LMFDB - Dirichlet character orbit 31433.bs

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31433, base_ring=CyclotomicField(172)) M = H._module chi = DirichletCharacter(H, M([129,12])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(259,31433)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$31433$
Conductor:	$31433$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$172$	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:	$\Q(\zeta_{172})$
Fixed field:	Number field defined by a degree 172 polynomial (not computed)

First 31 of 84 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{31433}(259,\cdot)$	$1$	$1$	$e\left(\frac{75}{86}\right)$	$e\left(\frac{141}{172}\right)$	$e\left(\frac{32}{43}\right)$	$e\left(\frac{37}{172}\right)$	$e\left(\frac{119}{172}\right)$	$e\left(\frac{59}{172}\right)$	$e\left(\frac{53}{86}\right)$	$e\left(\frac{55}{86}\right)$	$e\left(\frac{15}{172}\right)$	$e\left(\frac{167}{172}\right)$
$\chi_{31433}(302,\cdot)$	$1$	$1$	$e\left(\frac{23}{86}\right)$	$e\left(\frac{143}{172}\right)$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{79}{172}\right)$	$e\left(\frac{17}{172}\right)$	$e\left(\frac{33}{172}\right)$	$e\left(\frac{69}{86}\right)$	$e\left(\frac{57}{86}\right)$	$e\left(\frac{125}{172}\right)$	$e\left(\frac{73}{172}\right)$
$\chi_{31433}(990,\cdot)$	$1$	$1$	$e\left(\frac{51}{86}\right)$	$e\left(\frac{89}{172}\right)$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{149}{172}\right)$	$e\left(\frac{19}{172}\right)$	$e\left(\frac{47}{172}\right)$	$e\left(\frac{67}{86}\right)$	$e\left(\frac{3}{86}\right)$	$e\left(\frac{79}{172}\right)$	$e\left(\frac{31}{172}\right)$
$\chi_{31433}(1033,\cdot)$	$1$	$1$	$e\left(\frac{85}{86}\right)$	$e\left(\frac{91}{172}\right)$	$e\left(\frac{42}{43}\right)$	$e\left(\frac{19}{172}\right)$	$e\left(\frac{89}{172}\right)$	$e\left(\frac{21}{172}\right)$	$e\left(\frac{83}{86}\right)$	$e\left(\frac{5}{86}\right)$	$e\left(\frac{17}{172}\right)$	$e\left(\frac{109}{172}\right)$
$\chi_{31433}(1721,\cdot)$	$1$	$1$	$e\left(\frac{27}{86}\right)$	$e\left(\frac{37}{172}\right)$	$e\left(\frac{27}{43}\right)$	$e\left(\frac{89}{172}\right)$	$e\left(\frac{91}{172}\right)$	$e\left(\frac{35}{172}\right)$	$e\left(\frac{81}{86}\right)$	$e\left(\frac{37}{86}\right)$	$e\left(\frac{143}{172}\right)$	$e\left(\frac{67}{172}\right)$
$\chi_{31433}(1764,\cdot)$	$1$	$1$	$e\left(\frac{61}{86}\right)$	$e\left(\frac{39}{172}\right)$	$e\left(\frac{18}{43}\right)$	$e\left(\frac{131}{172}\right)$	$e\left(\frac{161}{172}\right)$	$e\left(\frac{9}{172}\right)$	$e\left(\frac{11}{86}\right)$	$e\left(\frac{39}{86}\right)$	$e\left(\frac{81}{172}\right)$	$e\left(\frac{145}{172}\right)$
$\chi_{31433}(2452,\cdot)$	$1$	$1$	$e\left(\frac{3}{86}\right)$	$e\left(\frac{157}{172}\right)$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{29}{172}\right)$	$e\left(\frac{163}{172}\right)$	$e\left(\frac{23}{172}\right)$	$e\left(\frac{9}{86}\right)$	$e\left(\frac{71}{86}\right)$	$e\left(\frac{35}{172}\right)$	$e\left(\frac{103}{172}\right)$
