LMFDB - Embedded newform 1859.1.c.b.846.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,1,Mod(846,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("1859.846");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1859.c (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:	$0.927761858485$
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 7.1.6424482779.1
Artin image:	$D_{14}$
Artin field:	Galois closure of 14.2.536561726709678316933.1

Embedding invariants

Embedding label			846.1
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	1859.846

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.80194 q^{3} +1.00000 q^{4} -1.24698 q^{5} +2.24698 q^{9} +O(q^{10})$	$q-1.80194 q^{3} +1.00000 q^{4} -1.24698 q^{5} +2.24698 q^{9} -1.00000 q^{11} -1.80194 q^{12} +2.24698 q^{15} +1.00000 q^{16} -1.24698 q^{20} -0.445042 q^{23} +0.554958 q^{25} -2.24698 q^{27} +0.445042 q^{31} +1.80194 q^{33} +2.24698 q^{36} +1.80194 q^{37} -1.00000 q^{44} -2.80194 q^{45} +0.445042 q^{47} -1.80194 q^{48} +1.00000 q^{49} +1.24698 q^{53} +1.24698 q^{55} +1.80194 q^{59} +2.24698 q^{60} +1.00000 q^{64} -2.00000 q^{67} +0.801938 q^{69} +1.80194 q^{71} -1.00000 q^{75} -1.24698 q^{80} +1.80194 q^{81} +0.445042 q^{89} -0.445042 q^{92} -0.801938 q^{93} -1.24698 q^{97} -2.24698 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{3} + 3 q^{4} + q^{5} + 2 q^{9}+O(q^{10}) $ 3 * q - q^3 + 3 * q^4 + q^5 + 2 * q^9	$ 3 q - q^{3} + 3 q^{4} + q^{5} + 2 q^{9} - 3 q^{11} - q^{12} + 2 q^{15} + 3 q^{16} + q^{20} - q^{23} + 2 q^{25} - 2 q^{27} + q^{31} + q^{33} + 2 q^{36} + q^{37} - 3 q^{44} - 4 q^{45} + q^{47} - q^{48} + 3 q^{49} - q^{53} - q^{55} + q^{59} + 2 q^{60} + 3 q^{64} - 6 q^{67} - 2 q^{69} + q^{71} - 3 q^{75} + q^{80} + q^{81} + q^{89} - q^{92} + 2 q^{93} + q^{97} - 2 q^{99}+O(q^{100}) $ 3 * q - q^3 + 3 * q^4 + q^5 + 2 * q^9 - 3 * q^11 - q^12 + 2 * q^15 + 3 * q^16 + q^20 - q^23 + 2 * q^25 - 2 * q^27 + q^31 + q^33 + 2 * q^36 + q^37 - 3 * q^44 - 4 * q^45 + q^47 - q^48 + 3 * q^49 - q^53 - q^55 + q^59 + 2 * q^60 + 3 * q^64 - 6 * q^67 - 2 * q^69 + q^71 - 3 * q^75 + q^80 + q^81 + q^89 - q^92 + 2 * q^93 + q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1859\mathbb{Z}\right)^\times$.

