Dirichlet character \(\chi_{8216}(6373,\cdot)\)

• Label: 8216.6373
• Modulus: $8216$
• Conductor: $8216$
• Order: $78$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(8216\)
Conductor:	\(8216\)
Order:	\(78\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 8216.hg

\(\chi_{8216}(29,\cdot)\) \(\chi_{8216}(477,\cdot)\) \(\chi_{8216}(549,\cdot)\) \(\chi_{8216}(581,\cdot)\) \(\chi_{8216}(1725,\cdot)\) \(\chi_{8216}(1933,\cdot)\) \(\chi_{8216}(2661,\cdot)\) \(\chi_{8216}(2733,\cdot)\) \(\chi_{8216}(3149,\cdot)\) \(\chi_{8216}(3357,\cdot)\) \(\chi_{8216}(3773,\cdot)\) \(\chi_{8216}(3877,\cdot)\) \(\chi_{8216}(4013,\cdot)\) \(\chi_{8216}(4221,\cdot)\) \(\chi_{8216}(4325,\cdot)\) \(\chi_{8216}(4533,\cdot)\) \(\chi_{8216}(4709,\cdot)\) \(\chi_{8216}(5573,\cdot)\) \(\chi_{8216}(5853,\cdot)\) \(\chi_{8216}(6197,\cdot)\) \(\chi_{8216}(6373,\cdot)\) \(\chi_{8216}(6789,\cdot)\) \(\chi_{8216}(7029,\cdot)\) \(\chi_{8216}(7101,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 78 polynomial

Values on generators

\((2055,4109,3161,3953)\) → \((1,-1,e\left(\frac{1}{3}\right),e\left(\frac{77}{78}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 8216 }(6373, a) \)	\(-1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(1\)