Dirichlet character \(\chi_{1700}(1287,\cdot)\)

• Label: 1700.1287
• Modulus: $1700$
• Conductor: $1700$
• Order: $80$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1700\)
Conductor:	\(1700\)
Order:	\(80\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1700.cm

\(\chi_{1700}(23,\cdot)\) \(\chi_{1700}(163,\cdot)\) \(\chi_{1700}(167,\cdot)\) \(\chi_{1700}(267,\cdot)\) \(\chi_{1700}(283,\cdot)\) \(\chi_{1700}(363,\cdot)\) \(\chi_{1700}(447,\cdot)\) \(\chi_{1700}(483,\cdot)\) \(\chi_{1700}(503,\cdot)\) \(\chi_{1700}(547,\cdot)\) \(\chi_{1700}(623,\cdot)\) \(\chi_{1700}(703,\cdot)\) \(\chi_{1700}(787,\cdot)\) \(\chi_{1700}(823,\cdot)\) \(\chi_{1700}(847,\cdot)\) \(\chi_{1700}(887,\cdot)\) \(\chi_{1700}(947,\cdot)\) \(\chi_{1700}(963,\cdot)\) \(\chi_{1700}(1127,\cdot)\) \(\chi_{1700}(1163,\cdot)\) \(\chi_{1700}(1183,\cdot)\) \(\chi_{1700}(1187,\cdot)\) \(\chi_{1700}(1227,\cdot)\) \(\chi_{1700}(1287,\cdot)\) \(\chi_{1700}(1303,\cdot)\) \(\chi_{1700}(1383,\cdot)\) \(\chi_{1700}(1467,\cdot)\) \(\chi_{1700}(1503,\cdot)\) \(\chi_{1700}(1523,\cdot)\) \(\chi_{1700}(1527,\cdot)\) ...

Related number fields

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

Values on generators

\((851,477,1601)\) → \((-1,e\left(\frac{9}{20}\right),e\left(\frac{13}{16}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\( \chi_{ 1700 }(1287, a) \)	\(-1\)	\(1\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)