$n$	$508$	$1354$
$\chi(n)$	$-1$	$1$

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 $

$2$	0	0	1.00000			$0$
$2$	0	0	−1.00000			$\pi$
$3$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$3$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$4$	1.00000	1.00000
$5$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$5$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$6$	0	0
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	0	0
$9$	2.24698	2.24698
$10$	0	0
$11$	−1.00000	−1.00000
$11$	−1.00000	−1.00000
$12$	−1.80194	−1.80194
$13$	0	0
$13$	0	0
$14$	0	0
$15$	2.24698	2.24698
$16$	1.00000	1.00000
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	−1.24698	−1.24698
$21$	0	0
$22$	0	0
$23$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$23$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$24$	0	0
$25$	0.554958	0.554958
$26$	0	0
$27$	−2.24698	−2.24698
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$31$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$32$	0	0
$33$	1.80194	1.80194
$34$	0	0
$35$	0	0
$36$	2.24698	2.24698
$37$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$37$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	−1.00000	−1.00000
$45$	−2.80194	−2.80194
$46$	0	0
$47$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$47$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$48$	−1.80194	−1.80194
$49$	1.00000	1.00000
$50$	0	0
$51$	0	0
$52$	0	0
$53$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$53$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$54$	0	0
$55$	1.24698	1.24698
$56$	0	0
$57$	0	0
$58$	0	0
$59$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$59$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$60$	2.24698	2.24698
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	0	0
$64$	1.00000	1.00000
$65$	0	0
$66$	0	0
$67$	−2.00000	−2.00000	−1.00000			$\pi$
$67$	−2.00000	−2.00000	−1.00000			$\pi$
$68$	0	0
$69$	0.801938	0.801938
$70$	0	0
$71$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$71$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$72$	0	0
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	−1.00000	−1.00000
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	−1.24698	−1.24698
$81$	1.80194	1.80194
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$89$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$90$	0	0
$91$	0	0
$92$	−0.445042	−0.445042
$93$	−0.801938	−0.801938
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$97$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$98$	0	0
$99$	−2.24698	−2.24698
$100$	0.554958	0.554958
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$103$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	−2.24698	−2.24698
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	−3.24698	−3.24698
$112$	0	0
$113$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$113$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$114$	0	0
$115$	0.554958	0.554958
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	1.00000	1.00000
$122$	0	0
$123$	0	0
$124$	0.445042	0.445042
$125$	0.554958	0.554958
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	1.80194	1.80194
$133$	0	0
$134$	0	0
$135$	2.80194	2.80194
$136$	0	0
$137$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$137$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	−0.801938	−0.801938
$142$	0	0
$143$	0	0
$144$	2.24698	2.24698
$145$	0	0
$146$	0	0
$147$	−1.80194	−1.80194
$148$	1.80194	1.80194
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	−0.554958	−0.554958
$156$	0	0
$157$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$157$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$158$	0	0
$159$	−2.24698	−2.24698
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$163$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$164$	0	0
$165$	−2.24698	−2.24698
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	0	0
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−1.00000
$177$	−3.24698	−3.24698
$178$	0	0
$179$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$179$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$180$	−2.80194	−2.80194
$181$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$181$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	−2.24698	−2.24698
$186$	0	0
$187$	0	0
$188$	0.445042	0.445042
$189$	0	0
$190$	0	0
$191$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$191$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$192$	−1.80194	−1.80194
