LMFDB - Dirichlet character orbit 12138.cn

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(12138, base_ring=CyclotomicField(204)) M = H._module chi = DirichletCharacter(H, M([0,136,111])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(319,12138)) 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:	$204$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2023.bg	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:	$\Q(\zeta_{204})$
Fixed field:	Number field defined by a degree 204 polynomial (not computed)

First 31 of 64 characters in Galois orbit

Character	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{12138}(319,\cdot)$	$1$	$1$	$e\left(\frac{191}{204}\right)$	$e\left(\frac{37}{204}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{137}{204}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{115}{204}\right)$	$e\left(\frac{107}{204}\right)$	$e\left(\frac{3}{68}\right)$
$\chi_{12138}(361,\cdot)$	$1$	$1$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{121}{204}\right)$	$e\left(\frac{125}{204}\right)$	$e\left(\frac{41}{68}\right)$
$\chi_{12138}(625,\cdot)$	$1$	$1$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{133}{204}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{131}{204}\right)$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{59}{68}\right)$
$\chi_{12138}(667,\cdot)$	$1$	$1$	$e\left(\frac{133}{204}\right)$	$e\left(\frac{155}{204}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{199}{204}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{145}{204}\right)$	$e\left(\frac{53}{68}\right)$
$\chi_{12138}(1033,\cdot)$	$1$	$1$	$e\left(\frac{131}{204}\right)$	$e\left(\frac{145}{204}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{43}{68}\right)$
$\chi_{12138}(1075,\cdot)$	$1$	$1$	$e\left(\frac{41}{204}\right)$	$e\left(\frac{103}{204}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{23}{204}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{61}{204}\right)$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{1}{68}\right)$
$\chi_{12138}(1339,\cdot)$	$1$	$1$	$e\left(\frac{115}{204}\right)$	$e\left(\frac{65}{204}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{169}{204}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{191}{204}\right)$	$e\left(\frac{199}{204}\right)$	$e\left(\frac{31}{68}\right)$
$\chi_{12138}(1381,\cdot)$	$1$	$1$	$e\left(\frac{193}{204}\right)$	$e\left(\frac{47}{204}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{169}{204}\right)$	$e\left(\frac{13}{68}\right)$
$\chi_{12138}(1747,\cdot)$	$1$	$1$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{5}{204}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{31}{204}\right)$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{15}{68}\right)$
$\chi_{12138}(1789,\cdot)$	$1$	$1$	$e\left(\frac{101}{204}\right)$	$e\left(\frac{199}{204}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{191}{204}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{1}{204}\right)$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{29}{68}\right)$
$\chi_{12138}(2053,\cdot)$	$1$	$1$	$e\left(\frac{55}{204}\right)$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{1}{204}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{47}{204}\right)$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{3}{68}\right)$
$\chi_{12138}(2095,\cdot)$	$1$	$1$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{127}{204}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{193}{204}\right)$	$e\left(\frac{41}{68}\right)$
$\chi_{12138}(2461,\cdot)$	$1$	$1$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{41}{204}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{35}{204}\right)$	$e\left(\frac{55}{68}\right)$
$\chi_{12138}(2503,\cdot)$	$1$	$1$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{155}{204}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{145}{204}\right)$	$e\left(\frac{197}{204}\right)$	$e\left(\frac{57}{68}\right)$
