -3.60388 q^{62} -0.801938 q^{63} +1.00000 q^{66} +2.00000 q^{67} -4.04892 q^{68} +0.198062 q^{69} +1.80194 q^{72} +1.24698 q^{73} -0.445042 q^{75} -1.00000 q^{76} +1.24698 q^{77} -1.44504 q^{78} +0.445042 q^{81} +1.24698 q^{83} -1.00000 q^{84} -2.80194 q^{88} -1.80194 q^{91} -1.00000 q^{92} -0.890084 q^{93} -3.60388 q^{94} +0.445042 q^{96} -1.80194 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - q^{3} + 2 q^{4} - 2 q^{6} + 3 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q - q^2 - q^3 + 2 * q^4 - 2 * q^6 + 3 * q^7 - 2 * q^8 + 2 * q^9	$ 3 q - q^{2} - q^{3} + 2 q^{4} - 2 q^{6} + 3 q^{7} - 2 q^{8} + 2 q^{9} - q^{11} - 3 q^{12} - q^{13} - q^{14} + q^{16} - q^{17} + 4 q^{18} - q^{19} - q^{21} - 2 q^{22} - q^{23} + 3 q^{24} + 3 q^{25} + 5 q^{26} - 2 q^{27} + 2 q^{28} + 6 q^{31} - 3 q^{32} - 2 q^{33} + 5 q^{34} - q^{36} - 2 q^{38} - 2 q^{39} - 2 q^{42} + 4 q^{44} - 2 q^{46} + 6 q^{47} + 2 q^{48} + 3 q^{49} - q^{50} - 2 q^{51} - 3 q^{52} - q^{53} - 4 q^{54} - 2 q^{56} + 5 q^{57} - 2 q^{62} + 2 q^{63} + 3 q^{66} + 6 q^{67} - 3 q^{68} + 5 q^{69} + q^{72} - q^{73} - q^{75} - 3 q^{76} - q^{77} - 4 q^{78} + q^{81} - q^{83} - 3 q^{84} - 4 q^{88} - q^{91} - 3 q^{92} - 2 q^{93} - 2 q^{94} + q^{96} - q^{98} - 3 q^{99}+O(q^{100}) $ 3 * q - q^2 - q^3 + 2 * q^4 - 2 * q^6 + 3 * q^7 - 2 * q^8 + 2 * q^9 - q^11 - 3 * q^12 - q^13 - q^14 + q^16 - q^17 + 4 * q^18 - q^19 - q^21 - 2 * q^22 - q^23 + 3 * q^24 + 3 * q^25 + 5 * q^26 - 2 * q^27 + 2 * q^28 + 6 * q^31 - 3 * q^32 - 2 * q^33 + 5 * q^34 - q^36 - 2 * q^38 - 2 * q^39 - 2 * q^42 + 4 * q^44 - 2 * q^46 + 6 * q^47 + 2 * q^48 + 3 * q^49 - q^50 - 2 * q^51 - 3 * q^52 - q^53 - 4 * q^54 - 2 * q^56 + 5 * q^57 - 2 * q^62 + 2 * q^63 + 3 * q^66 + 6 * q^67 - 3 * q^68 + 5 * q^69 + q^72 - q^73 - q^75 - 3 * q^76 - q^77 - 4 * q^78 + q^81 - q^83 - 3 * q^84 - 4 * q^88 - q^91 - 3 * q^92 - 2 * q^93 - 2 * q^94 + q^96 - q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3143\mathbb{Z}\right)^\times$.