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	1.00000	1.00000
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$199$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$200$	0	0
$201$	3.60388	3.60388
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−1.00000	−1.00000
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	1.24698	1.24698
$213$	−3.24698	−3.24698
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	1.24698	1.24698
$221$	0	0
$222$	0	0
$223$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$223$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$224$	0	0
$225$	1.24698	1.24698
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$229$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	−0.554958	−0.554958
$236$	1.80194	1.80194
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	2.24698	2.24698
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	−1.00000	−1.00000
$244$	0	0
$245$	−1.24698	−1.24698
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$251$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$252$	0	0
$253$	0.445042	0.445042
$254$	0	0
$255$	0	0
$256$	1.00000	1.00000
$257$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$257$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	−1.55496	−1.55496
$266$	0	0
$267$	−0.801938	−0.801938
$268$	−2.00000	−2.00000
$269$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$269$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−0.554958	−0.554958
$276$	0.801938	0.801938
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	1.00000	1.00000
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	1.80194	1.80194
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	1.00000	1.00000
$290$	0	0
$291$	2.24698	2.24698
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	−2.24698	−2.24698
$296$	0	0
$297$	2.24698	2.24698
$298$	0	0
$299$	0	0
$300$	−1.00000	−1.00000
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	−2.24698	−2.24698
$310$	0	0
$311$	−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	0
$313$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$313$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$317$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$318$	0	0
$319$	0	0
$320$	−1.24698	−1.24698
$321$	0	0
$322$	0	0
$323$	0	0
$324$	1.80194	1.80194
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$331$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$332$	0	0
$333$	4.04892	4.04892
$334$	0	0
$335$	2.49396	2.49396
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	−2.24698	−2.24698
$340$	0	0
$341$	−0.445042	−0.445042
$342$	0	0
$343$	0	0
$344$	0	0
$345$	−1.00000	−1.00000
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$353$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$354$	0	0
$355$	−2.24698	−2.24698
$356$	0.445042	0.445042
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	1.00000	1.00000
$362$	0	0
$363$	−1.80194	−1.80194
$364$	0	0
$365$	0	0
$366$	0	0
$367$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$367$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$368$	−0.445042	−0.445042
$369$	0	0
$370$	0	0
$371$	0	0
$372$	−0.801938	−0.801938
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	−1.00000	−1.00000
$376$	0	0
$377$	0	0
$378$	0	0
$379$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$379$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−2.00000	−2.00000	−1.00000			$\pi$
$383$	−2.00000	−2.00000	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	−1.24698	−1.24698
$389$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$389$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	−2.24698	−2.24698
$397$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$397$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$398$	0	0
$399$	0	0
$400$	0.554958	0.554958
$401$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$401$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	−2.24698	−2.24698
$406$	0	0
$407$	−1.80194	−1.80194
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	−0.801938	−0.801938
$412$	1.24698	1.24698
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$419$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$420$	0	0
$421$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$421$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$422$	0	0
$423$	1.00000	1.00000
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	−2.24698	−2.24698
$433$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$433$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	2.24698	2.24698
