LMFDB - Dirichlet character orbit 31360.lv

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31360, base_ring=CyclotomicField(224)) M = H._module chi = DirichletCharacter(H, M([0,105,168,176])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,31360)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$31360$
Conductor:	$31360$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$224$	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:	$\Q(\zeta_{224})$
Fixed field:	Number field defined by a degree 224 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{31360}(13,\cdot)$	$1$	$1$	$e\left(\frac{99}{224}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{61}{224}\right)$	$e\left(\frac{47}{224}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{73}{224}\right)$	$e\left(\frac{67}{224}\right)$	$i$
$\chi_{31360}(517,\cdot)$	$1$	$1$	$e\left(\frac{205}{224}\right)$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{115}{224}\right)$	$e\left(\frac{129}{224}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{167}{224}\right)$	$e\left(\frac{141}{224}\right)$	$-i$
$\chi_{31360}(573,\cdot)$	$1$	$1$	$e\left(\frac{55}{224}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{9}{224}\right)$	$e\left(\frac{51}{224}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{165}{224}\right)$	$e\left(\frac{87}{224}\right)$	$i$
$\chi_{31360}(1133,\cdot)$	$1$	$1$	$e\left(\frac{11}{224}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{181}{224}\right)$	$e\left(\frac{55}{224}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{33}{224}\right)$	$e\left(\frac{107}{224}\right)$	$i$
$\chi_{31360}(1637,\cdot)$	$1$	$1$	$e\left(\frac{117}{224}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{11}{224}\right)$	$e\left(\frac{137}{224}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{127}{224}\right)$	$e\left(\frac{181}{224}\right)$	$-i$
$\chi_{31360}(1693,\cdot)$	$1$	$1$	$e\left(\frac{191}{224}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{129}{224}\right)$	$e\left(\frac{59}{224}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{125}{224}\right)$	$e\left(\frac{127}{224}\right)$	$i$
$\chi_{31360}(2197,\cdot)$	$1$	$1$	$e\left(\frac{73}{224}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{183}{224}\right)$	$e\left(\frac{141}{224}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{219}{224}\right)$	$e\left(\frac{201}{224}\right)$	$-i$
$\chi_{31360}(2757,\cdot)$	$1$	$1$	$e\left(\frac{29}{224}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{131}{224}\right)$	$e\left(\frac{145}{224}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{87}{224}\right)$	$e\left(\frac{221}{224}\right)$	$-i$
$\chi_{31360}(2813,\cdot)$	$1$	$1$	$e\left(\frac{103}{224}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{25}{224}\right)$	$e\left(\frac{67}{224}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{85}{224}\right)$	$e\left(\frac{167}{224}\right)$	$i$
$\chi_{31360}(3317,\cdot)$	$1$	$1$	$e\left(\frac{209}{224}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{79}{224}\right)$	$e\left(\frac{149}{224}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{179}{224}\right)$	$e\left(\frac{17}{224}\right)$	$-i$
$\chi_{31360}(3373,\cdot)$	$1$	$1$	$e\left(\frac{59}{224}\right)$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{197}{224}\right)$	$e\left(\frac{71}{224}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{177}{224}\right)$	$e\left(\frac{187}{224}\right)$	$i$
$\chi_{31360}(3877,\cdot)$	$1$	$1$	$e\left(\frac{165}{224}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{27}{224}\right)$	$e\left(\frac{153}{224}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{47}{224}\right)$	$e\left(\frac{37}{224}\right)$	$-i$
$\chi_{31360}(3933,\cdot)$	$1$	$1$	$e\left(\frac{15}{224}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{145}{224}\right)$	$e\left(\frac{75}{224}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{45}{224}\right)$	$e\left(\frac{207}{224}\right)$	$i$
$\chi_{31360}(4437,\cdot)$	$1$	$1$	$e\left(\frac{121}{224}\right)$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{199}{224}\right)$	$e\left(\frac{157}{224}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{139}{224}\right)$	$e\left(\frac{57}{224}\right)$	$-i$
$\chi_{31360}(4493,\cdot)$	$1$	$1$	$e\left(\frac{195}{224}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{93}{224}\right)$	$e\left(\frac{79}{224}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{137}{224}\right)$	$e\left(\frac{3}{224}\right)$	$i$