$\chi_{31433}(2495,\cdot)$	$1$	$1$	$e\left(\frac{37}{86}\right)$	$e\left(\frac{159}{172}\right)$	$e\left(\frac{37}{43}\right)$	$e\left(\frac{71}{172}\right)$	$e\left(\frac{61}{172}\right)$	$e\left(\frac{169}{172}\right)$	$e\left(\frac{25}{86}\right)$	$e\left(\frac{73}{86}\right)$	$e\left(\frac{145}{172}\right)$	$e\left(\frac{9}{172}\right)$
$\chi_{31433}(3183,\cdot)$	$1$	$1$	$e\left(\frac{65}{86}\right)$	$e\left(\frac{105}{172}\right)$	$e\left(\frac{22}{43}\right)$	$e\left(\frac{141}{172}\right)$	$e\left(\frac{63}{172}\right)$	$e\left(\frac{11}{172}\right)$	$e\left(\frac{23}{86}\right)$	$e\left(\frac{19}{86}\right)$	$e\left(\frac{99}{172}\right)$	$e\left(\frac{139}{172}\right)$
$\chi_{31433}(3226,\cdot)$	$1$	$1$	$e\left(\frac{13}{86}\right)$	$e\left(\frac{107}{172}\right)$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{11}{172}\right)$	$e\left(\frac{133}{172}\right)$	$e\left(\frac{157}{172}\right)$	$e\left(\frac{39}{86}\right)$	$e\left(\frac{21}{86}\right)$	$e\left(\frac{37}{172}\right)$	$e\left(\frac{45}{172}\right)$
$\chi_{31433}(3914,\cdot)$	$1$	$1$	$e\left(\frac{41}{86}\right)$	$e\left(\frac{53}{172}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{81}{172}\right)$	$e\left(\frac{135}{172}\right)$	$e\left(\frac{171}{172}\right)$	$e\left(\frac{37}{86}\right)$	$e\left(\frac{53}{86}\right)$	$e\left(\frac{163}{172}\right)$	$e\left(\frac{3}{172}\right)$
$\chi_{31433}(3957,\cdot)$	$1$	$1$	$e\left(\frac{75}{86}\right)$	$e\left(\frac{55}{172}\right)$	$e\left(\frac{32}{43}\right)$	$e\left(\frac{123}{172}\right)$	$e\left(\frac{33}{172}\right)$	$e\left(\frac{145}{172}\right)$	$e\left(\frac{53}{86}\right)$	$e\left(\frac{55}{86}\right)$	$e\left(\frac{101}{172}\right)$	$e\left(\frac{81}{172}\right)$
$\chi_{31433}(4645,\cdot)$	$1$	$1$	$e\left(\frac{17}{86}\right)$	$e\left(\frac{1}{172}\right)$	$e\left(\frac{17}{43}\right)$	$e\left(\frac{21}{172}\right)$	$e\left(\frac{35}{172}\right)$	$e\left(\frac{159}{172}\right)$	$e\left(\frac{51}{86}\right)$	$e\left(\frac{1}{86}\right)$	$e\left(\frac{55}{172}\right)$	$e\left(\frac{39}{172}\right)$
$\chi_{31433}(4688,\cdot)$	$1$	$1$	$e\left(\frac{51}{86}\right)$	$e\left(\frac{3}{172}\right)$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{63}{172}\right)$	$e\left(\frac{105}{172}\right)$	$e\left(\frac{133}{172}\right)$	$e\left(\frac{67}{86}\right)$	$e\left(\frac{3}{86}\right)$	$e\left(\frac{165}{172}\right)$	$e\left(\frac{117}{172}\right)$
$\chi_{31433}(5376,\cdot)$	$1$	$1$	$e\left(\frac{79}{86}\right)$	$e\left(\frac{121}{172}\right)$	$e\left(\frac{36}{43}\right)$	$e\left(\frac{133}{172}\right)$	$e\left(\frac{107}{172}\right)$	$e\left(\frac{147}{172}\right)$	$e\left(\frac{65}{86}\right)$	$e\left(\frac{35}{86}\right)$	$e\left(\frac{119}{172}\right)$	$e\left(\frac{75}{172}\right)$
