Dirichlet character \(\chi_{8216}(51,\cdot)\)

• Label: 8216.51
• 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.hj

\(\chi_{8216}(51,\cdot)\) \(\chi_{8216}(155,\cdot)\) \(\chi_{8216}(467,\cdot)\) \(\chi_{8216}(1611,\cdot)\) \(\chi_{8216}(1819,\cdot)\) \(\chi_{8216}(2443,\cdot)\) \(\chi_{8216}(2547,\cdot)\) \(\chi_{8216}(2651,\cdot)\) \(\chi_{8216}(2963,\cdot)\) \(\chi_{8216}(3171,\cdot)\) \(\chi_{8216}(3275,\cdot)\) \(\chi_{8216}(3587,\cdot)\) \(\chi_{8216}(4315,\cdot)\) \(\chi_{8216}(4523,\cdot)\) \(\chi_{8216}(4627,\cdot)\) \(\chi_{8216}(4835,\cdot)\) \(\chi_{8216}(5771,\cdot)\) \(\chi_{8216}(6187,\cdot)\) \(\chi_{8216}(6291,\cdot)\) \(\chi_{8216}(6915,\cdot)\) \(\chi_{8216}(7123,\cdot)\) \(\chi_{8216}(7435,\cdot)\) \(\chi_{8216}(7747,\cdot)\) \(\chi_{8216}(8163,\cdot)\)

Related number fields

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

Values on generators

\((2055,4109,3161,3953)\) → \((-1,-1,-1,e\left(\frac{11}{39}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 8216 }(51, a) \)	\(-1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)