$n$	$899$	$2248$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$2$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$3$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$3$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$4$	2.24698	2.24698
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	0.801938	0.801938
$7$	1.00000	1.00000
$7$	1.00000	1.00000
$8$	−2.24698	−2.24698
$9$	−0.801938	−0.801938
$10$	0	0
$11$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$11$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$12$	−1.00000	−1.00000
$13$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$13$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$14$	−1.80194	−1.80194
$15$	0	0
$16$	1.80194	1.80194
$17$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$17$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$18$	1.44504	1.44504
$19$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$19$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$20$	0	0
$21$	−0.445042	−0.445042
$22$	−2.24698	−2.24698
$23$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$23$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$24$	1.00000	1.00000
$25$	1.00000	1.00000
$26$	3.24698	3.24698
$27$	0.801938	0.801938
$28$	2.24698	2.24698
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	2.00000	2.00000	1.00000			$0$
$31$	2.00000	2.00000	1.00000			$0$
$32$	−1.00000	−1.00000
$33$	−0.554958	−0.554958
$34$	3.24698	3.24698
$35$	0	0
$36$	−1.80194	−1.80194
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0.801938	0.801938
$39$	0.801938	0.801938
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0.801938	0.801938
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	2.80194	2.80194
$45$	0	0
$46$	0.801938	0.801938
$47$	2.00000	2.00000	1.00000			$0$
$47$	2.00000	2.00000	1.00000			$0$
$48$	−0.801938	−0.801938
$49$	1.00000	1.00000
$50$	−1.80194	−1.80194
$51$	0.801938	0.801938
$52$	−4.04892	−4.04892
$53$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$53$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$54$	−1.44504	−1.44504
$55$	0	0
$56$	−2.24698	−2.24698
$57$	0.198062	0.198062
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	−3.60388	−3.60388
$63$	−0.801938	−0.801938
$64$	0	0
$65$	0	0
$66$	1.00000	1.00000
$67$	2.00000	2.00000	1.00000			$0$
$67$	2.00000	2.00000	1.00000			$0$
$68$	−4.04892	−4.04892
$69$	0.198062	0.198062
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	1.80194	1.80194
$73$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$73$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$74$	0	0
$75$	−0.445042	−0.445042
$76$	−1.00000	−1.00000
$77$	1.24698	1.24698
$78$	−1.44504	−1.44504
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	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	$0.285714\pi$
$84$	−1.00000	−1.00000
$85$	0	0
$86$	0	0
$87$	0	0
$88$	−2.80194	−2.80194
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	−1.80194	−1.80194
$92$	−1.00000	−1.00000
$93$	−0.890084	−0.890084
$94$	−3.60388	−3.60388
$95$	0	0
$96$	0.445042	0.445042
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	−1.80194	−1.80194
$99$	−1.00000	−1.00000
$100$	2.24698	2.24698
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	−1.44504	−1.44504
$103$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$103$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$104$	4.04892	4.04892
$105$	0	0
$106$	3.24698	3.24698
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	1.80194	1.80194
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	1.80194	1.80194
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	−0.356896	−0.356896
$115$	0	0
$116$	0	0
$117$	1.44504	1.44504
$118$	0	0
$119$	−1.80194	−1.80194
$120$	0	0
$121$	0.554958	0.554958
$122$	0	0
$123$	0	0
$124$	4.49396	4.49396
$125$	0	0
$126$	1.44504	1.44504
$127$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$127$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$128$	1.00000	1.00000
$129$	0	0
$130$	0	0