$\chi_{31360}(5053,\cdot)$	$1$	$1$	$e\left(\frac{151}{224}\right)$	$e\left(\frac{39}{112}\right)$	$e\left(\frac{41}{224}\right)$	$e\left(\frac{83}{224}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{5}{224}\right)$	$e\left(\frac{23}{224}\right)$	$i$
$\chi_{31360}(5557,\cdot)$	$1$	$1$	$e\left(\frac{33}{224}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{95}{224}\right)$	$e\left(\frac{165}{224}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{25}{112}\right)$	$e\left(\frac{99}{224}\right)$	$e\left(\frac{97}{224}\right)$	$-i$
$\chi_{31360}(5613,\cdot)$	$1$	$1$	$e\left(\frac{107}{224}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{213}{224}\right)$	$e\left(\frac{87}{224}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{97}{224}\right)$	$e\left(\frac{43}{224}\right)$	$i$
$\chi_{31360}(6117,\cdot)$	$1$	$1$	$e\left(\frac{213}{224}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{43}{224}\right)$	$e\left(\frac{169}{224}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{191}{224}\right)$	$e\left(\frac{117}{224}\right)$	$-i$
$\chi_{31360}(6677,\cdot)$	$1$	$1$	$e\left(\frac{169}{224}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{215}{224}\right)$	$e\left(\frac{173}{224}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{59}{224}\right)$	$e\left(\frac{137}{224}\right)$	$-i$
$\chi_{31360}(6733,\cdot)$	$1$	$1$	$e\left(\frac{19}{224}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{109}{224}\right)$	$e\left(\frac{95}{224}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{57}{224}\right)$	$e\left(\frac{83}{224}\right)$	$i$
$\chi_{31360}(7237,\cdot)$	$1$	$1$	$e\left(\frac{125}{224}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{163}{224}\right)$	$e\left(\frac{177}{224}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{151}{224}\right)$	$e\left(\frac{157}{224}\right)$	$-i$
$\chi_{31360}(7293,\cdot)$	$1$	$1$	$e\left(\frac{199}{224}\right)$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{57}{224}\right)$	$e\left(\frac{99}{224}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{149}{224}\right)$	$e\left(\frac{103}{224}\right)$	$i$
$\chi_{31360}(7797,\cdot)$	$1$	$1$	$e\left(\frac{81}{224}\right)$	$e\left(\frac{81}{112}\right)$	$e\left(\frac{111}{224}\right)$	$e\left(\frac{181}{224}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{41}{112}\right)$	$e\left(\frac{19}{224}\right)$	$e\left(\frac{177}{224}\right)$	$-i$
$\chi_{31360}(7853,\cdot)$	$1$	$1$	$e\left(\frac{155}{224}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{5}{224}\right)$	$e\left(\frac{103}{224}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{17}{224}\right)$	$e\left(\frac{123}{224}\right)$	$i$
$\chi_{31360}(8357,\cdot)$	$1$	$1$	$e\left(\frac{37}{224}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{59}{224}\right)$	$e\left(\frac{185}{224}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{111}{224}\right)$	$e\left(\frac{197}{224}\right)$	$-i$
$\chi_{31360}(8413,\cdot)$	$1$	$1$	$e\left(\frac{111}{224}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{177}{224}\right)$	$e\left(\frac{107}{224}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{109}{224}\right)$	$e\left(\frac{143}{224}\right)$	$i$
$\chi_{31360}(8973,\cdot)$	$1$	$1$	$e\left(\frac{67}{224}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{125}{224}\right)$	$e\left(\frac{111}{224}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{201}{224}\right)$	$e\left(\frac{163}{224}\right)$	$i$
$\chi_{31360}(9477,\cdot)$	$1$	$1$	$e\left(\frac{173}{224}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{179}{224}\right)$	$e\left(\frac{193}{224}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{71}{224}\right)$	$e\left(\frac{13}{224}\right)$	$-i$
$\chi_{31360}(9533,\cdot)$	$1$	$1$	$e\left(\frac{23}{224}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{73}{224}\right)$	$e\left(\frac{115}{224}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{69}{224}\right)$	$e\left(\frac{183}{224}\right)$	$i$
$\chi_{31360}(10037,\cdot)$	$1$	$1$	$e\left(\frac{129}{224}\right)$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{127}{224}\right)$	$e\left(\frac{197}{224}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{163}{224}\right)$	$e\left(\frac{33}{224}\right)$	$-i$

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	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{31360}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{224}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{61}{224}\right)\)	\(e\left(\frac{47}{224}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{73}{224}\right)\)	\(e\left(\frac{67}{224}\right)\)	\(i\)
