Dirichlet character \(\chi_{1600}(813,\cdot)\)

• Label: 1600.813
• Modulus: $1600$
• Conductor: $1600$
• Order: $80$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1600\)
Conductor:	\(1600\)
Order:	\(80\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1600.cn

\(\chi_{1600}(13,\cdot)\) \(\chi_{1600}(37,\cdot)\) \(\chi_{1600}(117,\cdot)\) \(\chi_{1600}(173,\cdot)\) \(\chi_{1600}(197,\cdot)\) \(\chi_{1600}(253,\cdot)\) \(\chi_{1600}(277,\cdot)\) \(\chi_{1600}(333,\cdot)\) \(\chi_{1600}(413,\cdot)\) \(\chi_{1600}(437,\cdot)\) \(\chi_{1600}(517,\cdot)\) \(\chi_{1600}(573,\cdot)\) \(\chi_{1600}(597,\cdot)\) \(\chi_{1600}(653,\cdot)\) \(\chi_{1600}(677,\cdot)\) \(\chi_{1600}(733,\cdot)\) \(\chi_{1600}(813,\cdot)\) \(\chi_{1600}(837,\cdot)\) \(\chi_{1600}(917,\cdot)\) \(\chi_{1600}(973,\cdot)\) \(\chi_{1600}(997,\cdot)\) \(\chi_{1600}(1053,\cdot)\) \(\chi_{1600}(1077,\cdot)\) \(\chi_{1600}(1133,\cdot)\) \(\chi_{1600}(1213,\cdot)\) \(\chi_{1600}(1237,\cdot)\) \(\chi_{1600}(1317,\cdot)\) \(\chi_{1600}(1373,\cdot)\) \(\chi_{1600}(1397,\cdot)\) \(\chi_{1600}(1453,\cdot)\) ...

Related number fields

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

Values on generators

\((1151,901,577)\) → \((1,e\left(\frac{7}{16}\right),e\left(\frac{19}{20}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\( \chi_{ 1600 }(813, a) \)	\(-1\)	\(1\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)