$442$	0	0
$443$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$443$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$444$	−3.24698	−3.24698
$445$	−0.554958	−0.554958
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−2.00000	−2.00000	−1.00000			$\pi$
$449$	−2.00000	−2.00000	−1.00000			$\pi$
$450$	0	0
$451$	0	0
$452$	1.24698	1.24698
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	0.554958	0.554958
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$463$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$464$	0	0
$465$	1.00000	1.00000
$466$	0	0
$467$	2.00000	2.00000	1.00000			$0$
$467$	2.00000	2.00000	1.00000			$0$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	3.24698	3.24698
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	2.80194	2.80194
$478$	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
$484$	1.00000	1.00000
$485$	1.55496	1.55496
$486$	0	0
$487$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$487$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$488$	0	0
$489$	−0.801938	−0.801938
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	2.80194	2.80194
$496$	0.445042	0.445042
$497$	0	0
$498$	0	0
$499$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$499$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$500$	0.554958	0.554958
$501$	0	0
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	0	0
$509$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$509$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	−1.55496	−1.55496
$516$	0	0
$517$	−0.445042	−0.445042
$518$	0	0
$519$	0	0
$520$	0	0
$521$	2.00000	2.00000	1.00000			$0$
$521$	2.00000	2.00000	1.00000			$0$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	1.80194	1.80194
$529$	−0.801938	−0.801938
$530$	0	0
$531$	4.04892	4.04892
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	3.24698	3.24698
$538$	0	0
$539$	−1.00000	−1.00000
$540$	2.80194	2.80194
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	0.801938	0.801938
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0.445042	0.445042
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	4.04892	4.04892
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	−0.801938	−0.801938
$565$	−1.55496	−1.55496
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0.801938	0.801938
$574$	0	0
$575$	−0.246980	−0.246980
$576$	2.24698	2.24698
$577$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$577$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−1.24698	−1.24698
$584$	0	0
$585$	0	0
$586$	0	0
$587$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$587$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$588$	−1.80194	−1.80194
$589$	0	0
$590$	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	0
$597$	3.24698	3.24698
$598$	0	0
$599$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$599$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	−4.49396	−4.49396
$604$	0	0
$605$	−1.24698	−1.24698
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$617$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$618$	0	0
$619$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$619$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$620$	−0.554958	−0.554958
$621$	1.00000	1.00000
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−1.24698	−1.24698
$626$	0	0
$627$	0	0
$628$	−1.80194	−1.80194
$629$	0	0
$630$	0	0
$631$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$631$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	−2.24698	−2.24698
$637$	0	0
$638$	0	0
$639$	4.04892	4.04892
$640$	0	0
$641$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$641$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$642$	0	0
$643$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$643$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	2.00000	2.00000	1.00000			$0$
$647$	2.00000	2.00000	1.00000			$0$
$648$	0	0
$649$	−1.80194	−1.80194
$650$	0	0
$651$	0	0
$652$	0.445042	0.445042
$653$	−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
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	−2.24698	−2.24698
$661$	−2.00000	−2.00000	−1.00000			$\pi$
$661$	−2.00000	−2.00000	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	2.24698	2.24698
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	−1.24698	−1.24698
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$683$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$684$	0	0
$685$	−0.554958	−0.554958
$686$	0	0
$687$	−3.24698	−3.24698
$688$	0	0
$689$	0	0
$690$	0	0
