Dirichlet character \(\chi_{265}(73,\cdot)\)

• Label: 265.73
• Modulus: $265$
• Conductor: $265$
• Order: $52$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(265\)
Conductor:	\(265\)
Order:	\(52\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 265.o

\(\chi_{265}(3,\cdot)\) \(\chi_{265}(12,\cdot)\) \(\chi_{265}(22,\cdot)\) \(\chi_{265}(27,\cdot)\) \(\chi_{265}(48,\cdot)\) \(\chi_{265}(67,\cdot)\) \(\chi_{265}(73,\cdot)\) \(\chi_{265}(87,\cdot)\) \(\chi_{265}(88,\cdot)\) \(\chi_{265}(98,\cdot)\) \(\chi_{265}(108,\cdot)\) \(\chi_{265}(127,\cdot)\) \(\chi_{265}(138,\cdot)\) \(\chi_{265}(157,\cdot)\) \(\chi_{265}(167,\cdot)\) \(\chi_{265}(177,\cdot)\) \(\chi_{265}(178,\cdot)\) \(\chi_{265}(192,\cdot)\) \(\chi_{265}(198,\cdot)\) \(\chi_{265}(217,\cdot)\) \(\chi_{265}(238,\cdot)\) \(\chi_{265}(243,\cdot)\) \(\chi_{265}(253,\cdot)\) \(\chi_{265}(262,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Values on generators

\((107,161)\) → \((-i,e\left(\frac{49}{52}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\( \chi_{ 265 }(73, a) \)	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{45}{52}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum