Dirichlet character \(\chi_{6800}(653,\cdot)\)

• Label: 6800.653
• 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.jq

\(\chi_{6800}(37,\cdot)\) \(\chi_{6800}(277,\cdot)\) \(\chi_{6800}(333,\cdot)\) \(\chi_{6800}(437,\cdot)\) \(\chi_{6800}(653,\cdot)\) \(\chi_{6800}(677,\cdot)\) \(\chi_{6800}(1133,\cdot)\) \(\chi_{6800}(1213,\cdot)\) \(\chi_{6800}(1397,\cdot)\) \(\chi_{6800}(1637,\cdot)\) \(\chi_{6800}(1797,\cdot)\) \(\chi_{6800}(2013,\cdot)\) \(\chi_{6800}(2037,\cdot)\) \(\chi_{6800}(2573,\cdot)\) \(\chi_{6800}(2997,\cdot)\) \(\chi_{6800}(3053,\cdot)\) \(\chi_{6800}(3373,\cdot)\) \(\chi_{6800}(3397,\cdot)\) \(\chi_{6800}(3853,\cdot)\) \(\chi_{6800}(3933,\cdot)\) \(\chi_{6800}(4117,\cdot)\) \(\chi_{6800}(4413,\cdot)\) \(\chi_{6800}(4517,\cdot)\) \(\chi_{6800}(4733,\cdot)\) \(\chi_{6800}(5213,\cdot)\) \(\chi_{6800}(5477,\cdot)\) \(\chi_{6800}(5717,\cdot)\) \(\chi_{6800}(5773,\cdot)\) \(\chi_{6800}(5877,\cdot)\) \(\chi_{6800}(6117,\cdot)\) ...

Related number fields

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

Values on generators

\((5951,1701,2177,1601)\) → \((1,-i,e\left(\frac{7}{20}\right),e\left(\frac{11}{16}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\( \chi_{ 6800 }(653, a) \)	\(1\)	\(1\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)