Dirichlet character \(\chi_{6800}(5059,\cdot)\)

• Label: 6800.5059
• Modulus: $6800$
• Conductor: $6800$
• Order: $80$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(6800\)
Conductor:	\(6800\)
Order:	\(80\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 6800.kf

\(\chi_{6800}(139,\cdot)\) \(\chi_{6800}(379,\cdot)\) \(\chi_{6800}(419,\cdot)\) \(\chi_{6800}(539,\cdot)\) \(\chi_{6800}(779,\cdot)\) \(\chi_{6800}(979,\cdot)\) \(\chi_{6800}(1739,\cdot)\) \(\chi_{6800}(1779,\cdot)\) \(\chi_{6800}(1859,\cdot)\) \(\chi_{6800}(2139,\cdot)\) \(\chi_{6800}(2339,\cdot)\) \(\chi_{6800}(2659,\cdot)\) \(\chi_{6800}(2859,\cdot)\) \(\chi_{6800}(3139,\cdot)\) \(\chi_{6800}(3219,\cdot)\) \(\chi_{6800}(3259,\cdot)\) \(\chi_{6800}(4019,\cdot)\) \(\chi_{6800}(4219,\cdot)\) \(\chi_{6800}(4459,\cdot)\) \(\chi_{6800}(4579,\cdot)\) \(\chi_{6800}(4619,\cdot)\) \(\chi_{6800}(4859,\cdot)\) \(\chi_{6800}(5059,\cdot)\) \(\chi_{6800}(5379,\cdot)\) \(\chi_{6800}(5579,\cdot)\) \(\chi_{6800}(5819,\cdot)\) \(\chi_{6800}(5859,\cdot)\) \(\chi_{6800}(5939,\cdot)\) \(\chi_{6800}(5979,\cdot)\) \(\chi_{6800}(6219,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

Values on generators

\((5951,1701,2177,1601)\) → \((-1,-i,e\left(\frac{7}{10}\right),e\left(\frac{3}{16}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\( \chi_{ 6800 }(5059, a) \)	\(1\)	\(1\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)