$131$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$131$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$132$	−1.24698	−1.24698
$133$	−0.445042	−0.445042
$134$	−3.60388	−3.60388
$135$	0	0
$136$	4.04892	4.04892
$137$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$137$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$138$	−0.356896	−0.356896
$139$	−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
$141$	−0.890084	−0.890084
$142$	0	0
$143$	−2.24698	−2.24698
$144$	−1.44504	−1.44504
$145$	0	0
$146$	−2.24698	−2.24698
$147$	−0.445042	−0.445042
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0.801938	0.801938
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	1.00000	1.00000
$153$	1.44504	1.44504
$154$	−2.24698	−2.24698
$155$	0	0
$156$	1.80194	1.80194
$157$	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
$159$	0.801938	0.801938
$160$	0	0
$161$	−0.445042	−0.445042
$162$	−0.801938	−0.801938
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	0	0
$166$	−2.24698	−2.24698
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	1.00000	1.00000
$169$	2.24698	2.24698
$170$	0	0
$171$	0.356896	0.356896
$172$	0	0
$173$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$173$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$174$	0	0
$175$	1.00000	1.00000
$176$	2.24698	2.24698
$177$	0	0
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	3.24698	3.24698
$183$	0	0
$184$	1.00000	1.00000
$185$	0	0
$186$	1.60388	1.60388
$187$	−2.24698	−2.24698
$188$	4.49396	4.49396
$189$	0.801938	0.801938
$190$	0	0
$191$	2.00000	2.00000	1.00000			$0$
$191$	2.00000	2.00000	1.00000			$0$
$192$	0	0
$193$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$193$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$194$	0	0
$195$	0	0
$196$	2.24698	2.24698
$197$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$197$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$198$	1.80194	1.80194
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	−2.24698	−2.24698
$201$	−0.890084	−0.890084
$202$	0	0
$203$	0	0
$204$	1.80194	1.80194
$205$	0	0
$206$	−2.24698	−2.24698
$207$	0.356896	0.356896
$208$	−3.24698	−3.24698
$209$	−0.554958	−0.554958
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	−4.04892	−4.04892
$213$	0	0
$214$	0	0
$215$	0	0
$216$	−1.80194	−1.80194
$217$	2.00000	2.00000
$218$	0	0
$219$	−0.554958	−0.554958
$220$	0	0
$221$	3.24698	3.24698
$222$	0	0
$223$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$223$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$224$	−1.00000	−1.00000
$225$	−0.801938	−0.801938
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0.445042	0.445042
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	−0.554958	−0.554958
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	−2.60388	−2.60388
$235$	0	0
$236$	0	0
$237$	0	0
$238$	3.24698	3.24698
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$241$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$242$	−1.00000	−1.00000
$243$	−1.00000	−1.00000
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0.801938	0.801938
$248$	−4.49396	−4.49396
$249$	−0.554958	−0.554958
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	−1.80194	−1.80194
$253$	−0.554958	−0.554958
$254$	3.24698	3.24698
$255$	0	0
$256$	−1.80194	−1.80194
$257$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$257$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	−2.24698	−2.24698
$263$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$263$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$264$	1.24698	1.24698
$265$	0	0
$266$	0.801938	0.801938
$267$	0	0
$268$	4.49396	4.49396
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	−3.24698	−3.24698
$273$	0.801938	0.801938
$274$	0.801938	0.801938
$275$	1.24698	1.24698
$276$	0.445042	0.445042
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	3.24698	3.24698
$279$	−1.60388	−1.60388
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	1.60388	1.60388
$283$	2.00000	2.00000	1.00000			$0$
$283$	2.00000	2.00000	1.00000			$0$
