Dirichlet character \(\chi_{2352}(845,\cdot)\)

• Label: 2352.845
• Modulus: $2352$
• Conductor: $2352$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2352\)
Conductor:	\(2352\)
Order:	\(84\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2352.dr

\(\chi_{2352}(5,\cdot)\) \(\chi_{2352}(101,\cdot)\) \(\chi_{2352}(173,\cdot)\) \(\chi_{2352}(269,\cdot)\) \(\chi_{2352}(341,\cdot)\) \(\chi_{2352}(437,\cdot)\) \(\chi_{2352}(605,\cdot)\) \(\chi_{2352}(677,\cdot)\) \(\chi_{2352}(773,\cdot)\) \(\chi_{2352}(845,\cdot)\) \(\chi_{2352}(941,\cdot)\) \(\chi_{2352}(1013,\cdot)\) \(\chi_{2352}(1181,\cdot)\) \(\chi_{2352}(1277,\cdot)\) \(\chi_{2352}(1349,\cdot)\) \(\chi_{2352}(1445,\cdot)\) \(\chi_{2352}(1517,\cdot)\) \(\chi_{2352}(1613,\cdot)\) \(\chi_{2352}(1781,\cdot)\) \(\chi_{2352}(1853,\cdot)\) \(\chi_{2352}(1949,\cdot)\) \(\chi_{2352}(2021,\cdot)\) \(\chi_{2352}(2117,\cdot)\) \(\chi_{2352}(2189,\cdot)\)

Related number fields

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

Values on generators

\((1471,1765,785,2257)\) → \((1,-i,-1,e\left(\frac{11}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)
\( \chi_{ 2352 }(845, a) \)	\(1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{84}\right)\)