Dirichlet character \(\chi_{1960}(1747,\cdot)\)

• Label: 1960.1747
• Modulus: $1960$
• Conductor: $1960$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1960\)
Conductor:	\(1960\)
Order:	\(84\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1960.dq

\(\chi_{1960}(107,\cdot)\) \(\chi_{1960}(123,\cdot)\) \(\chi_{1960}(163,\cdot)\) \(\chi_{1960}(347,\cdot)\) \(\chi_{1960}(387,\cdot)\) \(\chi_{1960}(403,\cdot)\) \(\chi_{1960}(443,\cdot)\) \(\chi_{1960}(627,\cdot)\) \(\chi_{1960}(683,\cdot)\) \(\chi_{1960}(723,\cdot)\) \(\chi_{1960}(907,\cdot)\) \(\chi_{1960}(947,\cdot)\) \(\chi_{1960}(963,\cdot)\) \(\chi_{1960}(1003,\cdot)\) \(\chi_{1960}(1187,\cdot)\) \(\chi_{1960}(1227,\cdot)\) \(\chi_{1960}(1283,\cdot)\) \(\chi_{1960}(1467,\cdot)\) \(\chi_{1960}(1507,\cdot)\) \(\chi_{1960}(1523,\cdot)\) \(\chi_{1960}(1563,\cdot)\) \(\chi_{1960}(1747,\cdot)\) \(\chi_{1960}(1787,\cdot)\) \(\chi_{1960}(1803,\cdot)\)

Related number fields

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

Values on generators

\((1471,981,1177,1081)\) → \((-1,-1,i,e\left(\frac{2}{21}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\( \chi_{ 1960 }(1747, a) \)	\(1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)