$\chi_{12138}(2767,\cdot)$	$1$	$1$	$e\left(\frac{199}{204}\right)$	$e\left(\frac{77}{204}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{37}{204}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{107}{204}\right)$	$e\left(\frac{151}{204}\right)$	$e\left(\frac{43}{68}\right)$
$\chi_{12138}(2809,\cdot)$	$1$	$1$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{35}{204}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{197}{204}\right)$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{1}{68}\right)$
$\chi_{12138}(3175,\cdot)$	$1$	$1$	$e\left(\frac{155}{204}\right)$	$e\left(\frac{61}{204}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{77}{204}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{151}{204}\right)$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{27}{68}\right)$
$\chi_{12138}(3481,\cdot)$	$1$	$1$	$e\left(\frac{139}{204}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{73}{204}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{167}{204}\right)$	$e\left(\frac{127}{204}\right)$	$e\left(\frac{15}{68}\right)$
$\chi_{12138}(3523,\cdot)$	$1$	$1$	$e\left(\frac{169}{204}\right)$	$e\left(\frac{131}{204}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{55}{204}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{137}{204}\right)$	$e\left(\frac{37}{204}\right)$	$e\left(\frac{29}{68}\right)$
$\chi_{12138}(3889,\cdot)$	$1$	$1$	$e\left(\frac{95}{204}\right)$	$e\left(\frac{169}{204}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{191}{204}\right)$	$e\left(\frac{67}{68}\right)$
$\chi_{12138}(3931,\cdot)$	$1$	$1$	$e\left(\frac{77}{204}\right)$	$e\left(\frac{79}{204}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{25}{204}\right)$	$e\left(\frac{41}{204}\right)$	$e\left(\frac{45}{68}\right)$
$\chi_{12138}(4195,\cdot)$	$1$	$1$	$e\left(\frac{79}{204}\right)$	$e\left(\frac{89}{204}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{23}{204}\right)$	$e\left(\frac{103}{204}\right)$	$e\left(\frac{55}{68}\right)$
$\chi_{12138}(4237,\cdot)$	$1$	$1$	$e\left(\frac{25}{204}\right)$	$e\left(\frac{23}{204}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{77}{204}\right)$	$e\left(\frac{61}{204}\right)$	$e\left(\frac{57}{68}\right)$
$\chi_{12138}(4603,\cdot)$	$1$	$1$	$e\left(\frac{35}{204}\right)$	$e\left(\frac{73}{204}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{67}{204}\right)$	$e\left(\frac{167}{204}\right)$	$e\left(\frac{39}{68}\right)$
$\chi_{12138}(4645,\cdot)$	$1$	$1$	$e\left(\frac{137}{204}\right)$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{47}{204}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{169}{204}\right)$	$e\left(\frac{65}{204}\right)$	$e\left(\frac{5}{68}\right)$
$\chi_{12138}(4909,\cdot)$	$1$	$1$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{197}{204}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{145}{204}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{79}{204}\right)$	$e\left(\frac{27}{68}\right)$
$\chi_{12138}(5317,\cdot)$	$1$	$1$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{181}{204}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{127}{204}\right)$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{11}{68}\right)$
$\chi_{12138}(5359,\cdot)$	$1$	$1$	$e\left(\frac{197}{204}\right)$	$e\left(\frac{67}{204}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{89}{204}\right)$	$e\left(\frac{33}{68}\right)$
$\chi_{12138}(5623,\cdot)$	$1$	$1$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{101}{204}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{181}{204}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{55}{204}\right)$	$e\left(\frac{67}{68}\right)$
$\chi_{12138}(5665,\cdot)$	$1$	$1$	$e\left(\frac{145}{204}\right)$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{151}{204}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{45}{68}\right)$
$\chi_{12138}(6073,\cdot)$	$1$	$1$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{61}{68}\right)$

