LMFDB - Dirichlet character orbit 12138.cb

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(12138, base_ring=CyclotomicField(102)) M = H._module chi = DirichletCharacter(H, M([0,68,69])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(67,12138)) 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:	$102$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2023.bb	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:	$\Q(\zeta_{51})$
Fixed field:	Number field defined by a degree 102 polynomial (not computed)

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{12138}(67,\cdot)$	$1$	$1$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{23}{34}\right)$
$\chi_{12138}(373,\cdot)$	$1$	$1$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{33}{34}\right)$
$\chi_{12138}(781,\cdot)$	$1$	$1$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{1}{34}\right)$
$\chi_{12138}(1087,\cdot)$	$1$	$1$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{11}{34}\right)$
$\chi_{12138}(1495,\cdot)$	$1$	$1$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{13}{34}\right)$
$\chi_{12138}(1801,\cdot)$	$1$	$1$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{23}{34}\right)$
$\chi_{12138}(2209,\cdot)$	$1$	$1$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{25}{34}\right)$
$\chi_{12138}(2515,\cdot)$	$1$	$1$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{1}{34}\right)$
$\chi_{12138}(2923,\cdot)$	$1$	$1$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{3}{34}\right)$
$\chi_{12138}(3229,\cdot)$	$1$	$1$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{13}{34}\right)$
$\chi_{12138}(3637,\cdot)$	$1$	$1$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{15}{34}\right)$
$\chi_{12138}(3943,\cdot)$	$1$	$1$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{25}{34}\right)$
$\chi_{12138}(4351,\cdot)$	$1$	$1$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{27}{34}\right)$
$\chi_{12138}(4657,\cdot)$	$1$	$1$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{3}{34}\right)$
$\chi_{12138}(5065,\cdot)$	$1$	$1$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{5}{34}\right)$
$\chi_{12138}(5371,\cdot)$	$1$	$1$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{15}{34}\right)$
$\chi_{12138}(6085,\cdot)$	$1$	$1$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{27}{34}\right)$
$\chi_{12138}(6493,\cdot)$	$1$	$1$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{29}{34}\right)$
$\chi_{12138}(6799,\cdot)$	$1$	$1$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{5}{34}\right)$
$\chi_{12138}(7207,\cdot)$	$1$	$1$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{7}{34}\right)$
$\chi_{12138}(7921,\cdot)$	$1$	$1$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{19}{34}\right)$
$\chi_{12138}(8227,\cdot)$	$1$	$1$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{29}{34}\right)$
$\chi_{12138}(8635,\cdot)$	$1$	$1$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{31}{34}\right)$
$\chi_{12138}(8941,\cdot)$	$1$	$1$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{7}{34}\right)$
$\chi_{12138}(9349,\cdot)$	$1$	$1$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{9}{34}\right)$
$\chi_{12138}(9655,\cdot)$	$1$	$1$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{19}{34}\right)$
$\chi_{12138}(10063,\cdot)$	$1$	$1$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{21}{34}\right)$
$\chi_{12138}(10369,\cdot)$	$1$	$1$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{31}{34}\right)$
$\chi_{12138}(10777,\cdot)$	$1$	$1$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{33}{34}\right)$
$\chi_{12138}(11083,\cdot)$	$1$	$1$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{9}{34}\right)$
$\chi_{12138}(11491,\cdot)$	$1$	$1$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{11}{34}\right)$

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	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{12138}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{25}{51}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{23}{34}\right)\)
\(\chi_{12138}(373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{33}{34}\right)\)
\(\chi_{12138}(781,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{1}{34}\right)\)
\(\chi_{12138}(1087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{11}{34}\right)\)
\(\chi_{12138}(1495,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{13}{34}\right)\)
\(\chi_{12138}(1801,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{23}{34}\right)\)
\(\chi_{12138}(2209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{25}{34}\right)\)
\(\chi_{12138}(2515,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{1}{34}\right)\)
\(\chi_{12138}(2923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{3}{34}\right)\)
\(\chi_{12138}(3229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{13}{34}\right)\)
\(\chi_{12138}(3637,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{15}{34}\right)\)
\(\chi_{12138}(3943,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{25}{34}\right)\)
\(\chi_{12138}(4351,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{27}{34}\right)\)
\(\chi_{12138}(4657,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{3}{34}\right)\)
\(\chi_{12138}(5065,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{5}{34}\right)\)
\(\chi_{12138}(5371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{15}{34}\right)\)
\(\chi_{12138}(6085,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{27}{34}\right)\)
\(\chi_{12138}(6493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{29}{34}\right)\)
\(\chi_{12138}(6799,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{5}{34}\right)\)
\(\chi_{12138}(7207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{7}{34}\right)\)
\(\chi_{12138}(7921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{19}{34}\right)\)
\(\chi_{12138}(8227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{29}{34}\right)\)
\(\chi_{12138}(8635,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{31}{34}\right)\)
\(\chi_{12138}(8941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{7}{34}\right)\)
\(\chi_{12138}(9349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{9}{34}\right)\)
\(\chi_{12138}(9655,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{25}{51}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{19}{34}\right)\)
\(\chi_{12138}(10063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{21}{34}\right)\)
\(\chi_{12138}(10369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{31}{34}\right)\)
\(\chi_{12138}(10777,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{33}{34}\right)\)
\(\chi_{12138}(11083,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{9}{34}\right)\)
\(\chi_{12138}(11491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{11}{34}\right)\)

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First 31 of 32 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.cb
Modulus	$12138$
Conductor	$2023$
Order	$102$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(12138\)
Conductor:	\(2023\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(102\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2023.bb	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)