$284$	0	0
$285$	0	0
$286$	4.04892	4.04892
$287$	0	0
$288$	0.801938	0.801938
$289$	2.24698	2.24698
$290$	0	0
$291$	0	0
$292$	2.80194	2.80194
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0.801938	0.801938
$295$	0	0
$296$	0	0
$297$	1.00000	1.00000
$298$	0	0
$299$	0.801938	0.801938
$300$	−1.00000	−1.00000
$301$	0	0
$302$	0	0
$303$	0	0
$304$	−0.801938	−0.801938
$305$	0	0
$306$	−2.60388	−2.60388
$307$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$307$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$308$	2.80194	2.80194
$309$	−0.554958	−0.554958
$310$	0	0
$311$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$311$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$312$	−1.80194	−1.80194
$313$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$313$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$314$	−2.24698	−2.24698
$315$	0	0
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	−1.44504	−1.44504
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0.801938	0.801938
$323$	0.801938	0.801938
$324$	1.00000	1.00000
$325$	−1.80194	−1.80194
$326$	0	0
$327$	0	0
$328$	0	0
$329$	2.00000	2.00000
$330$	0	0
$331$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$331$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$332$	2.80194	2.80194
$333$	0	0
$334$	0	0
$335$	0	0
$336$	−0.801938	−0.801938
$337$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$337$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$338$	−4.04892	−4.04892
$339$	0	0
$340$	0	0
$341$	2.49396	2.49396
$342$	−0.643104	−0.643104
$343$	1.00000	1.00000
$344$	0	0
$345$	0	0
$346$	0.801938	0.801938
$347$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$347$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	−1.80194	−1.80194
$351$	−1.44504	−1.44504
$352$	−1.24698	−1.24698
$353$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$353$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0.801938	0.801938
$358$	0	0
$359$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$359$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$360$	0	0
$361$	−0.801938	−0.801938
$362$	0	0
$363$	−0.246980	−0.246980
$364$	−4.04892	−4.04892
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	−0.801938	−0.801938
$369$	0	0
$370$	0	0
$371$	−1.80194	−1.80194
$372$	−2.00000	−2.00000
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	4.04892	4.04892
$375$	0	0
$376$	−4.49396	−4.49396
$377$	0	0
$378$	−1.44504	−1.44504
$379$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$379$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$380$	0	0
$381$	0.801938	0.801938
$382$	−3.60388	−3.60388
$383$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$383$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$384$	−0.445042	−0.445042
$385$	0	0
$386$	0.801938	0.801938
$387$	0	0
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	0.801938	0.801938
$392$	−2.24698	−2.24698
$393$	−0.554958	−0.554958
$394$	−2.24698	−2.24698
$395$	0	0
$396$	−2.24698	−2.24698
$397$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$397$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$398$	0	0
$399$	0.198062	0.198062
$400$	1.80194	1.80194
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	1.60388	1.60388
$403$	−3.60388	−3.60388
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	−1.80194	−1.80194
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0.198062	0.198062
$412$	2.80194	2.80194
$413$	0	0
$414$	−0.643104	−0.643104
$415$	0	0
$416$	1.80194	1.80194
$417$	0.801938	0.801938
$418$	1.00000	1.00000
$419$	−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	0
$423$	−1.60388	−1.60388
$424$	4.04892	4.04892
$425$	−1.80194	−1.80194
$426$	0	0
$427$	0	0
$428$	0	0
$429$	1.00000	1.00000
$430$	0	0
$431$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$431$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$432$	1.44504	1.44504
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	−3.60388	−3.60388
$435$	0	0
$436$	0	0
$437$	0.198062	0.198062