$\chi_{31433}(5419,\cdot)$	$1$	$1$	$e\left(\frac{27}{86}\right)$	$e\left(\frac{123}{172}\right)$	$e\left(\frac{27}{43}\right)$	$e\left(\frac{3}{172}\right)$	$e\left(\frac{5}{172}\right)$	$e\left(\frac{121}{172}\right)$	$e\left(\frac{81}{86}\right)$	$e\left(\frac{37}{86}\right)$	$e\left(\frac{57}{172}\right)$	$e\left(\frac{153}{172}\right)$
$\chi_{31433}(6107,\cdot)$	$1$	$1$	$e\left(\frac{55}{86}\right)$	$e\left(\frac{69}{172}\right)$	$e\left(\frac{12}{43}\right)$	$e\left(\frac{73}{172}\right)$	$e\left(\frac{7}{172}\right)$	$e\left(\frac{135}{172}\right)$	$e\left(\frac{79}{86}\right)$	$e\left(\frac{69}{86}\right)$	$e\left(\frac{11}{172}\right)$	$e\left(\frac{111}{172}\right)$
$\chi_{31433}(6150,\cdot)$	$1$	$1$	$e\left(\frac{3}{86}\right)$	$e\left(\frac{71}{172}\right)$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{115}{172}\right)$	$e\left(\frac{77}{172}\right)$	$e\left(\frac{109}{172}\right)$	$e\left(\frac{9}{86}\right)$	$e\left(\frac{71}{86}\right)$	$e\left(\frac{121}{172}\right)$	$e\left(\frac{17}{172}\right)$
$\chi_{31433}(6838,\cdot)$	$1$	$1$	$e\left(\frac{31}{86}\right)$	$e\left(\frac{17}{172}\right)$	$e\left(\frac{31}{43}\right)$	$e\left(\frac{13}{172}\right)$	$e\left(\frac{79}{172}\right)$	$e\left(\frac{123}{172}\right)$	$e\left(\frac{7}{86}\right)$	$e\left(\frac{17}{86}\right)$	$e\left(\frac{75}{172}\right)$	$e\left(\frac{147}{172}\right)$
$\chi_{31433}(6881,\cdot)$	$1$	$1$	$e\left(\frac{65}{86}\right)$	$e\left(\frac{19}{172}\right)$	$e\left(\frac{22}{43}\right)$	$e\left(\frac{55}{172}\right)$	$e\left(\frac{149}{172}\right)$	$e\left(\frac{97}{172}\right)$	$e\left(\frac{23}{86}\right)$	$e\left(\frac{19}{86}\right)$	$e\left(\frac{13}{172}\right)$	$e\left(\frac{53}{172}\right)$
$\chi_{31433}(7569,\cdot)$	$1$	$1$	$e\left(\frac{7}{86}\right)$	$e\left(\frac{137}{172}\right)$	$e\left(\frac{7}{43}\right)$	$e\left(\frac{125}{172}\right)$	$e\left(\frac{151}{172}\right)$	$e\left(\frac{111}{172}\right)$	$e\left(\frac{21}{86}\right)$	$e\left(\frac{51}{86}\right)$	$e\left(\frac{139}{172}\right)$	$e\left(\frac{11}{172}\right)$
$\chi_{31433}(7612,\cdot)$	$1$	$1$	$e\left(\frac{41}{86}\right)$	$e\left(\frac{139}{172}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{167}{172}\right)$	$e\left(\frac{49}{172}\right)$	$e\left(\frac{85}{172}\right)$	$e\left(\frac{37}{86}\right)$	$e\left(\frac{53}{86}\right)$	$e\left(\frac{77}{172}\right)$	$e\left(\frac{89}{172}\right)$
$\chi_{31433}(8300,\cdot)$	$1$	$1$	$e\left(\frac{69}{86}\right)$	$e\left(\frac{85}{172}\right)$	$e\left(\frac{26}{43}\right)$	$e\left(\frac{65}{172}\right)$	$e\left(\frac{51}{172}\right)$	$e\left(\frac{99}{172}\right)$	$e\left(\frac{35}{86}\right)$	$e\left(\frac{85}{86}\right)$	$e\left(\frac{31}{172}\right)$	$e\left(\frac{47}{172}\right)$
$\chi_{31433}(8343,\cdot)$	$1$	$1$	$e\left(\frac{17}{86}\right)$	$e\left(\frac{87}{172}\right)$	$e\left(\frac{17}{43}\right)$	$e\left(\frac{107}{172}\right)$	$e\left(\frac{121}{172}\right)$	$e\left(\frac{73}{172}\right)$	$e\left(\frac{51}{86}\right)$	$e\left(\frac{1}{86}\right)$	$e\left(\frac{141}{172}\right)$	$e\left(\frac{125}{172}\right)$
