Dirichlet character \(\chi_{25857}(50,\cdot)\)

• Label: 25857.50
• Modulus: $25857$
• Conductor: $25857$
• Order: $156$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(25857\)
Conductor:	\(25857\)
Order:	\(156\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 25857.kc

\(\chi_{25857}(50,\cdot)\) \(\chi_{25857}(254,\cdot)\) \(\chi_{25857}(509,\cdot)\) \(\chi_{25857}(1631,\cdot)\) \(\chi_{25857}(2039,\cdot)\) \(\chi_{25857}(2243,\cdot)\) \(\chi_{25857}(2498,\cdot)\) \(\chi_{25857}(3620,\cdot)\) \(\chi_{25857}(4028,\cdot)\) \(\chi_{25857}(4232,\cdot)\) \(\chi_{25857}(4487,\cdot)\) \(\chi_{25857}(5609,\cdot)\) \(\chi_{25857}(6017,\cdot)\) \(\chi_{25857}(6221,\cdot)\) \(\chi_{25857}(6476,\cdot)\) \(\chi_{25857}(7598,\cdot)\) \(\chi_{25857}(8006,\cdot)\) \(\chi_{25857}(8210,\cdot)\) \(\chi_{25857}(8465,\cdot)\) \(\chi_{25857}(9587,\cdot)\) \(\chi_{25857}(9995,\cdot)\) \(\chi_{25857}(10199,\cdot)\) \(\chi_{25857}(10454,\cdot)\) \(\chi_{25857}(11576,\cdot)\) \(\chi_{25857}(11984,\cdot)\) \(\chi_{25857}(12188,\cdot)\) \(\chi_{25857}(12443,\cdot)\) \(\chi_{25857}(13565,\cdot)\) \(\chi_{25857}(13973,\cdot)\) \(\chi_{25857}(14432,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{156})$
Fixed field:	Number field defined by a degree 156 polynomial (not computed)

Values on generators

\((14366,14536,19774)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{19}{156}\right),-1)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(19\)
\( \chi_{ 25857 }(50, a) \)	\(1\)	\(1\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)