$438$	1.00000	1.00000
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	−0.801938	−0.801938
$442$	−5.85086	−5.85086
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	0	0
$446$	−2.24698	−2.24698
$447$	0	0
$448$	0	0
$449$	1.00000	1.00000
$449$	1.00000	1.00000
$450$	1.44504	1.44504
$451$	0	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	−0.445042	−0.445042
$457$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$457$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$458$	0	0
$459$	−1.44504	−1.44504
$460$	0	0
$461$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$461$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$462$	1.00000	1.00000
$463$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$463$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	3.24698	3.24698
$469$	2.00000	2.00000
$470$	0	0
$471$	−0.554958	−0.554958
$472$	0	0
$473$	0	0
$474$	0	0
$475$	−0.445042	−0.445042
$476$	−4.04892	−4.04892
$477$	1.44504	1.44504
$478$	0	0
$479$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$479$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$480$	0	0
$481$	0	0
$482$	−2.24698	−2.24698
$483$	0.198062	0.198062
$484$	1.24698	1.24698
$485$	0	0
$486$	1.80194	1.80194
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	−1.44504	−1.44504
$495$	0	0
$496$	3.60388	3.60388
$497$	0	0
$498$	1.00000	1.00000
$499$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$499$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$503$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$504$	1.80194	1.80194
$505$	0	0
$506$	1.00000	1.00000
$507$	−1.00000	−1.00000
$508$	−4.04892	−4.04892
$509$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$509$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$510$	0	0
$511$	1.24698	1.24698
$512$	2.24698	2.24698
$513$	−0.356896	−0.356896
$514$	0.801938	0.801938
$515$	0	0
$516$	0	0
$517$	2.49396	2.49396
$518$	0	0
$519$	0.198062	0.198062
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$523$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$524$	2.80194	2.80194
$525$	−0.445042	−0.445042
$526$	0.801938	0.801938
$527$	−3.60388	−3.60388
$528$	−1.00000	−1.00000
$529$	−0.801938	−0.801938
$530$	0	0
$531$	0	0
$532$	−1.00000	−1.00000
$533$	0	0
$534$	0	0
$535$	0	0
$536$	−4.49396	−4.49396
$537$	0	0
$538$	0	0
$539$	1.24698	1.24698
$540$	0	0
$541$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$541$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$542$	0	0
$543$	0	0
$544$	1.80194	1.80194
$545$	0	0
$546$	−1.44504	−1.44504
$547$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$547$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$548$	−1.00000	−1.00000
$549$	0	0
$550$	−2.24698	−2.24698
$551$	0	0
$552$	−0.445042	−0.445042
$553$	0	0
$554$	0	0
$555$	0	0
$556$	−4.04892	−4.04892
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	2.89008	2.89008
$559$	0	0
$560$	0	0
$561$	1.00000	1.00000
$562$	0	0
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	−2.00000	−2.00000
$565$	0	0
$566$	−3.60388	−3.60388
$567$	0.445042	0.445042
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$571$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$572$	−5.04892	−5.04892
$573$	−0.890084	−0.890084
$574$	0	0
$575$	−0.445042	−0.445042
$576$	0	0
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	−4.04892	−4.04892
$579$	0.198062	0.198062
$580$	0	0
$581$	1.24698	1.24698
$582$	0	0
$583$	−2.24698	−2.24698
$584$	−2.80194	−2.80194
$585$	0	0
$586$	0	0
$587$	2.00000	2.00000	1.00000			$0$
$587$	2.00000	2.00000	1.00000			$0$
$588$	−1.00000	−1.00000
$589$	−0.890084	−0.890084
$590$	0	0
$591$	−0.554958	−0.554958
$592$	0	0
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	−1.80194	−1.80194
$595$	0	0
$596$	0	0
$597$	0	0
$598$	−1.44504	−1.44504
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	1.00000	1.00000
$601$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$601$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$602$	0	0
$603$	−1.60388	−1.60388