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	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{12138}(319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{204}\right)\)	\(e\left(\frac{37}{204}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{137}{204}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{115}{204}\right)\)	\(e\left(\frac{107}{204}\right)\)	\(e\left(\frac{3}{68}\right)\)
\(\chi_{12138}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{121}{204}\right)\)	\(e\left(\frac{125}{204}\right)\)	\(e\left(\frac{41}{68}\right)\)
\(\chi_{12138}(625,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{133}{204}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{131}{204}\right)\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{59}{68}\right)\)
\(\chi_{12138}(667,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{204}\right)\)	\(e\left(\frac{155}{204}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{199}{204}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{145}{204}\right)\)	\(e\left(\frac{53}{68}\right)\)
\(\chi_{12138}(1033,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{204}\right)\)	\(e\left(\frac{145}{204}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{43}{68}\right)\)
\(\chi_{12138}(1075,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{204}\right)\)	\(e\left(\frac{103}{204}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{23}{204}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{61}{204}\right)\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{1}{68}\right)\)
\(\chi_{12138}(1339,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{204}\right)\)	\(e\left(\frac{65}{204}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{169}{204}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{191}{204}\right)\)	\(e\left(\frac{199}{204}\right)\)	\(e\left(\frac{31}{68}\right)\)
\(\chi_{12138}(1381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{204}\right)\)	\(e\left(\frac{47}{204}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{169}{204}\right)\)	\(e\left(\frac{13}{68}\right)\)
\(\chi_{12138}(1747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{5}{204}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{31}{204}\right)\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{15}{68}\right)\)
\(\chi_{12138}(1789,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{204}\right)\)	\(e\left(\frac{199}{204}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{191}{204}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{1}{204}\right)\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{29}{68}\right)\)
\(\chi_{12138}(2053,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{204}\right)\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{1}{204}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{47}{204}\right)\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{3}{68}\right)\)
\(\chi_{12138}(2095,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{127}{204}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{193}{204}\right)\)	\(e\left(\frac{41}{68}\right)\)
\(\chi_{12138}(2461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{41}{204}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{35}{204}\right)\)	\(e\left(\frac{55}{68}\right)\)
\(\chi_{12138}(2503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{155}{204}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{145}{204}\right)\)	\(e\left(\frac{197}{204}\right)\)	\(e\left(\frac{57}{68}\right)\)
\(\chi_{12138}(2767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{204}\right)\)	\(e\left(\frac{77}{204}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{37}{204}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{107}{204}\right)\)	\(e\left(\frac{151}{204}\right)\)	\(e\left(\frac{43}{68}\right)\)
\(\chi_{12138}(2809,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{35}{204}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{197}{204}\right)\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{1}{68}\right)\)
\(\chi_{12138}(3175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{204}\right)\)	\(e\left(\frac{61}{204}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{77}{204}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{151}{204}\right)\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{27}{68}\right)\)
\(\chi_{12138}(3481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{204}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{73}{204}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{167}{204}\right)\)	\(e\left(\frac{127}{204}\right)\)	\(e\left(\frac{15}{68}\right)\)
\(\chi_{12138}(3523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{204}\right)\)	\(e\left(\frac{131}{204}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{55}{204}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{137}{204}\right)\)	\(e\left(\frac{37}{204}\right)\)	\(e\left(\frac{29}{68}\right)\)
\(\chi_{12138}(3889,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{204}\right)\)	\(e\left(\frac{169}{204}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{191}{204}\right)\)	\(e\left(\frac{67}{68}\right)\)
\(\chi_{12138}(3931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{204}\right)\)	\(e\left(\frac{79}{204}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{25}{204}\right)\)	\(e\left(\frac{41}{204}\right)\)	\(e\left(\frac{45}{68}\right)\)
\(\chi_{12138}(4195,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{204}\right)\)	\(e\left(\frac{89}{204}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{23}{204}\right)\)	\(e\left(\frac{103}{204}\right)\)	\(e\left(\frac{55}{68}\right)\)
\(\chi_{12138}(4237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{204}\right)\)	\(e\left(\frac{23}{204}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{77}{204}\right)\)	\(e\left(\frac{61}{204}\right)\)	\(e\left(\frac{57}{68}\right)\)
\(\chi_{12138}(4603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{204}\right)\)	\(e\left(\frac{73}{204}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{67}{204}\right)\)	\(e\left(\frac{167}{204}\right)\)	\(e\left(\frac{39}{68}\right)\)
\(\chi_{12138}(4645,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{204}\right)\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{47}{204}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{169}{204}\right)\)	\(e\left(\frac{65}{204}\right)\)	\(e\left(\frac{5}{68}\right)\)
\(\chi_{12138}(4909,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{197}{204}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{145}{204}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{79}{204}\right)\)	\(e\left(\frac{27}{68}\right)\)
\(\chi_{12138}(5317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{181}{204}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{127}{204}\right)\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{11}{68}\right)\)
\(\chi_{12138}(5359,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{204}\right)\)	\(e\left(\frac{67}{204}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{89}{204}\right)\)	\(e\left(\frac{33}{68}\right)\)
\(\chi_{12138}(5623,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{101}{204}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{181}{204}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{55}{204}\right)\)	\(e\left(\frac{67}{68}\right)\)
\(\chi_{12138}(5665,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{204}\right)\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{151}{204}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{45}{68}\right)\)
\(\chi_{12138}(6073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{61}{68}\right)\)

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First 31 of 64 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.cn
Modulus	$12138$
Conductor	$2023$
Order	$204$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(12138\)
Conductor:	\(2023\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(204\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2023.bg	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)