Dirichlet character \(\chi_{1720}(413,\cdot)\)

• Label: 1720.413
• Modulus: $1720$
• Conductor: $1720$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1720\)
Conductor:	\(1720\)
Order:	\(84\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1720.dp

\(\chi_{1720}(77,\cdot)\) \(\chi_{1720}(157,\cdot)\) \(\chi_{1720}(277,\cdot)\) \(\chi_{1720}(373,\cdot)\) \(\chi_{1720}(413,\cdot)\) \(\chi_{1720}(493,\cdot)\) \(\chi_{1720}(693,\cdot)\) \(\chi_{1720}(717,\cdot)\) \(\chi_{1720}(757,\cdot)\) \(\chi_{1720}(837,\cdot)\) \(\chi_{1720}(893,\cdot)\) \(\chi_{1720}(933,\cdot)\) \(\chi_{1720}(1037,\cdot)\) \(\chi_{1720}(1093,\cdot)\) \(\chi_{1720}(1173,\cdot)\) \(\chi_{1720}(1237,\cdot)\) \(\chi_{1720}(1277,\cdot)\) \(\chi_{1720}(1293,\cdot)\) \(\chi_{1720}(1437,\cdot)\) \(\chi_{1720}(1453,\cdot)\) \(\chi_{1720}(1517,\cdot)\) \(\chi_{1720}(1533,\cdot)\) \(\chi_{1720}(1637,\cdot)\) \(\chi_{1720}(1653,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

\((431,861,1377,1121)\) → \((1,-1,-i,e\left(\frac{17}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\( \chi_{ 1720 }(413, a) \)	\(1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)