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$607$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$608$	0.445042	0.445042
$609$	0	0
$610$	0	0
$611$	−3.60388	−3.60388
$612$	3.24698	3.24698
$613$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$613$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$614$	0.801938	0.801938
$615$	0	0
$616$	−2.80194	−2.80194
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	1.00000	1.00000
$619$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$619$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$620$	0	0
$621$	−0.356896	−0.356896
$622$	3.24698	3.24698
$623$	0	0
$624$	1.44504	1.44504
$625$	1.00000	1.00000
$626$	3.24698	3.24698
$627$	0.246980	0.246980
$628$	2.80194	2.80194
$629$	0	0
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	1.80194	1.80194
$637$	−1.80194	−1.80194
$638$	0	0
$639$	0	0
$640$	0	0
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	−1.00000	−1.00000
$645$	0	0
$646$	−1.44504	−1.44504
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	−1.00000	−1.00000
$649$	0	0
$650$	3.24698	3.24698
$651$	−0.890084	−0.890084
$652$	0	0
$653$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$653$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−1.00000	−1.00000
$658$	−3.60388	−3.60388
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	3.24698	3.24698
$663$	−1.44504	−1.44504
$664$	−2.80194	−2.80194
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	−0.554958	−0.554958
$670$	0	0
$671$	0	0
$672$	0.445042	0.445042
$673$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$673$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$674$	0.801938	0.801938
$675$	0.801938	0.801938
$676$	5.04892	5.04892
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	−4.49396	−4.49396
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0.801938	0.801938
$685$	0	0
$686$	−1.80194	−1.80194
$687$	0	0
$688$	0	0
$689$	3.24698	3.24698
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	−1.00000	−1.00000
$693$	−1.00000	−1.00000
$694$	−2.24698	−2.24698
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	2.24698	2.24698
$701$	2.00000	2.00000	1.00000			$0$
$701$	2.00000	2.00000	1.00000			$0$
$702$	2.60388	2.60388
$703$	0	0
$704$	0	0
$705$	0	0
$706$	−2.24698	−2.24698
$707$	0	0
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	−0.890084	−0.890084
$714$	−1.44504	−1.44504
$715$	0	0
$716$	0	0
$717$	0	0
$718$	−2.24698	−2.24698
$719$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$719$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$720$	0	0
$721$	1.24698	1.24698
$722$	1.44504	1.44504
$723$	−0.554958	−0.554958
$724$	0	0
$725$	0	0
$726$	0.445042	0.445042
$727$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$727$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$728$	4.04892	4.04892
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$733$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$734$	0	0
$735$	0	0
$736$	0.445042	0.445042
$737$	2.49396	2.49396
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	−0.356896	−0.356896
$742$	3.24698	3.24698
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	2.00000	2.00000
$745$	0	0
$746$	0	0
$747$	−1.00000	−1.00000
$748$	−5.04892	−5.04892
$749$	0	0
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	3.60388	3.60388
$753$	0	0
$754$	0	0
$755$	0	0
$756$	1.80194	1.80194
$757$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$757$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$758$	−2.24698	−2.24698
$759$	0.246980	0.246980
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	−1.44504	−1.44504
$763$	0	0
$764$	4.49396	4.49396
$765$	0	0
$766$	0.801938	0.801938
$767$	0	0
$768$	0.801938	0.801938
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0.198062	0.198062
$772$	−1.00000	−1.00000
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	2.00000	2.00000
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	−1.44504	−1.44504
$783$	0	0
$784$	1.80194	1.80194
$785$	0	0
$786$	1.00000	1.00000