$\chi_{31433}(9031,\cdot)$	$1$	$1$	$e\left(\frac{45}{86}\right)$	$e\left(\frac{33}{172}\right)$	$e\left(\frac{2}{43}\right)$	$e\left(\frac{5}{172}\right)$	$e\left(\frac{123}{172}\right)$	$e\left(\frac{87}{172}\right)$	$e\left(\frac{49}{86}\right)$	$e\left(\frac{33}{86}\right)$	$e\left(\frac{95}{172}\right)$	$e\left(\frac{83}{172}\right)$
$\chi_{31433}(9074,\cdot)$	$1$	$1$	$e\left(\frac{79}{86}\right)$	$e\left(\frac{35}{172}\right)$	$e\left(\frac{36}{43}\right)$	$e\left(\frac{47}{172}\right)$	$e\left(\frac{21}{172}\right)$	$e\left(\frac{61}{172}\right)$	$e\left(\frac{65}{86}\right)$	$e\left(\frac{35}{86}\right)$	$e\left(\frac{33}{172}\right)$	$e\left(\frac{161}{172}\right)$
$\chi_{31433}(9762,\cdot)$	$1$	$1$	$e\left(\frac{21}{86}\right)$	$e\left(\frac{153}{172}\right)$	$e\left(\frac{21}{43}\right)$	$e\left(\frac{117}{172}\right)$	$e\left(\frac{23}{172}\right)$	$e\left(\frac{75}{172}\right)$	$e\left(\frac{63}{86}\right)$	$e\left(\frac{67}{86}\right)$	$e\left(\frac{159}{172}\right)$	$e\left(\frac{119}{172}\right)$
$\chi_{31433}(9805,\cdot)$	$1$	$1$	$e\left(\frac{55}{86}\right)$	$e\left(\frac{155}{172}\right)$	$e\left(\frac{12}{43}\right)$	$e\left(\frac{159}{172}\right)$	$e\left(\frac{93}{172}\right)$	$e\left(\frac{49}{172}\right)$	$e\left(\frac{79}{86}\right)$	$e\left(\frac{69}{86}\right)$	$e\left(\frac{97}{172}\right)$	$e\left(\frac{25}{172}\right)$
$\chi_{31433}(10493,\cdot)$	$1$	$1$	$e\left(\frac{83}{86}\right)$	$e\left(\frac{101}{172}\right)$	$e\left(\frac{40}{43}\right)$	$e\left(\frac{57}{172}\right)$	$e\left(\frac{95}{172}\right)$	$e\left(\frac{63}{172}\right)$	$e\left(\frac{77}{86}\right)$	$e\left(\frac{15}{86}\right)$	$e\left(\frac{51}{172}\right)$	$e\left(\frac{155}{172}\right)$
$\chi_{31433}(10536,\cdot)$	$1$	$1$	$e\left(\frac{31}{86}\right)$	$e\left(\frac{103}{172}\right)$	$e\left(\frac{31}{43}\right)$	$e\left(\frac{99}{172}\right)$	$e\left(\frac{165}{172}\right)$	$e\left(\frac{37}{172}\right)$	$e\left(\frac{7}{86}\right)$	$e\left(\frac{17}{86}\right)$	$e\left(\frac{161}{172}\right)$	$e\left(\frac{61}{172}\right)$
$\chi_{31433}(11224,\cdot)$	$1$	$1$	$e\left(\frac{59}{86}\right)$	$e\left(\frac{49}{172}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{169}{172}\right)$	$e\left(\frac{167}{172}\right)$	$e\left(\frac{51}{172}\right)$	$e\left(\frac{5}{86}\right)$	$e\left(\frac{49}{86}\right)$	$e\left(\frac{115}{172}\right)$	$e\left(\frac{19}{172}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{31433}(259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{86}\right)\)	\(e\left(\frac{141}{172}\right)\)	\(e\left(\frac{32}{43}\right)\)	\(e\left(\frac{37}{172}\right)\)	\(e\left(\frac{119}{172}\right)\)	\(e\left(\frac{59}{172}\right)\)	\(e\left(\frac{53}{86}\right)\)	\(e\left(\frac{55}{86}\right)\)	\(e\left(\frac{15}{172}\right)\)	\(e\left(\frac{167}{172}\right)\)
