LMFDB - Dirichlet character orbit 113.i

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(113, base_ring=CyclotomicField(56)) M = H._module chi = DirichletCharacter(H, M([1])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(9,113)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$113$
Conductor:	$113$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$56$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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:	$\Q(\zeta_{56})$
Fixed field:	Number field defined by a degree 56 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{113}(9,\cdot)$	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{113}(11,\cdot)$	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{113}(13,\cdot)$	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{113}(22,\cdot)$	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{113}(25,\cdot)$	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{113}(26,\cdot)$	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{113}(31,\cdot)$	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{113}(36,\cdot)$	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{113}(41,\cdot)$	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{113}(50,\cdot)$	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{113}(51,\cdot)$	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{113}(52,\cdot)$	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{113}(61,\cdot)$	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{113}(62,\cdot)$	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{113}(63,\cdot)$	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{113}(72,\cdot)$	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{113}(77,\cdot)$	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{113}(82,\cdot)$	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{113}(87,\cdot)$	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{113}(88,\cdot)$	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{113}(91,\cdot)$	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{113}(100,\cdot)$	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{113}(102,\cdot)$	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{113}(104,\cdot)$	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{9}{28}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{113}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{113}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{113}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{113}(22,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{113}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{113}(26,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{113}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{113}(36,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{113}(41,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{113}(50,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{113}(51,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{113}(52,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{113}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{113}(62,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{113}(63,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{113}(72,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{113}(77,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{113}(82,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{113}(87,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{113}(88,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{113}(91,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{113}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{113}(102,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{113}(104,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{9}{28}\right)\)

Introduction

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Varieties

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Representations

Groups

Database

Properties

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Basic properties

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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	113.i
Modulus	$113$
Conductor	$113$
Order	$56$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(113\)
Conductor:	\(113\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(56\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)