Dirichlet character \(\chi_{2704}(181,\cdot)\)

• Label: 2704.181
• Modulus: $2704$
• Conductor: $2704$
• Order: $52$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2704\)
Conductor:	\(2704\)
Order:	\(52\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2704.cb

\(\chi_{2704}(77,\cdot)\) \(\chi_{2704}(181,\cdot)\) \(\chi_{2704}(285,\cdot)\) \(\chi_{2704}(389,\cdot)\) \(\chi_{2704}(493,\cdot)\) \(\chi_{2704}(597,\cdot)\) \(\chi_{2704}(701,\cdot)\) \(\chi_{2704}(805,\cdot)\) \(\chi_{2704}(909,\cdot)\) \(\chi_{2704}(1117,\cdot)\) \(\chi_{2704}(1221,\cdot)\) \(\chi_{2704}(1325,\cdot)\) \(\chi_{2704}(1429,\cdot)\) \(\chi_{2704}(1533,\cdot)\) \(\chi_{2704}(1637,\cdot)\) \(\chi_{2704}(1741,\cdot)\) \(\chi_{2704}(1845,\cdot)\) \(\chi_{2704}(1949,\cdot)\) \(\chi_{2704}(2053,\cdot)\) \(\chi_{2704}(2157,\cdot)\) \(\chi_{2704}(2261,\cdot)\) \(\chi_{2704}(2469,\cdot)\) \(\chi_{2704}(2573,\cdot)\) \(\chi_{2704}(2677,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Values on generators

\((2367,677,1185)\) → \((1,i,e\left(\frac{21}{26}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 2704 }(181, a) \)	\(1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(i\)	\(e\left(\frac{43}{52}\right)\)	\(-1\)