Dirichlet character \(\chi_{1960}(1573,\cdot)\)

• Label: 1960.1573
• 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.dm

\(\chi_{1960}(157,\cdot)\) \(\chi_{1960}(173,\cdot)\) \(\chi_{1960}(213,\cdot)\) \(\chi_{1960}(397,\cdot)\) \(\chi_{1960}(437,\cdot)\) \(\chi_{1960}(453,\cdot)\) \(\chi_{1960}(493,\cdot)\) \(\chi_{1960}(677,\cdot)\) \(\chi_{1960}(733,\cdot)\) \(\chi_{1960}(773,\cdot)\) \(\chi_{1960}(957,\cdot)\) \(\chi_{1960}(997,\cdot)\) \(\chi_{1960}(1013,\cdot)\) \(\chi_{1960}(1053,\cdot)\) \(\chi_{1960}(1237,\cdot)\) \(\chi_{1960}(1277,\cdot)\) \(\chi_{1960}(1333,\cdot)\) \(\chi_{1960}(1517,\cdot)\) \(\chi_{1960}(1557,\cdot)\) \(\chi_{1960}(1573,\cdot)\) \(\chi_{1960}(1613,\cdot)\) \(\chi_{1960}(1797,\cdot)\) \(\chi_{1960}(1837,\cdot)\) \(\chi_{1960}(1853,\cdot)\)

Related number fields

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

Values on generators

\((1471,981,1177,1081)\) → \((1,-1,-i,e\left(\frac{29}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\( \chi_{ 1960 }(1573, a) \)	\(1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)