\(\chi_{31360}(517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{224}\right)\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{115}{224}\right)\)	\(e\left(\frac{129}{224}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{167}{224}\right)\)	\(e\left(\frac{141}{224}\right)\)	\(-i\)
\(\chi_{31360}(573,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{224}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{9}{224}\right)\)	\(e\left(\frac{51}{224}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{165}{224}\right)\)	\(e\left(\frac{87}{224}\right)\)	\(i\)
\(\chi_{31360}(1133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{224}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{181}{224}\right)\)	\(e\left(\frac{55}{224}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{33}{224}\right)\)	\(e\left(\frac{107}{224}\right)\)	\(i\)
\(\chi_{31360}(1637,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{117}{224}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{11}{224}\right)\)	\(e\left(\frac{137}{224}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{127}{224}\right)\)	\(e\left(\frac{181}{224}\right)\)	\(-i\)
\(\chi_{31360}(1693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{224}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{129}{224}\right)\)	\(e\left(\frac{59}{224}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{125}{224}\right)\)	\(e\left(\frac{127}{224}\right)\)	\(i\)
\(\chi_{31360}(2197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{224}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{183}{224}\right)\)	\(e\left(\frac{141}{224}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{219}{224}\right)\)	\(e\left(\frac{201}{224}\right)\)	\(-i\)
\(\chi_{31360}(2757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{224}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{131}{224}\right)\)	\(e\left(\frac{145}{224}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{87}{224}\right)\)	\(e\left(\frac{221}{224}\right)\)	\(-i\)
\(\chi_{31360}(2813,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{224}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{25}{224}\right)\)	\(e\left(\frac{67}{224}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{85}{224}\right)\)	\(e\left(\frac{167}{224}\right)\)	\(i\)
\(\chi_{31360}(3317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{209}{224}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{79}{224}\right)\)	\(e\left(\frac{149}{224}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{179}{224}\right)\)	\(e\left(\frac{17}{224}\right)\)	\(-i\)
\(\chi_{31360}(3373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{224}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{197}{224}\right)\)	\(e\left(\frac{71}{224}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{177}{224}\right)\)	\(e\left(\frac{187}{224}\right)\)	\(i\)
\(\chi_{31360}(3877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{165}{224}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{27}{224}\right)\)	\(e\left(\frac{153}{224}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{47}{224}\right)\)	\(e\left(\frac{37}{224}\right)\)	\(-i\)
\(\chi_{31360}(3933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{224}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{145}{224}\right)\)	\(e\left(\frac{75}{224}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{45}{224}\right)\)	\(e\left(\frac{207}{224}\right)\)	\(i\)
\(\chi_{31360}(4437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{224}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{199}{224}\right)\)	\(e\left(\frac{157}{224}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{139}{224}\right)\)	\(e\left(\frac{57}{224}\right)\)	\(-i\)
\(\chi_{31360}(4493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{195}{224}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{93}{224}\right)\)	\(e\left(\frac{79}{224}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{137}{224}\right)\)	\(e\left(\frac{3}{224}\right)\)	\(i\)
\(\chi_{31360}(5053,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{224}\right)\)	\(e\left(\frac{39}{112}\right)\)	\(e\left(\frac{41}{224}\right)\)	\(e\left(\frac{83}{224}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{5}{224}\right)\)	\(e\left(\frac{23}{224}\right)\)	\(i\)
\(\chi_{31360}(5557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{224}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{95}{224}\right)\)	\(e\left(\frac{165}{224}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(e\left(\frac{99}{224}\right)\)	\(e\left(\frac{97}{224}\right)\)	\(-i\)