\(\chi_{31433}(302,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{86}\right)\)	\(e\left(\frac{143}{172}\right)\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{79}{172}\right)\)	\(e\left(\frac{17}{172}\right)\)	\(e\left(\frac{33}{172}\right)\)	\(e\left(\frac{69}{86}\right)\)	\(e\left(\frac{57}{86}\right)\)	\(e\left(\frac{125}{172}\right)\)	\(e\left(\frac{73}{172}\right)\)
\(\chi_{31433}(990,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{86}\right)\)	\(e\left(\frac{89}{172}\right)\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{149}{172}\right)\)	\(e\left(\frac{19}{172}\right)\)	\(e\left(\frac{47}{172}\right)\)	\(e\left(\frac{67}{86}\right)\)	\(e\left(\frac{3}{86}\right)\)	\(e\left(\frac{79}{172}\right)\)	\(e\left(\frac{31}{172}\right)\)
\(\chi_{31433}(1033,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{86}\right)\)	\(e\left(\frac{91}{172}\right)\)	\(e\left(\frac{42}{43}\right)\)	\(e\left(\frac{19}{172}\right)\)	\(e\left(\frac{89}{172}\right)\)	\(e\left(\frac{21}{172}\right)\)	\(e\left(\frac{83}{86}\right)\)	\(e\left(\frac{5}{86}\right)\)	\(e\left(\frac{17}{172}\right)\)	\(e\left(\frac{109}{172}\right)\)
\(\chi_{31433}(1721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{86}\right)\)	\(e\left(\frac{37}{172}\right)\)	\(e\left(\frac{27}{43}\right)\)	\(e\left(\frac{89}{172}\right)\)	\(e\left(\frac{91}{172}\right)\)	\(e\left(\frac{35}{172}\right)\)	\(e\left(\frac{81}{86}\right)\)	\(e\left(\frac{37}{86}\right)\)	\(e\left(\frac{143}{172}\right)\)	\(e\left(\frac{67}{172}\right)\)
\(\chi_{31433}(1764,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{86}\right)\)	\(e\left(\frac{39}{172}\right)\)	\(e\left(\frac{18}{43}\right)\)	\(e\left(\frac{131}{172}\right)\)	\(e\left(\frac{161}{172}\right)\)	\(e\left(\frac{9}{172}\right)\)	\(e\left(\frac{11}{86}\right)\)	\(e\left(\frac{39}{86}\right)\)	\(e\left(\frac{81}{172}\right)\)	\(e\left(\frac{145}{172}\right)\)
\(\chi_{31433}(2452,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{86}\right)\)	\(e\left(\frac{157}{172}\right)\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{29}{172}\right)\)	\(e\left(\frac{163}{172}\right)\)	\(e\left(\frac{23}{172}\right)\)	\(e\left(\frac{9}{86}\right)\)	\(e\left(\frac{71}{86}\right)\)	\(e\left(\frac{35}{172}\right)\)	\(e\left(\frac{103}{172}\right)\)
\(\chi_{31433}(2495,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{86}\right)\)	\(e\left(\frac{159}{172}\right)\)	\(e\left(\frac{37}{43}\right)\)	\(e\left(\frac{71}{172}\right)\)	\(e\left(\frac{61}{172}\right)\)	\(e\left(\frac{169}{172}\right)\)	\(e\left(\frac{25}{86}\right)\)	\(e\left(\frac{73}{86}\right)\)	\(e\left(\frac{145}{172}\right)\)	\(e\left(\frac{9}{172}\right)\)
\(\chi_{31433}(3183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{86}\right)\)	\(e\left(\frac{105}{172}\right)\)	\(e\left(\frac{22}{43}\right)\)	\(e\left(\frac{141}{172}\right)\)	\(e\left(\frac{63}{172}\right)\)	\(e\left(\frac{11}{172}\right)\)	\(e\left(\frac{23}{86}\right)\)	\(e\left(\frac{19}{86}\right)\)	\(e\left(\frac{99}{172}\right)\)	\(e\left(\frac{139}{172}\right)\)
