LMFDB - Dirichlet character orbit 12138.bz

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(12138, base_ring=CyclotomicField(68)) M = H._module chi = DirichletCharacter(H, M([34,34,27])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(293,12138)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$12138$
Conductor:	$6069$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$68$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 6069.by	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:	$\Q(\zeta_{68})$
Fixed field:	Number field defined by a degree 68 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{12138}(293,\cdot)$	$1$	$1$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{61}{68}\right)$
$\chi_{12138}(965,\cdot)$	$1$	$1$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{23}{68}\right)$
$\chi_{12138}(1007,\cdot)$	$1$	$1$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{21}{68}\right)$
$\chi_{12138}(1679,\cdot)$	$1$	$1$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{63}{68}\right)$
$\chi_{12138}(1721,\cdot)$	$1$	$1$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{49}{68}\right)$
$\chi_{12138}(2393,\cdot)$	$1$	$1$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{35}{68}\right)$
$\chi_{12138}(2435,\cdot)$	$1$	$1$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{9}{68}\right)$
$\chi_{12138}(3107,\cdot)$	$1$	$1$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{7}{68}\right)$
$\chi_{12138}(3149,\cdot)$	$1$	$1$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{37}{68}\right)$
$\chi_{12138}(3821,\cdot)$	$1$	$1$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{47}{68}\right)$
$\chi_{12138}(3863,\cdot)$	$1$	$1$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{65}{68}\right)$
$\chi_{12138}(4535,\cdot)$	$1$	$1$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{19}{68}\right)$
$\chi_{12138}(4577,\cdot)$	$1$	$1$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{25}{68}\right)$
$\chi_{12138}(5249,\cdot)$	$1$	$1$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{59}{68}\right)$
$\chi_{12138}(5291,\cdot)$	$1$	$1$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{53}{68}\right)$
$\chi_{12138}(5963,\cdot)$	$1$	$1$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{31}{68}\right)$
$\chi_{12138}(6005,\cdot)$	$1$	$1$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{13}{68}\right)$
$\chi_{12138}(6677,\cdot)$	$1$	$1$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{3}{68}\right)$
$\chi_{12138}(6719,\cdot)$	$1$	$1$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{41}{68}\right)$
$\chi_{12138}(7391,\cdot)$	$1$	$1$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{43}{68}\right)$
$\chi_{12138}(7433,\cdot)$	$1$	$1$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{1}{68}\right)$
$\chi_{12138}(8105,\cdot)$	$1$	$1$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{15}{68}\right)$
$\chi_{12138}(8147,\cdot)$	$1$	$1$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{29}{68}\right)$
$\chi_{12138}(8819,\cdot)$	$1$	$1$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{55}{68}\right)$
$\chi_{12138}(8861,\cdot)$	$1$	$1$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{57}{68}\right)$
$\chi_{12138}(9533,\cdot)$	$1$	$1$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{27}{68}\right)$
$\chi_{12138}(10247,\cdot)$	$1$	$1$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{67}{68}\right)$
$\chi_{12138}(10289,\cdot)$	$1$	$1$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{45}{68}\right)$
$\chi_{12138}(10961,\cdot)$	$1$	$1$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{39}{68}\right)$
$\chi_{12138}(11003,\cdot)$	$1$	$1$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{5}{68}\right)$
$\chi_{12138}(11675,\cdot)$	$1$	$1$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{11}{68}\right)$

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	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{12138}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{61}{68}\right)\)
\(\chi_{12138}(965,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)
\(\chi_{12138}(1007,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)
\(\chi_{12138}(1679,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)
\(\chi_{12138}(1721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)
\(\chi_{12138}(2393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)
\(\chi_{12138}(2435,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)
\(\chi_{12138}(3107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)
\(\chi_{12138}(3149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{37}{68}\right)\)
\(\chi_{12138}(3821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{47}{68}\right)\)
\(\chi_{12138}(3863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)
\(\chi_{12138}(4535,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{19}{68}\right)\)
\(\chi_{12138}(4577,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)
\(\chi_{12138}(5249,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{59}{68}\right)\)
\(\chi_{12138}(5291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)
\(\chi_{12138}(5963,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)
\(\chi_{12138}(6005,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{13}{68}\right)\)
\(\chi_{12138}(6677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)
\(\chi_{12138}(6719,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{41}{68}\right)\)
\(\chi_{12138}(7391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)
\(\chi_{12138}(7433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)
\(\chi_{12138}(8105,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{15}{68}\right)\)
\(\chi_{12138}(8147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)
\(\chi_{12138}(8819,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)
\(\chi_{12138}(8861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)
\(\chi_{12138}(9533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)
\(\chi_{12138}(10247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{67}{68}\right)\)
\(\chi_{12138}(10289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{45}{68}\right)\)
\(\chi_{12138}(10961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)
\(\chi_{12138}(11003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)
\(\chi_{12138}(11675,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)

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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.bz
Modulus	$12138$
Conductor	$6069$
Order	$68$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(12138\)
Conductor:	\(6069\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(68\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 6069.by	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)