\(\chi_{31360}(5613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{224}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{213}{224}\right)\)	\(e\left(\frac{87}{224}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{97}{224}\right)\)	\(e\left(\frac{43}{224}\right)\)	\(i\)
\(\chi_{31360}(6117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{213}{224}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{43}{224}\right)\)	\(e\left(\frac{169}{224}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{191}{224}\right)\)	\(e\left(\frac{117}{224}\right)\)	\(-i\)
\(\chi_{31360}(6677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{224}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{215}{224}\right)\)	\(e\left(\frac{173}{224}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{59}{224}\right)\)	\(e\left(\frac{137}{224}\right)\)	\(-i\)
\(\chi_{31360}(6733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{224}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{109}{224}\right)\)	\(e\left(\frac{95}{224}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{57}{224}\right)\)	\(e\left(\frac{83}{224}\right)\)	\(i\)
\(\chi_{31360}(7237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{224}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{163}{224}\right)\)	\(e\left(\frac{177}{224}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{151}{224}\right)\)	\(e\left(\frac{157}{224}\right)\)	\(-i\)
\(\chi_{31360}(7293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{224}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{57}{224}\right)\)	\(e\left(\frac{99}{224}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{149}{224}\right)\)	\(e\left(\frac{103}{224}\right)\)	\(i\)
\(\chi_{31360}(7797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{224}\right)\)	\(e\left(\frac{81}{112}\right)\)	\(e\left(\frac{111}{224}\right)\)	\(e\left(\frac{181}{224}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{41}{112}\right)\)	\(e\left(\frac{19}{224}\right)\)	\(e\left(\frac{177}{224}\right)\)	\(-i\)
\(\chi_{31360}(7853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{224}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{5}{224}\right)\)	\(e\left(\frac{103}{224}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{17}{224}\right)\)	\(e\left(\frac{123}{224}\right)\)	\(i\)
\(\chi_{31360}(8357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{224}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{59}{224}\right)\)	\(e\left(\frac{185}{224}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{111}{224}\right)\)	\(e\left(\frac{197}{224}\right)\)	\(-i\)
\(\chi_{31360}(8413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{224}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{177}{224}\right)\)	\(e\left(\frac{107}{224}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{109}{224}\right)\)	\(e\left(\frac{143}{224}\right)\)	\(i\)
\(\chi_{31360}(8973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{224}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{125}{224}\right)\)	\(e\left(\frac{111}{224}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{201}{224}\right)\)	\(e\left(\frac{163}{224}\right)\)	\(i\)
\(\chi_{31360}(9477,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{224}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{179}{224}\right)\)	\(e\left(\frac{193}{224}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{71}{224}\right)\)	\(e\left(\frac{13}{224}\right)\)	\(-i\)
\(\chi_{31360}(9533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{224}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{73}{224}\right)\)	\(e\left(\frac{115}{224}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{69}{224}\right)\)	\(e\left(\frac{183}{224}\right)\)	\(i\)
\(\chi_{31360}(10037,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{129}{224}\right)\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{127}{224}\right)\)	\(e\left(\frac{197}{224}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{163}{224}\right)\)	\(e\left(\frac{33}{224}\right)\)	\(-i\)

Introduction

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Basic properties

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First 31 of 96 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.lv
Modulus	$31360$
Conductor	$31360$
Order	$224$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(31360\)
Conductor:	\(31360\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(224\)	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)