\(\chi_{31433}(3226,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{86}\right)\)	\(e\left(\frac{107}{172}\right)\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{11}{172}\right)\)	\(e\left(\frac{133}{172}\right)\)	\(e\left(\frac{157}{172}\right)\)	\(e\left(\frac{39}{86}\right)\)	\(e\left(\frac{21}{86}\right)\)	\(e\left(\frac{37}{172}\right)\)	\(e\left(\frac{45}{172}\right)\)
\(\chi_{31433}(3914,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{86}\right)\)	\(e\left(\frac{53}{172}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{81}{172}\right)\)	\(e\left(\frac{135}{172}\right)\)	\(e\left(\frac{171}{172}\right)\)	\(e\left(\frac{37}{86}\right)\)	\(e\left(\frac{53}{86}\right)\)	\(e\left(\frac{163}{172}\right)\)	\(e\left(\frac{3}{172}\right)\)
\(\chi_{31433}(3957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{86}\right)\)	\(e\left(\frac{55}{172}\right)\)	\(e\left(\frac{32}{43}\right)\)	\(e\left(\frac{123}{172}\right)\)	\(e\left(\frac{33}{172}\right)\)	\(e\left(\frac{145}{172}\right)\)	\(e\left(\frac{53}{86}\right)\)	\(e\left(\frac{55}{86}\right)\)	\(e\left(\frac{101}{172}\right)\)	\(e\left(\frac{81}{172}\right)\)
\(\chi_{31433}(4645,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{86}\right)\)	\(e\left(\frac{1}{172}\right)\)	\(e\left(\frac{17}{43}\right)\)	\(e\left(\frac{21}{172}\right)\)	\(e\left(\frac{35}{172}\right)\)	\(e\left(\frac{159}{172}\right)\)	\(e\left(\frac{51}{86}\right)\)	\(e\left(\frac{1}{86}\right)\)	\(e\left(\frac{55}{172}\right)\)	\(e\left(\frac{39}{172}\right)\)
\(\chi_{31433}(4688,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{86}\right)\)	\(e\left(\frac{3}{172}\right)\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{63}{172}\right)\)	\(e\left(\frac{105}{172}\right)\)	\(e\left(\frac{133}{172}\right)\)	\(e\left(\frac{67}{86}\right)\)	\(e\left(\frac{3}{86}\right)\)	\(e\left(\frac{165}{172}\right)\)	\(e\left(\frac{117}{172}\right)\)
\(\chi_{31433}(5376,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{86}\right)\)	\(e\left(\frac{121}{172}\right)\)	\(e\left(\frac{36}{43}\right)\)	\(e\left(\frac{133}{172}\right)\)	\(e\left(\frac{107}{172}\right)\)	\(e\left(\frac{147}{172}\right)\)	\(e\left(\frac{65}{86}\right)\)	\(e\left(\frac{35}{86}\right)\)	\(e\left(\frac{119}{172}\right)\)	\(e\left(\frac{75}{172}\right)\)
\(\chi_{31433}(5419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{86}\right)\)	\(e\left(\frac{123}{172}\right)\)	\(e\left(\frac{27}{43}\right)\)	\(e\left(\frac{3}{172}\right)\)	\(e\left(\frac{5}{172}\right)\)	\(e\left(\frac{121}{172}\right)\)	\(e\left(\frac{81}{86}\right)\)	\(e\left(\frac{37}{86}\right)\)	\(e\left(\frac{57}{172}\right)\)	\(e\left(\frac{153}{172}\right)\)
\(\chi_{31433}(6107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{86}\right)\)	\(e\left(\frac{69}{172}\right)\)	\(e\left(\frac{12}{43}\right)\)	\(e\left(\frac{73}{172}\right)\)	\(e\left(\frac{7}{172}\right)\)	\(e\left(\frac{135}{172}\right)\)	\(e\left(\frac{79}{86}\right)\)	\(e\left(\frac{69}{86}\right)\)	\(e\left(\frac{11}{172}\right)\)	\(e\left(\frac{111}{172}\right)\)