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	2.80194	2.80194
$789$	0.198062	0.198062
$790$	0	0
$791$	0	0
$792$	2.24698	2.24698
$793$	0	0
$794$	3.24698	3.24698
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	−0.356896	−0.356896
$799$	−3.60388	−3.60388
$800$	−1.00000	−1.00000
$801$	0	0
$802$	0	0
$803$	1.55496	1.55496
$804$	−2.00000	−2.00000
$805$	0	0
$806$	6.49396	6.49396
$807$	0	0
$808$	0	0
$809$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$809$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	1.44504	1.44504
$817$	0	0
$818$	0	0
$819$	1.44504	1.44504
$820$	0	0
$821$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$821$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$822$	−0.356896	−0.356896
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	−2.80194	−2.80194
$825$	−0.554958	−0.554958
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0.801938	0.801938
$829$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$829$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	−1.80194	−1.80194
$834$	−1.44504	−1.44504
$835$	0	0
$836$	−1.24698	−1.24698
$837$	1.60388	1.60388
$838$	3.24698	3.24698
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	1.00000	1.00000
$842$	3.24698	3.24698
$843$	0	0
$844$	0	0
$845$	0	0
$846$	2.89008	2.89008
$847$	0.554958	0.554958
$848$	−3.24698	−3.24698
$849$	−0.890084	−0.890084
$850$	3.24698	3.24698
$851$	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
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	−1.80194	−1.80194
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	−2.24698	−2.24698
$863$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$863$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$864$	−0.801938	−0.801938
$865$	0	0
$866$	0	0
$867$	−1.00000	−1.00000
$868$	4.49396	4.49396
$869$	0	0
$870$	0	0
$871$	−3.60388	−3.60388
$872$	0	0
$873$	0	0
$874$	−0.356896	−0.356896
$875$	0	0
$876$	−1.24698	−1.24698
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$881$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$882$	1.44504	1.44504
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	7.29590	7.29590
$885$	0	0
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	−1.80194	−1.80194
$890$	0	0
$891$	0.554958	0.554958
$892$	2.80194	2.80194
$893$	−0.890084	−0.890084
$894$	0	0
$895$	0	0
$896$	1.00000	1.00000
$897$	−0.356896	−0.356896
$898$	−1.80194	−1.80194
$899$	0	0
$900$	−1.80194	−1.80194
$901$	3.24698	3.24698
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$907$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0.356896	0.356896
$913$	1.55496	1.55496
$914$	0.801938	0.801938
$915$	0	0
$916$	0	0
$917$	1.24698	1.24698
$918$	2.60388	2.60388
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0.198062	0.198062
$922$	0.801938	0.801938
$923$	0	0
$924$	−1.24698	−1.24698
$925$	0	0
$926$	3.24698	3.24698
$927$	−1.00000	−1.00000
$928$	0	0
$929$	2.00000	2.00000	1.00000			$0$
$929$	2.00000	2.00000	1.00000			$0$
$930$	0	0
$931$	−0.445042	−0.445042
$932$	0	0
$933$	0.801938	0.801938
$934$	0	0
$935$	0	0
$936$	−3.24698	−3.24698
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	−3.60388	−3.60388
$939$	0.801938	0.801938
$940$	0	0
$941$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$941$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$942$	1.00000	1.00000
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$947$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$948$	0	0
$949$	−2.24698	−2.24698
$950$	0.801938	0.801938
$951$	0	0
$952$	4.04892	4.04892
$953$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$953$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$954$	−2.60388	−2.60388
$955$	0	0
$956$	0	0
$957$	0	0
$958$	−2.24698	−2.24698
$959$	−0.445042	−0.445042
$960$	0	0
$961$	3.00000	3.00000
$962$	0	0
$963$	0	0
$964$	2.80194	2.80194
$965$	0	0
$966$	−0.356896	−0.356896
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	−1.24698	−1.24698
$969$	−0.356896	−0.356896
$970$	0	0
