Dirichlet character \(\chi_{8216}(7757,\cdot)\)

• Label: 8216.7757
• 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.ho

\(\chi_{8216}(61,\cdot)\) \(\chi_{8216}(373,\cdot)\) \(\chi_{8216}(861,\cdot)\) \(\chi_{8216}(965,\cdot)\) \(\chi_{8216}(1621,\cdot)\) \(\chi_{8216}(1829,\cdot)\) \(\chi_{8216}(2245,\cdot)\) \(\chi_{8216}(2349,\cdot)\) \(\chi_{8216}(3253,\cdot)\) \(\chi_{8216}(3389,\cdot)\) \(\chi_{8216}(3493,\cdot)\) \(\chi_{8216}(4293,\cdot)\) \(\chi_{8216}(5125,\cdot)\) \(\chi_{8216}(5229,\cdot)\) \(\chi_{8216}(5749,\cdot)\) \(\chi_{8216}(5781,\cdot)\) \(\chi_{8216}(6061,\cdot)\) \(\chi_{8216}(6821,\cdot)\) \(\chi_{8216}(7309,\cdot)\) \(\chi_{8216}(7517,\cdot)\) \(\chi_{8216}(7653,\cdot)\) \(\chi_{8216}(7757,\cdot)\) \(\chi_{8216}(7933,\cdot)\) \(\chi_{8216}(8037,\cdot)\)

Related number fields

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

Values on generators

\((2055,4109,3161,3953)\) → \((1,-1,e\left(\frac{2}{3}\right),e\left(\frac{21}{26}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 8216 }(7757, a) \)	\(-1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)