\(\chi_{31433}(6150,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{86}\right)\)	\(e\left(\frac{71}{172}\right)\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{115}{172}\right)\)	\(e\left(\frac{77}{172}\right)\)	\(e\left(\frac{109}{172}\right)\)	\(e\left(\frac{9}{86}\right)\)	\(e\left(\frac{71}{86}\right)\)	\(e\left(\frac{121}{172}\right)\)	\(e\left(\frac{17}{172}\right)\)
\(\chi_{31433}(6838,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{86}\right)\)	\(e\left(\frac{17}{172}\right)\)	\(e\left(\frac{31}{43}\right)\)	\(e\left(\frac{13}{172}\right)\)	\(e\left(\frac{79}{172}\right)\)	\(e\left(\frac{123}{172}\right)\)	\(e\left(\frac{7}{86}\right)\)	\(e\left(\frac{17}{86}\right)\)	\(e\left(\frac{75}{172}\right)\)	\(e\left(\frac{147}{172}\right)\)
\(\chi_{31433}(6881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{86}\right)\)	\(e\left(\frac{19}{172}\right)\)	\(e\left(\frac{22}{43}\right)\)	\(e\left(\frac{55}{172}\right)\)	\(e\left(\frac{149}{172}\right)\)	\(e\left(\frac{97}{172}\right)\)	\(e\left(\frac{23}{86}\right)\)	\(e\left(\frac{19}{86}\right)\)	\(e\left(\frac{13}{172}\right)\)	\(e\left(\frac{53}{172}\right)\)
\(\chi_{31433}(7569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{86}\right)\)	\(e\left(\frac{137}{172}\right)\)	\(e\left(\frac{7}{43}\right)\)	\(e\left(\frac{125}{172}\right)\)	\(e\left(\frac{151}{172}\right)\)	\(e\left(\frac{111}{172}\right)\)	\(e\left(\frac{21}{86}\right)\)	\(e\left(\frac{51}{86}\right)\)	\(e\left(\frac{139}{172}\right)\)	\(e\left(\frac{11}{172}\right)\)
\(\chi_{31433}(7612,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{86}\right)\)	\(e\left(\frac{139}{172}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{167}{172}\right)\)	\(e\left(\frac{49}{172}\right)\)	\(e\left(\frac{85}{172}\right)\)	\(e\left(\frac{37}{86}\right)\)	\(e\left(\frac{53}{86}\right)\)	\(e\left(\frac{77}{172}\right)\)	\(e\left(\frac{89}{172}\right)\)
\(\chi_{31433}(8300,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{86}\right)\)	\(e\left(\frac{85}{172}\right)\)	\(e\left(\frac{26}{43}\right)\)	\(e\left(\frac{65}{172}\right)\)	\(e\left(\frac{51}{172}\right)\)	\(e\left(\frac{99}{172}\right)\)	\(e\left(\frac{35}{86}\right)\)	\(e\left(\frac{85}{86}\right)\)	\(e\left(\frac{31}{172}\right)\)	\(e\left(\frac{47}{172}\right)\)
\(\chi_{31433}(8343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{86}\right)\)	\(e\left(\frac{87}{172}\right)\)	\(e\left(\frac{17}{43}\right)\)	\(e\left(\frac{107}{172}\right)\)	\(e\left(\frac{121}{172}\right)\)	\(e\left(\frac{73}{172}\right)\)	\(e\left(\frac{51}{86}\right)\)	\(e\left(\frac{1}{86}\right)\)	\(e\left(\frac{141}{172}\right)\)	\(e\left(\frac{125}{172}\right)\)