$971$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$971$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$972$	−2.24698	−2.24698
$973$	−1.80194	−1.80194
$974$	0	0
$975$	0.801938	0.801938
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	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
$987$	−0.890084	−0.890084
$988$	1.80194	1.80194
$989$	0	0
$990$	0	0
$991$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$991$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$992$	−2.00000	−2.00000
$993$	0.801938	0.801938
$994$	0	0
$995$	0	0
$996$	−1.24698	−1.24698
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0.801938	0.801938
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3143.1.d.c.3142.1	✓	3
7.6	odd	2		3143.1.d.d.3142.1	yes	3
449.448	even	2		3143.1.d.d.3142.1	yes	3
3143.3142	odd	2	CM	3143.1.d.c.3142.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3143.1.d.c.3142.1	✓	3	1.1	even	1	trivial
3143.1.d.c.3142.1	✓	3	3143.3142	odd	2	CM
3143.1.d.d.3142.1	yes	3	7.6	odd	2
3143.1.d.d.3142.1	yes	3	449.448	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:	\( N \)	\(=\)	\( 3143 = 7 \cdot 449 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3143.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.80194 q^{2} -0.445042 q^{3} +2.24698 q^{4} +0.801938 q^{6} +1.00000 q^{7} -2.24698 q^{8} -0.801938 q^{9} +O(q^{10})\)	\(q-1.80194 q^{2} -0.445042 q^{3} +2.24698 q^{4} +0.801938 q^{6} +1.00000 q^{7} -2.24698 q^{8} -0.801938 q^{9} +1.24698 q^{11} -1.00000 q^{12} -1.80194 q^{13} -1.80194 q^{14} +1.80194 q^{16} -1.80194 q^{17} +1.44504 q^{18} -0.445042 q^{19} -0.445042 q^{21} -2.24698 q^{22} -0.445042 q^{23} +1.00000 q^{24} +1.00000 q^{25} +3.24698 q^{26} +0.801938 q^{27} +2.24698 q^{28} +2.00000 q^{31} -1.00000 q^{32} -0.554958 q^{33} +3.24698 q^{34} -1.80194 q^{36} +0.801938 q^{38} +0.801938 q^{39} +0.801938 q^{42} +2.80194 q^{44} +0.801938 q^{46} +2.00000 q^{47} -0.801938 q^{48} +1.00000 q^{49} -1.80194 q^{50} +0.801938 q^{51} -4.04892 q^{52} -1.80194 q^{53} -1.44504 q^{54} -2.24698 q^{56} +0.198062 q^{57} -3.60388 q^{62} -0.801938 q^{63} +1.00000 q^{66} +2.00000 q^{67} -4.04892 q^{68} +0.198062 q^{69} +1.80194 q^{72} +1.24698 q^{73} -0.445042 q^{75} -1.00000 q^{76} +1.24698 q^{77} -1.44504 q^{78} +0.445042 q^{81} +1.24698 q^{83} -1.00000 q^{84} -2.80194 q^{88} -1.80194 q^{91} -1.00000 q^{92} -0.890084 q^{93} -3.60388 q^{94} +0.445042 q^{96} -1.80194 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - q^{3} + 2 q^{4} - 2 q^{6} + 3 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q - q^2 - q^3 + 2 * q^4 - 2 * q^6 + 3 * q^7 - 2 * q^8 + 2 * q^9	\( 3 q - q^{2} - q^{3} + 2 q^{4} - 2 q^{6} + 3 q^{7} - 2 q^{8} + 2 q^{9} - q^{11} - 3 q^{12} - q^{13} - q^{14} + q^{16} - q^{17} + 4 q^{18} - q^{19} - q^{21} - 2 q^{22} - q^{23} + 3 q^{24} + 3 q^{25} + 5 q^{26} - 2 q^{27} + 2 q^{28} + 6 q^{31} - 3 q^{32} - 2 q^{33} + 5 q^{34} - q^{36} - 2 q^{38} - 2 q^{39} - 2 q^{42} + 4 q^{44} - 2 q^{46} + 6 q^{47} + 2 q^{48} + 3 q^{49} - q^{50} - 2 q^{51} - 3 q^{52} - q^{53} - 4 q^{54} - 2 q^{56} + 5 q^{57} - 2 q^{62} + 2 q^{63} + 3 q^{66} + 6 q^{67} - 3 q^{68} + 5 q^{69} + q^{72} - q^{73} - q^{75} - 3 q^{76} - q^{77} - 4 q^{78} + q^{81} - q^{83} - 3 q^{84} - 4 q^{88} - q^{91} - 3 q^{92} - 2 q^{93} - 2 q^{94} + q^{96} - q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q - q^2 - q^3 + 2 * q^4 - 2 * q^6 + 3 * q^7 - 2 * q^8 + 2 * q^9 - q^11 - 3 * q^12 - q^13 - q^14 + q^16 - q^17 + 4 * q^18 - q^19 - q^21 - 2 * q^22 - q^23 + 3 * q^24 + 3 * q^25 + 5 * q^26 - 2 * q^27 + 2 * q^28 + 6 * q^31 - 3 * q^32 - 2 * q^33 + 5 * q^34 - q^36 - 2 * q^38 - 2 * q^39 - 2 * q^42 + 4 * q^44 - 2 * q^46 + 6 * q^47 + 2 * q^48 + 3 * q^49 - q^50 - 2 * q^51 - 3 * q^52 - q^53 - 4 * q^54 - 2 * q^56 + 5 * q^57 - 2 * q^62 + 2 * q^63 + 3 * q^66 + 6 * q^67 - 3 * q^68 + 5 * q^69 + q^72 - q^73 - q^75 - 3 * q^76 - q^77 - 4 * q^78 + q^81 - q^83 - 3 * q^84 - 4 * q^88 - q^91 - 3 * q^92 - 2 * q^93 - 2 * q^94 + q^96 - q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more