$691$	1.80194	1.80194	0.900969	−	0.433884i	$-0.142857\pi$
$691$	1.80194	1.80194	0.900969	+	0.433884i	$0.142857\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	−1.00000	−1.00000
$705$	1.00000	1.00000
$706$	0	0
$707$	0	0
$708$	−3.24698	−3.24698
$709$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$709$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	−0.198062	−0.198062
$714$	0	0
$715$	0	0
$716$	−1.80194	−1.80194
$717$	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	$0.285714\pi$
$720$	−2.80194	−2.80194
$721$	0	0
$722$	0	0
$723$	0	0
$724$	−0.445042	−0.445042
$725$	0	0
$726$	0	0
$727$	−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
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	2.24698	2.24698
$736$	0	0
$737$	2.00000	2.00000
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	−2.24698	−2.24698
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$751$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$752$	0.445042	0.445042
$753$	−2.24698	−2.24698
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$757$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$758$	0	0
$759$	−0.801938	−0.801938
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	−0.445042	−0.445042
$765$	0	0
$766$	0	0
$767$	0	0
$768$	−1.80194	−1.80194
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	3.24698	3.24698
$772$	0	0
$773$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$773$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$774$	0	0
$775$	0.246980	0.246980
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	−1.80194	−1.80194
$782$	0	0
$783$	0	0
$784$	1.00000	1.00000
$785$	2.24698	2.24698
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	2.80194	2.80194
$796$	−1.80194	−1.80194
$797$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$797$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	1.00000	1.00000
$802$	0	0
$803$	0	0
$804$	3.60388	3.60388
$805$	0	0
$806$	0	0
$807$	3.24698	3.24698
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−0.554958	−0.554958
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$823$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$824$	0	0
$825$	1.00000	1.00000
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	−1.00000	−1.00000
$829$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$829$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−1.00000	−1.00000
$838$	0	0
$839$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$839$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$840$	0	0
$841$	1.00000	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	1.24698	1.24698
$849$	0	0
$850$	0	0
$851$	−0.801938	−0.801938
$852$	−3.24698	−3.24698
$853$	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			$\pi$
$858$	0	0
$859$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$859$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$863$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−1.80194	−1.80194
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	−2.80194	−2.80194
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	1.24698	1.24698
$881$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$881$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$882$	0	0
$883$	1.24698	1.24698	0.623490	−	0.781831i	$-0.285714\pi$
$883$	1.24698	1.24698	0.623490	+	0.781831i	$0.285714\pi$
$884$	0	0
$885$	4.04892	4.04892
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−1.80194	−1.80194
$892$	−1.24698	−1.24698
$893$	0	0
$894$	0	0
$895$	2.24698	2.24698
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	1.24698	1.24698
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0.554958	0.554958
$906$	0	0
$907$	−1.80194	−1.80194	−0.900969	−	0.433884i	$-0.857143\pi$
$907$	−1.80194	−1.80194	−0.900969	+	0.433884i	$0.857143\pi$
$908$	0	0
$909$	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	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	1.80194	1.80194
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	1.00000	1.00000
$926$	0	0
$927$	2.80194	2.80194
$928$	0	0
$929$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$929$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0.801938	0.801938
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	−2.24698	−2.24698
$940$	−0.554958	−0.554958
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	1.80194	1.80194
$945$	0	0
$946$	0	0
$947$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$947$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	−3.24698	−3.24698
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0.554958	0.554958
