Dirichlet character \(\chi_{2112}(251,\cdot)\)

• Label: 2112.251
• Modulus: $2112$
• Conductor: $2112$
• Order: $80$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2112\)
Conductor:	\(2112\)
Order:	\(80\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2112.cv

\(\chi_{2112}(59,\cdot)\) \(\chi_{2112}(179,\cdot)\) \(\chi_{2112}(203,\cdot)\) \(\chi_{2112}(251,\cdot)\) \(\chi_{2112}(323,\cdot)\) \(\chi_{2112}(443,\cdot)\) \(\chi_{2112}(467,\cdot)\) \(\chi_{2112}(515,\cdot)\) \(\chi_{2112}(587,\cdot)\) \(\chi_{2112}(707,\cdot)\) \(\chi_{2112}(731,\cdot)\) \(\chi_{2112}(779,\cdot)\) \(\chi_{2112}(851,\cdot)\) \(\chi_{2112}(971,\cdot)\) \(\chi_{2112}(995,\cdot)\) \(\chi_{2112}(1043,\cdot)\) \(\chi_{2112}(1115,\cdot)\) \(\chi_{2112}(1235,\cdot)\) \(\chi_{2112}(1259,\cdot)\) \(\chi_{2112}(1307,\cdot)\) \(\chi_{2112}(1379,\cdot)\) \(\chi_{2112}(1499,\cdot)\) \(\chi_{2112}(1523,\cdot)\) \(\chi_{2112}(1571,\cdot)\) \(\chi_{2112}(1643,\cdot)\) \(\chi_{2112}(1763,\cdot)\) \(\chi_{2112}(1787,\cdot)\) \(\chi_{2112}(1835,\cdot)\) \(\chi_{2112}(1907,\cdot)\) \(\chi_{2112}(2027,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

Values on generators

\((2047,133,1409,1729)\) → \((-1,e\left(\frac{1}{16}\right),-1,e\left(\frac{3}{5}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 2112 }(251, a) \)	\(1\)	\(1\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{23}{80}\right)\)