\(\chi_{31433}(9031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{86}\right)\)	\(e\left(\frac{33}{172}\right)\)	\(e\left(\frac{2}{43}\right)\)	\(e\left(\frac{5}{172}\right)\)	\(e\left(\frac{123}{172}\right)\)	\(e\left(\frac{87}{172}\right)\)	\(e\left(\frac{49}{86}\right)\)	\(e\left(\frac{33}{86}\right)\)	\(e\left(\frac{95}{172}\right)\)	\(e\left(\frac{83}{172}\right)\)
\(\chi_{31433}(9074,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{86}\right)\)	\(e\left(\frac{35}{172}\right)\)	\(e\left(\frac{36}{43}\right)\)	\(e\left(\frac{47}{172}\right)\)	\(e\left(\frac{21}{172}\right)\)	\(e\left(\frac{61}{172}\right)\)	\(e\left(\frac{65}{86}\right)\)	\(e\left(\frac{35}{86}\right)\)	\(e\left(\frac{33}{172}\right)\)	\(e\left(\frac{161}{172}\right)\)
\(\chi_{31433}(9762,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{86}\right)\)	\(e\left(\frac{153}{172}\right)\)	\(e\left(\frac{21}{43}\right)\)	\(e\left(\frac{117}{172}\right)\)	\(e\left(\frac{23}{172}\right)\)	\(e\left(\frac{75}{172}\right)\)	\(e\left(\frac{63}{86}\right)\)	\(e\left(\frac{67}{86}\right)\)	\(e\left(\frac{159}{172}\right)\)	\(e\left(\frac{119}{172}\right)\)
\(\chi_{31433}(9805,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{86}\right)\)	\(e\left(\frac{155}{172}\right)\)	\(e\left(\frac{12}{43}\right)\)	\(e\left(\frac{159}{172}\right)\)	\(e\left(\frac{93}{172}\right)\)	\(e\left(\frac{49}{172}\right)\)	\(e\left(\frac{79}{86}\right)\)	\(e\left(\frac{69}{86}\right)\)	\(e\left(\frac{97}{172}\right)\)	\(e\left(\frac{25}{172}\right)\)
\(\chi_{31433}(10493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{86}\right)\)	\(e\left(\frac{101}{172}\right)\)	\(e\left(\frac{40}{43}\right)\)	\(e\left(\frac{57}{172}\right)\)	\(e\left(\frac{95}{172}\right)\)	\(e\left(\frac{63}{172}\right)\)	\(e\left(\frac{77}{86}\right)\)	\(e\left(\frac{15}{86}\right)\)	\(e\left(\frac{51}{172}\right)\)	\(e\left(\frac{155}{172}\right)\)
\(\chi_{31433}(10536,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{86}\right)\)	\(e\left(\frac{103}{172}\right)\)	\(e\left(\frac{31}{43}\right)\)	\(e\left(\frac{99}{172}\right)\)	\(e\left(\frac{165}{172}\right)\)	\(e\left(\frac{37}{172}\right)\)	\(e\left(\frac{7}{86}\right)\)	\(e\left(\frac{17}{86}\right)\)	\(e\left(\frac{161}{172}\right)\)	\(e\left(\frac{61}{172}\right)\)
\(\chi_{31433}(11224,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{86}\right)\)	\(e\left(\frac{49}{172}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{169}{172}\right)\)	\(e\left(\frac{167}{172}\right)\)	\(e\left(\frac{51}{172}\right)\)	\(e\left(\frac{5}{86}\right)\)	\(e\left(\frac{49}{86}\right)\)	\(e\left(\frac{115}{172}\right)\)	\(e\left(\frac{19}{172}\right)\)

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First 31 of 84 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	31433.bs
Modulus	$31433$
Conductor	$31433$
Order	$172$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(31433\)
Conductor:	\(31433\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(172\)	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)