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	2.24698	2.24698
$961$	−0.801938	−0.801938
$962$	0	0
$963$	0	0
$964$	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	0
$970$	0	0
$971$	2.00000	2.00000	1.00000			$0$
$971$	2.00000	2.00000	1.00000			$0$
$972$	−1.00000	−1.00000
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−1.24698	−1.24698	−0.623490	−	0.781831i	$-0.714286\pi$
$977$	−1.24698	−1.24698	−0.623490	+	0.781831i	$0.714286\pi$
$978$	0	0
$979$	−0.445042	−0.445042
$980$	−1.24698	−1.24698
$981$	0	0
$982$	0	0
$983$	0.445042	0.445042	0.222521	−	0.974928i	$-0.428571\pi$
$983$	0.445042	0.445042	0.222521	+	0.974928i	$0.428571\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−0.445042	−0.445042	−0.222521	−	0.974928i	$-0.571429\pi$
$991$	−0.445042	−0.445042	−0.222521	+	0.974928i	$0.571429\pi$
$992$	0	0
$993$	2.24698	2.24698
$994$	0	0
$995$	2.24698	2.24698
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	−4.04892	−4.04892

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.1.c.b.846.1	yes	3
11.10	odd	2	CM	1859.1.c.b.846.1	yes	3
13.2	odd	12		1859.1.i.c.1330.6		12
13.3	even	3		1859.1.k.b.1374.3		6
13.4	even	6		1859.1.k.a.1836.3		6
13.5	odd	4		1859.1.d.a.1858.2		6
13.6	odd	12		1859.1.i.c.868.6		12
13.7	odd	12		1859.1.i.c.868.5		12
13.8	odd	4		1859.1.d.a.1858.1		6
13.9	even	3		1859.1.k.b.1836.3		6
13.10	even	6		1859.1.k.a.1374.3		6
13.11	odd	12		1859.1.i.c.1330.5		12
13.12	even	2		1859.1.c.a.846.1	✓	3
143.10	odd	6		1859.1.k.a.1374.3		6
143.21	even	4		1859.1.d.a.1858.1		6
143.32	even	12		1859.1.i.c.868.6		12
143.43	odd	6		1859.1.k.a.1836.3		6
143.54	even	12		1859.1.i.c.1330.6		12
143.76	even	12		1859.1.i.c.1330.5		12
143.87	odd	6		1859.1.k.b.1836.3		6
143.98	even	12		1859.1.i.c.868.5		12
143.109	even	4		1859.1.d.a.1858.2		6
143.120	odd	6		1859.1.k.b.1374.3		6
143.142	odd	2		1859.1.c.a.846.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.1.c.a.846.1	✓	3	13.12	even	2
1859.1.c.a.846.1	✓	3	143.142	odd	2
1859.1.c.b.846.1	yes	3	1.1	even	1	trivial
1859.1.c.b.846.1	yes	3	11.10	odd	2	CM
1859.1.d.a.1858.1		6	13.8	odd	4
1859.1.d.a.1858.1		6	143.21	even	4
1859.1.d.a.1858.2		6	13.5	odd	4
1859.1.d.a.1858.2		6	143.109	even	4
1859.1.i.c.868.5		12	13.7	odd	12
1859.1.i.c.868.5		12	143.98	even	12
1859.1.i.c.868.6		12	13.6	odd	12
1859.1.i.c.868.6		12	143.32	even	12
1859.1.i.c.1330.5		12	13.11	odd	12
1859.1.i.c.1330.5		12	143.76	even	12
1859.1.i.c.1330.6		12	13.2	odd	12
1859.1.i.c.1330.6		12	143.54	even	12
1859.1.k.a.1374.3		6	13.10	even	6
1859.1.k.a.1374.3		6	143.10	odd	6
1859.1.k.a.1836.3		6	13.4	even	6
1859.1.k.a.1836.3		6	143.43	odd	6
1859.1.k.b.1374.3		6	13.3	even	3
1859.1.k.b.1374.3		6	143.120	odd	6
1859.1.k.b.1836.3		6	13.9	even	3
1859.1.k.b.1836.3		6	143.87	odd	6

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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1859.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.80194 q^{3} +1.00000 q^{4} -1.24698 q^{5} +2.24698 q^{9} +O(q^{10})\)	\(q-1.80194 q^{3} +1.00000 q^{4} -1.24698 q^{5} +2.24698 q^{9} -1.00000 q^{11} -1.80194 q^{12} +2.24698 q^{15} +1.00000 q^{16} -1.24698 q^{20} -0.445042 q^{23} +0.554958 q^{25} -2.24698 q^{27} +0.445042 q^{31} +1.80194 q^{33} +2.24698 q^{36} +1.80194 q^{37} -1.00000 q^{44} -2.80194 q^{45} +0.445042 q^{47} -1.80194 q^{48} +1.00000 q^{49} +1.24698 q^{53} +1.24698 q^{55} +1.80194 q^{59} +2.24698 q^{60} +1.00000 q^{64} -2.00000 q^{67} +0.801938 q^{69} +1.80194 q^{71} -1.00000 q^{75} -1.24698 q^{80} +1.80194 q^{81} +0.445042 q^{89} -0.445042 q^{92} -0.801938 q^{93} -1.24698 q^{97} -2.24698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{3} + 3 q^{4} + q^{5} + 2 q^{9}+O(q^{10}) \) 3 * q - q^3 + 3 * q^4 + q^5 + 2 * q^9	\( 3 q - q^{3} + 3 q^{4} + q^{5} + 2 q^{9} - 3 q^{11} - q^{12} + 2 q^{15} + 3 q^{16} + q^{20} - q^{23} + 2 q^{25} - 2 q^{27} + q^{31} + q^{33} + 2 q^{36} + q^{37} - 3 q^{44} - 4 q^{45} + q^{47} - q^{48} + 3 q^{49} - q^{53} - q^{55} + q^{59} + 2 q^{60} + 3 q^{64} - 6 q^{67} - 2 q^{69} + q^{71} - 3 q^{75} + q^{80} + q^{81} + q^{89} - q^{92} + 2 q^{93} + q^{97} - 2 q^{99}+O(q^{100}) \) 3 * q - q^3 + 3 * q^4 + q^5 + 2 * q^9 - 3 * q^11 - q^12 + 2 * q^15 + 3 * q^16 + q^20 - q^23 + 2 * q^25 - 2 * q^27 + q^31 + q^33 + 2 * q^36 + q^37 - 3 * q^44 - 4 * q^45 + q^47 - q^48 + 3 * q^49 - q^53 - q^55 + q^59 + 2 * q^60 + 3 * q^64 - 6 * q^67 - 2 * q^69 + q^71 - 3 * q^75 + q^80 + q^81 + q^89 - q^92 + 2 * q^93 + q^97 - 2 * q^99

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