LMFDB - Dirichlet character orbit 12138.cr

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(12138, base_ring=CyclotomicField(272)) M = H._module chi = DirichletCharacter(H, M([0,136,189])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(97,12138)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$12138$
Conductor:	$2023$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$272$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2023.bi	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{272})$
Fixed field:	Number field defined by a degree 272 polynomial (not computed)

First 31 of 128 characters in Galois orbit

Character	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{12138}(97,\cdot)$	$1$	$1$	$e\left(\frac{169}{272}\right)$	$e\left(\frac{267}{272}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{259}{272}\right)$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{233}{272}\right)$	$e\left(\frac{205}{272}\right)$	$e\left(\frac{173}{272}\right)$	$e\left(\frac{87}{272}\right)$
$\chi_{12138}(139,\cdot)$	$1$	$1$	$e\left(\frac{109}{272}\right)$	$e\left(\frac{103}{272}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{159}{272}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{205}{272}\right)$	$e\left(\frac{129}{272}\right)$	$e\left(\frac{81}{272}\right)$	$e\left(\frac{3}{272}\right)$
$\chi_{12138}(181,\cdot)$	$1$	$1$	$e\left(\frac{123}{272}\right)$	$e\left(\frac{241}{272}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{137}{272}\right)$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{139}{272}\right)$	$e\left(\frac{183}{272}\right)$	$e\left(\frac{39}{272}\right)$	$e\left(\frac{213}{272}\right)$
$\chi_{12138}(265,\cdot)$	$1$	$1$	$e\left(\frac{199}{272}\right)$	$e\left(\frac{213}{272}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{173}{272}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{247}{272}\right)$	$e\left(\frac{243}{272}\right)$	$e\left(\frac{83}{272}\right)$	$e\left(\frac{265}{272}\right)$
$\chi_{12138}(517,\cdot)$	$1$	$1$	$e\left(\frac{15}{272}\right)$	$e\left(\frac{109}{272}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{229}{272}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{143}{272}\right)$	$e\left(\frac{155}{272}\right)$	$e\left(\frac{91}{272}\right)$	$e\left(\frac{225}{272}\right)$
$\chi_{12138}(601,\cdot)$	$1$	$1$	$e\left(\frac{67}{272}\right)$	$e\left(\frac{233}{272}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{225}{272}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{131}{272}\right)$	$e\left(\frac{239}{272}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{189}{272}\right)$
$\chi_{12138}(685,\cdot)$	$1$	$1$	$e\left(\frac{129}{272}\right)$	$e\left(\frac{67}{272}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{11}{272}\right)$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{33}{272}\right)$	$e\left(\frac{245}{272}\right)$	$e\left(\frac{21}{272}\right)$	$e\left(\frac{31}{272}\right)$
$\chi_{12138}(811,\cdot)$	$1$	$1$	$e\left(\frac{105}{272}\right)$	$e\left(\frac{219}{272}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{243}{272}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{185}{272}\right)$	$e\left(\frac{269}{272}\right)$	$e\left(\frac{93}{272}\right)$	$e\left(\frac{215}{272}\right)$
$\chi_{12138}(853,\cdot)$	$1$	$1$	$e\left(\frac{125}{272}\right)$	$e\left(\frac{183}{272}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{95}{272}\right)$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{13}{272}\right)$	$e\left(\frac{113}{272}\right)$	$e\left(\frac{33}{272}\right)$	$e\left(\frac{243}{272}\right)$
$\chi_{12138}(895,\cdot)$	$1$	$1$	$e\left(\frac{251}{272}\right)$	$e\left(\frac{65}{272}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{169}{272}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{235}{272}\right)$	$e\left(\frac{55}{272}\right)$	$e\left(\frac{199}{272}\right)$	$e\left(\frac{229}{272}\right)$
$\chi_{12138}(979,\cdot)$	$1$	$1$	$e\left(\frac{231}{272}\right)$	$e\left(\frac{101}{272}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{45}{272}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{135}{272}\right)$	$e\left(\frac{211}{272}\right)$	$e\left(\frac{259}{272}\right)$	$e\left(\frac{201}{272}\right)$
$\chi_{12138}(1315,\cdot)$	$1$	$1$	$e\left(\frac{211}{272}\right)$	$e\left(\frac{137}{272}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{193}{272}\right)$	$e\left(\frac{75}{136}\right)$	$e\left(\frac{35}{272}\right)$	$e\left(\frac{95}{272}\right)$	$e\left(\frac{47}{272}\right)$	$e\left(\frac{173}{272}\right)$
