Dirichlet character \(\chi_{67}(23,\cdot)\)

• Label: 67.23
• Modulus: $67$
• Conductor: $67$
• Order: $33$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(67\)
Conductor:	\(67\)
Order:	\(33\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 67.g

\(\chi_{67}(4,\cdot)\) \(\chi_{67}(6,\cdot)\) \(\chi_{67}(10,\cdot)\) \(\chi_{67}(16,\cdot)\) \(\chi_{67}(17,\cdot)\) \(\chi_{67}(19,\cdot)\) \(\chi_{67}(21,\cdot)\) \(\chi_{67}(23,\cdot)\) \(\chi_{67}(26,\cdot)\) \(\chi_{67}(33,\cdot)\) \(\chi_{67}(35,\cdot)\) \(\chi_{67}(36,\cdot)\) \(\chi_{67}(39,\cdot)\) \(\chi_{67}(47,\cdot)\) \(\chi_{67}(49,\cdot)\) \(\chi_{67}(54,\cdot)\) \(\chi_{67}(55,\cdot)\) \(\chi_{67}(56,\cdot)\) \(\chi_{67}(60,\cdot)\) \(\chi_{67}(65,\cdot)\)

Related number fields

Field of values:	\(\Q(\zeta_{33})\)
Fixed field:	Number field defined by a degree 33 polynomial

Values on generators

\(2\) → \(e\left(\frac{14}{33}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 67 }(23, a) \)	\(1\)	\(1\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum