LMFDB - Dirichlet character orbit 31360.ku

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31360, base_ring=CyclotomicField(112)) M = H._module chi = DirichletCharacter(H, M([0,105,0,40])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(41,31360)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$31360$
Conductor:	$3136$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$112$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 3136.cs	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{112})$
Fixed field:	Number field defined by a degree 112 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{31360}(41,\cdot)$	$-1$	$1$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{83}{112}\right)$	$1$
$\chi_{31360}(601,\cdot)$	$-1$	$1$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{41}{112}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{37}{112}\right)$	$1$
$\chi_{31360}(1161,\cdot)$	$-1$	$1$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{103}{112}\right)$	$1$
$\chi_{31360}(1721,\cdot)$	$-1$	$1$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{57}{112}\right)$	$1$
$\chi_{31360}(2281,\cdot)$	$-1$	$1$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{11}{112}\right)$	$1$
$\chi_{31360}(3401,\cdot)$	$-1$	$1$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{31}{112}\right)$	$1$
$\chi_{31360}(3961,\cdot)$	$-1$	$1$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{97}{112}\right)$	$1$
$\chi_{31360}(4521,\cdot)$	$-1$	$1$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{51}{112}\right)$	$1$
$\chi_{31360}(5081,\cdot)$	$-1$	$1$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{5}{112}\right)$	$1$
$\chi_{31360}(5641,\cdot)$	$-1$	$1$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{69}{112}\right)$	$e\left(\frac{71}{112}\right)$	$1$
$\chi_{31360}(6201,\cdot)$	$-1$	$1$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{25}{112}\right)$	$1$
$\chi_{31360}(7321,\cdot)$	$-1$	$1$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{39}{112}\right)$	$e\left(\frac{45}{112}\right)$	$1$
$\chi_{31360}(7881,\cdot)$	$-1$	$1$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{81}{112}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{111}{112}\right)$	$1$
$\chi_{31360}(8441,\cdot)$	$-1$	$1$	$e\left(\frac{81}{112}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{69}{112}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{65}{112}\right)$	$1$
$\chi_{31360}(9001,\cdot)$	$-1$	$1$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{19}{112}\right)$	$1$
$\chi_{31360}(9561,\cdot)$	$-1$	$1$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{85}{112}\right)$	$1$
$\chi_{31360}(10121,\cdot)$	$-1$	$1$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{39}{112}\right)$	$1$
$\chi_{31360}(11241,\cdot)$	$-1$	$1$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{81}{112}\right)$	$e\left(\frac{59}{112}\right)$	$1$
$\chi_{31360}(11801,\cdot)$	$-1$	$1$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{81}{112}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{13}{112}\right)$	$1$
$\chi_{31360}(12361,\cdot)$	$-1$	$1$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{79}{112}\right)$	$1$
$\chi_{31360}(12921,\cdot)$	$-1$	$1$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{33}{112}\right)$	$1$
$\chi_{31360}(13481,\cdot)$	$-1$	$1$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{41}{112}\right)$	$e\left(\frac{99}{112}\right)$	$1$
$\chi_{31360}(14041,\cdot)$	$-1$	$1$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{53}{112}\right)$	$1$
$\chi_{31360}(15161,\cdot)$	$-1$	$1$	$e\left(\frac{41}{112}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{73}{112}\right)$	$1$
$\chi_{31360}(15721,\cdot)$	$-1$	$1$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{39}{112}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{27}{112}\right)$	$1$
$\chi_{31360}(16281,\cdot)$	$-1$	$1$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{93}{112}\right)$	$1$
$\chi_{31360}(16841,\cdot)$	$-1$	$1$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{47}{112}\right)$	$1$
$\chi_{31360}(17401,\cdot)$	$-1$	$1$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{1}{112}\right)$	$1$
$\chi_{31360}(17961,\cdot)$	$-1$	$1$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{67}{112}\right)$	$1$
$\chi_{31360}(19081,\cdot)$	$-1$	$1$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{87}{112}\right)$	$1$
$\chi_{31360}(19641,\cdot)$	$-1$	$1$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{39}{112}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{41}{112}\right)$	$1$

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	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{31360}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(1\)
\(\chi_{31360}(601,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{41}{112}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(1\)
\(\chi_{31360}(1161,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(1\)
\(\chi_{31360}(1721,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(1\)
\(\chi_{31360}(2281,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(1\)
\(\chi_{31360}(3401,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(1\)
\(\chi_{31360}(3961,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(1\)
\(\chi_{31360}(4521,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(1\)
\(\chi_{31360}(5081,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(1\)
\(\chi_{31360}(5641,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{69}{112}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(1\)
\(\chi_{31360}(6201,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(1\)
\(\chi_{31360}(7321,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{39}{112}\right)\)	\(e\left(\frac{45}{112}\right)\)	\(1\)
\(\chi_{31360}(7881,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{81}{112}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(1\)
\(\chi_{31360}(8441,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{81}{112}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{69}{112}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(1\)
\(\chi_{31360}(9001,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(1\)
\(\chi_{31360}(9561,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{85}{112}\right)\)	\(1\)
\(\chi_{31360}(10121,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{39}{112}\right)\)	\(1\)
\(\chi_{31360}(11241,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{81}{112}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(1\)
\(\chi_{31360}(11801,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{81}{112}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(1\)
\(\chi_{31360}(12361,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(1\)
\(\chi_{31360}(12921,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(1\)
\(\chi_{31360}(13481,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{41}{112}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(1\)
\(\chi_{31360}(14041,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(1\)
\(\chi_{31360}(15161,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{112}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(1\)
\(\chi_{31360}(15721,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{39}{112}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(1\)
\(\chi_{31360}(16281,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{93}{112}\right)\)	\(1\)
\(\chi_{31360}(16841,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(1\)
\(\chi_{31360}(17401,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(1\)
\(\chi_{31360}(17961,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(1\)
\(\chi_{31360}(19081,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(1\)
\(\chi_{31360}(19641,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{39}{112}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{41}{112}\right)\)	\(1\)

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Basic properties

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First 31 of 48 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	31360.ku
Modulus	$31360$
Conductor	$3136$
Order	$112$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(31360\)
Conductor:	\(3136\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(112\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 3136.cs	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)