$\chi_{12138}(1357,\cdot)$	$1$	$1$	$e\left(\frac{69}{272}\right)$	$e\left(\frac{175}{272}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{183}{272}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{5}{272}\right)$	$e\left(\frac{169}{272}\right)$	$e\left(\frac{201}{272}\right)$	$e\left(\frac{219}{272}\right)$
$\chi_{12138}(1399,\cdot)$	$1$	$1$	$e\left(\frac{193}{272}\right)$	$e\left(\frac{115}{272}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{103}{136}\right)$	$e\left(\frac{27}{272}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{81}{272}\right)$	$e\left(\frac{181}{272}\right)$	$e\left(\frac{101}{272}\right)$	$e\left(\frac{175}{272}\right)$
$\chi_{12138}(1525,\cdot)$	$1$	$1$	$e\left(\frac{41}{272}\right)$	$e\left(\frac{171}{272}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{227}{272}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{137}{272}\right)$	$e\left(\frac{61}{272}\right)$	$e\left(\frac{13}{272}\right)$	$e\left(\frac{71}{272}\right)$
$\chi_{12138}(1567,\cdot)$	$1$	$1$	$e\left(\frac{141}{272}\right)$	$e\left(\frac{263}{272}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{31}{272}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{93}{272}\right)$	$e\left(\frac{97}{272}\right)$	$e\left(\frac{257}{272}\right)$	$e\left(\frac{211}{272}\right)$
$\chi_{12138}(1609,\cdot)$	$1$	$1$	$e\left(\frac{107}{272}\right)$	$e\left(\frac{161}{272}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{117}{136}\right)$	$e\left(\frac{201}{272}\right)$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{59}{272}\right)$	$e\left(\frac{199}{272}\right)$	$e\left(\frac{87}{272}\right)$	$e\left(\frac{245}{272}\right)$
$\chi_{12138}(1693,\cdot)$	$1$	$1$	$e\left(\frac{263}{272}\right)$	$e\left(\frac{261}{272}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{189}{272}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{23}{272}\right)$	$e\left(\frac{179}{272}\right)$	$e\left(\frac{163}{272}\right)$	$e\left(\frac{137}{272}\right)$
$\chi_{12138}(1945,\cdot)$	$1$	$1$	$e\left(\frac{223}{272}\right)$	$e\left(\frac{61}{272}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{213}{272}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{95}{272}\right)$	$e\left(\frac{219}{272}\right)$	$e\left(\frac{11}{272}\right)$	$e\left(\frac{81}{272}\right)$
$\chi_{12138}(2029,\cdot)$	$1$	$1$	$e\left(\frac{83}{272}\right)$	$e\left(\frac{41}{272}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{161}{272}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{211}{272}\right)$	$e\left(\frac{223}{272}\right)$	$e\left(\frac{159}{272}\right)$	$e\left(\frac{157}{272}\right)$
$\chi_{12138}(2071,\cdot)$	$1$	$1$	$e\left(\frac{53}{272}\right)$	$e\left(\frac{95}{272}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{247}{272}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{197}{272}\right)$	$e\left(\frac{185}{272}\right)$	$e\left(\frac{249}{272}\right)$	$e\left(\frac{251}{272}\right)$
$\chi_{12138}(2113,\cdot)$	$1$	$1$	$e\left(\frac{257}{272}\right)$	$e\left(\frac{163}{272}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{43}{272}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{129}{272}\right)$	$e\left(\frac{117}{272}\right)$	$e\left(\frac{181}{272}\right)$	$e\left(\frac{47}{272}\right)$
$\chi_{12138}(2239,\cdot)$	$1$	$1$	$e\left(\frac{249}{272}\right)$	$e\left(\frac{123}{272}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{211}{272}\right)$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{89}{272}\right)$	$e\left(\frac{125}{272}\right)$	$e\left(\frac{205}{272}\right)$	$e\left(\frac{199}{272}\right)$
$\chi_{12138}(2281,\cdot)$	$1$	$1$	$e\left(\frac{157}{272}\right)$	$e\left(\frac{71}{272}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{239}{272}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{173}{272}\right)$	$e\left(\frac{81}{272}\right)$	$e\left(\frac{209}{272}\right)$	$e\left(\frac{179}{272}\right)$
$\chi_{12138}(2323,\cdot)$	$1$	$1$	$e\left(\frac{235}{272}\right)$	$e\left(\frac{257}{272}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{233}{272}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{155}{272}\right)$	$e\left(\frac{71}{272}\right)$	$e\left(\frac{247}{272}\right)$	$e\left(\frac{261}{272}\right)$
