Dirichlet character \(\chi_{1175}(51,\cdot)\)

• Label: 1175.51
• Modulus: $1175$
• Conductor: $47$
• Order: $23$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1175\)
Conductor:	\(47\)
Order:	\(23\)
Real:	no
Primitive:	no, induced from \(\chi_{47}(4,\cdot)\)
Minimal:	yes
Parity:	even

Galois orbit 1175.m

\(\chi_{1175}(51,\cdot)\) \(\chi_{1175}(101,\cdot)\) \(\chi_{1175}(126,\cdot)\) \(\chi_{1175}(251,\cdot)\) \(\chi_{1175}(401,\cdot)\) \(\chi_{1175}(426,\cdot)\) \(\chi_{1175}(451,\cdot)\) \(\chi_{1175}(476,\cdot)\) \(\chi_{1175}(526,\cdot)\) \(\chi_{1175}(551,\cdot)\) \(\chi_{1175}(576,\cdot)\) \(\chi_{1175}(601,\cdot)\) \(\chi_{1175}(676,\cdot)\) \(\chi_{1175}(726,\cdot)\) \(\chi_{1175}(776,\cdot)\) \(\chi_{1175}(801,\cdot)\) \(\chi_{1175}(826,\cdot)\) \(\chi_{1175}(901,\cdot)\) \(\chi_{1175}(976,\cdot)\) \(\chi_{1175}(1001,\cdot)\) \(\chi_{1175}(1051,\cdot)\) \(\chi_{1175}(1076,\cdot)\)

Related number fields

Field of values:	\(\Q(\zeta_{23})\)
Fixed field:	Number field defined by a degree 23 polynomial

Values on generators

\((377,851)\) → \((1,e\left(\frac{18}{23}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\( \chi_{ 1175 }(51, a) \)	\(1\)	\(1\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)