Dirichlet character \(\chi_{31433}(8300,\cdot)\)

• Label: 31433.8300
• Modulus: $31433$
• Conductor: $31433$
• Order: $172$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(31433\)
Conductor:	\(31433\)
Order:	\(172\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 31433.bs

\(\chi_{31433}(259,\cdot)\) \(\chi_{31433}(302,\cdot)\) \(\chi_{31433}(990,\cdot)\) \(\chi_{31433}(1033,\cdot)\) \(\chi_{31433}(1721,\cdot)\) \(\chi_{31433}(1764,\cdot)\) \(\chi_{31433}(2452,\cdot)\) \(\chi_{31433}(2495,\cdot)\) \(\chi_{31433}(3183,\cdot)\) \(\chi_{31433}(3226,\cdot)\) \(\chi_{31433}(3914,\cdot)\) \(\chi_{31433}(3957,\cdot)\) \(\chi_{31433}(4645,\cdot)\) \(\chi_{31433}(4688,\cdot)\) \(\chi_{31433}(5376,\cdot)\) \(\chi_{31433}(5419,\cdot)\) \(\chi_{31433}(6107,\cdot)\) \(\chi_{31433}(6150,\cdot)\) \(\chi_{31433}(6838,\cdot)\) \(\chi_{31433}(6881,\cdot)\) \(\chi_{31433}(7569,\cdot)\) \(\chi_{31433}(7612,\cdot)\) \(\chi_{31433}(8300,\cdot)\) \(\chi_{31433}(8343,\cdot)\) \(\chi_{31433}(9031,\cdot)\) \(\chi_{31433}(9074,\cdot)\) \(\chi_{31433}(9762,\cdot)\) \(\chi_{31433}(9805,\cdot)\) \(\chi_{31433}(10493,\cdot)\) \(\chi_{31433}(10536,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{172})$
Fixed field:	Number field defined by a degree 172 polynomial (not computed)

Values on generators

\((14793,16644)\) → \((-i,e\left(\frac{32}{43}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 31433 }(8300, a) \)	\(1\)	\(1\)	\(e\left(\frac{69}{86}\right)\)	\(e\left(\frac{85}{172}\right)\)	\(e\left(\frac{26}{43}\right)\)	\(e\left(\frac{65}{172}\right)\)	\(e\left(\frac{51}{172}\right)\)	\(e\left(\frac{99}{172}\right)\)	\(e\left(\frac{35}{86}\right)\)	\(e\left(\frac{85}{86}\right)\)	\(e\left(\frac{31}{172}\right)\)	\(e\left(\frac{47}{172}\right)\)