$\chi_{12138}(2407,\cdot)$	$1$	$1$	$e\left(\frac{23}{272}\right)$	$e\left(\frac{149}{272}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{61}{272}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{183}{272}\right)$	$e\left(\frac{147}{272}\right)$	$e\left(\frac{67}{272}\right)$	$e\left(\frac{73}{272}\right)$
$\chi_{12138}(2659,\cdot)$	$1$	$1$	$e\left(\frac{191}{272}\right)$	$e\left(\frac{173}{272}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{69}{272}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{251}{272}\right)$	$e\left(\frac{107}{272}\right)$	$e\left(\frac{145}{272}\right)$
$\chi_{12138}(2743,\cdot)$	$1$	$1$	$e\left(\frac{227}{272}\right)$	$e\left(\frac{217}{272}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{129}{272}\right)$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{115}{272}\right)$	$e\left(\frac{79}{272}\right)$	$e\left(\frac{271}{272}\right)$	$e\left(\frac{141}{272}\right)$
$\chi_{12138}(2785,\cdot)$	$1$	$1$	$e\left(\frac{37}{272}\right)$	$e\left(\frac{15}{272}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{39}{272}\right)$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{117}{272}\right)$	$e\left(\frac{201}{272}\right)$	$e\left(\frac{25}{272}\right)$	$e\left(\frac{11}{272}\right)$
$\chi_{12138}(2827,\cdot)$	$1$	$1$	$e\left(\frac{49}{272}\right)$	$e\left(\frac{211}{272}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{59}{272}\right)$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{177}{272}\right)$	$e\left(\frac{53}{272}\right)$	$e\left(\frac{261}{272}\right)$	$e\left(\frac{191}{272}\right)$
$\chi_{12138}(2953,\cdot)$	$1$	$1$	$e\left(\frac{185}{272}\right)$	$e\left(\frac{75}{272}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{195}{272}\right)$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{41}{272}\right)$	$e\left(\frac{189}{272}\right)$	$e\left(\frac{125}{272}\right)$	$e\left(\frac{55}{272}\right)$

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 $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{12138}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{272}\right)\)	\(e\left(\frac{267}{272}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{259}{272}\right)\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{233}{272}\right)\)	\(e\left(\frac{205}{272}\right)\)	\(e\left(\frac{173}{272}\right)\)	\(e\left(\frac{87}{272}\right)\)
\(\chi_{12138}(139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{272}\right)\)	\(e\left(\frac{103}{272}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{159}{272}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{205}{272}\right)\)	\(e\left(\frac{129}{272}\right)\)	\(e\left(\frac{81}{272}\right)\)	\(e\left(\frac{3}{272}\right)\)
\(\chi_{12138}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{272}\right)\)	\(e\left(\frac{241}{272}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{137}{272}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{139}{272}\right)\)	\(e\left(\frac{183}{272}\right)\)	\(e\left(\frac{39}{272}\right)\)	\(e\left(\frac{213}{272}\right)\)
\(\chi_{12138}(265,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{272}\right)\)	\(e\left(\frac{213}{272}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{173}{272}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{247}{272}\right)\)	\(e\left(\frac{243}{272}\right)\)	\(e\left(\frac{83}{272}\right)\)	\(e\left(\frac{265}{272}\right)\)
\(\chi_{12138}(517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{272}\right)\)	\(e\left(\frac{109}{272}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{229}{272}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{143}{272}\right)\)	\(e\left(\frac{155}{272}\right)\)	\(e\left(\frac{91}{272}\right)\)	\(e\left(\frac{225}{272}\right)\)
\(\chi_{12138}(601,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{272}\right)\)	\(e\left(\frac{233}{272}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{225}{272}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{131}{272}\right)\)	\(e\left(\frac{239}{272}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{189}{272}\right)\)
\(\chi_{12138}(685,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{129}{272}\right)\)	\(e\left(\frac{67}{272}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{11}{272}\right)\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{33}{272}\right)\)	\(e\left(\frac{245}{272}\right)\)	\(e\left(\frac{21}{272}\right)\)	\(e\left(\frac{31}{272}\right)\)
\(\chi_{12138}(811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{105}{272}\right)\)	\(e\left(\frac{219}{272}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{243}{272}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{185}{272}\right)\)	\(e\left(\frac{269}{272}\right)\)	\(e\left(\frac{93}{272}\right)\)	\(e\left(\frac{215}{272}\right)\)
\(\chi_{12138}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{272}\right)\)	\(e\left(\frac{183}{272}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{95}{272}\right)\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{13}{272}\right)\)	\(e\left(\frac{113}{272}\right)\)	\(e\left(\frac{33}{272}\right)\)	\(e\left(\frac{243}{272}\right)\)
\(\chi_{12138}(895,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{251}{272}\right)\)	\(e\left(\frac{65}{272}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{169}{272}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{235}{272}\right)\)	\(e\left(\frac{55}{272}\right)\)	\(e\left(\frac{199}{272}\right)\)	\(e\left(\frac{229}{272}\right)\)
\(\chi_{12138}(979,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{231}{272}\right)\)	\(e\left(\frac{101}{272}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{45}{272}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{135}{272}\right)\)	\(e\left(\frac{211}{272}\right)\)	\(e\left(\frac{259}{272}\right)\)	\(e\left(\frac{201}{272}\right)\)
\(\chi_{12138}(1315,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{211}{272}\right)\)	\(e\left(\frac{137}{272}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{193}{272}\right)\)	\(e\left(\frac{75}{136}\right)\)	\(e\left(\frac{35}{272}\right)\)	\(e\left(\frac{95}{272}\right)\)	\(e\left(\frac{47}{272}\right)\)	\(e\left(\frac{173}{272}\right)\)
\(\chi_{12138}(1357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{272}\right)\)	\(e\left(\frac{175}{272}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{183}{272}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{5}{272}\right)\)	\(e\left(\frac{169}{272}\right)\)	\(e\left(\frac{201}{272}\right)\)	\(e\left(\frac{219}{272}\right)\)
\(\chi_{12138}(1399,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{272}\right)\)	\(e\left(\frac{115}{272}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{103}{136}\right)\)	\(e\left(\frac{27}{272}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{81}{272}\right)\)	\(e\left(\frac{181}{272}\right)\)	\(e\left(\frac{101}{272}\right)\)	\(e\left(\frac{175}{272}\right)\)
\(\chi_{12138}(1525,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{272}\right)\)	\(e\left(\frac{171}{272}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{227}{272}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{137}{272}\right)\)	\(e\left(\frac{61}{272}\right)\)	\(e\left(\frac{13}{272}\right)\)	\(e\left(\frac{71}{272}\right)\)
\(\chi_{12138}(1567,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{141}{272}\right)\)	\(e\left(\frac{263}{272}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{31}{272}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{93}{272}\right)\)	\(e\left(\frac{97}{272}\right)\)	\(e\left(\frac{257}{272}\right)\)	\(e\left(\frac{211}{272}\right)\)
\(\chi_{12138}(1609,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{272}\right)\)	\(e\left(\frac{161}{272}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{117}{136}\right)\)	\(e\left(\frac{201}{272}\right)\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{59}{272}\right)\)	\(e\left(\frac{199}{272}\right)\)	\(e\left(\frac{87}{272}\right)\)	\(e\left(\frac{245}{272}\right)\)
\(\chi_{12138}(1693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{263}{272}\right)\)	\(e\left(\frac{261}{272}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{189}{272}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{23}{272}\right)\)	\(e\left(\frac{179}{272}\right)\)	\(e\left(\frac{163}{272}\right)\)	\(e\left(\frac{137}{272}\right)\)
\(\chi_{12138}(1945,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{223}{272}\right)\)	\(e\left(\frac{61}{272}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{213}{272}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{95}{272}\right)\)	\(e\left(\frac{219}{272}\right)\)	\(e\left(\frac{11}{272}\right)\)	\(e\left(\frac{81}{272}\right)\)
\(\chi_{12138}(2029,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{272}\right)\)	\(e\left(\frac{41}{272}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{161}{272}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{211}{272}\right)\)	\(e\left(\frac{223}{272}\right)\)	\(e\left(\frac{159}{272}\right)\)	\(e\left(\frac{157}{272}\right)\)
\(\chi_{12138}(2071,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{272}\right)\)	\(e\left(\frac{95}{272}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{247}{272}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{197}{272}\right)\)	\(e\left(\frac{185}{272}\right)\)	\(e\left(\frac{249}{272}\right)\)	\(e\left(\frac{251}{272}\right)\)
\(\chi_{12138}(2113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{257}{272}\right)\)	\(e\left(\frac{163}{272}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{43}{272}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{129}{272}\right)\)	\(e\left(\frac{117}{272}\right)\)	\(e\left(\frac{181}{272}\right)\)	\(e\left(\frac{47}{272}\right)\)
\(\chi_{12138}(2239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{249}{272}\right)\)	\(e\left(\frac{123}{272}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{211}{272}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{89}{272}\right)\)	\(e\left(\frac{125}{272}\right)\)	\(e\left(\frac{205}{272}\right)\)	\(e\left(\frac{199}{272}\right)\)
\(\chi_{12138}(2281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{272}\right)\)	\(e\left(\frac{71}{272}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{239}{272}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{173}{272}\right)\)	\(e\left(\frac{81}{272}\right)\)	\(e\left(\frac{209}{272}\right)\)	\(e\left(\frac{179}{272}\right)\)
\(\chi_{12138}(2323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{235}{272}\right)\)	\(e\left(\frac{257}{272}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{233}{272}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{155}{272}\right)\)	\(e\left(\frac{71}{272}\right)\)	\(e\left(\frac{247}{272}\right)\)	\(e\left(\frac{261}{272}\right)\)
\(\chi_{12138}(2407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{272}\right)\)	\(e\left(\frac{149}{272}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{61}{272}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{183}{272}\right)\)	\(e\left(\frac{147}{272}\right)\)	\(e\left(\frac{67}{272}\right)\)	\(e\left(\frac{73}{272}\right)\)
\(\chi_{12138}(2659,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{272}\right)\)	\(e\left(\frac{173}{272}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{69}{272}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{251}{272}\right)\)	\(e\left(\frac{107}{272}\right)\)	\(e\left(\frac{145}{272}\right)\)
\(\chi_{12138}(2743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{272}\right)\)	\(e\left(\frac{217}{272}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{129}{272}\right)\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{115}{272}\right)\)	\(e\left(\frac{79}{272}\right)\)	\(e\left(\frac{271}{272}\right)\)	\(e\left(\frac{141}{272}\right)\)
\(\chi_{12138}(2785,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{272}\right)\)	\(e\left(\frac{15}{272}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{39}{272}\right)\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{117}{272}\right)\)	\(e\left(\frac{201}{272}\right)\)	\(e\left(\frac{25}{272}\right)\)	\(e\left(\frac{11}{272}\right)\)
\(\chi_{12138}(2827,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{272}\right)\)	\(e\left(\frac{211}{272}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{59}{272}\right)\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{177}{272}\right)\)	\(e\left(\frac{53}{272}\right)\)	\(e\left(\frac{261}{272}\right)\)	\(e\left(\frac{191}{272}\right)\)
\(\chi_{12138}(2953,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{272}\right)\)	\(e\left(\frac{75}{272}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{195}{272}\right)\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{41}{272}\right)\)	\(e\left(\frac{189}{272}\right)\)	\(e\left(\frac{125}{272}\right)\)	\(e\left(\frac{55}{272}\right)\)

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First 31 of 128 characters in Galois orbit

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

Label	12138.cr
Modulus	$12138$
Conductor	$2023$
Order	$272$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(12138\)
Conductor:	\(2023\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(272\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2023.bi	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)