Dirichlet character \(\chi_{34272}(21053,\cdot)\)

• Label: 34272.21053
• Modulus: $34272$
• Conductor: $34272$
• Order: $48$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(34272\)
Conductor:	\(34272\)
Order:	\(48\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 34272.bnl

\(\chi_{34272}(7205,\cdot)\) \(\chi_{34272}(10229,\cdot)\) \(\chi_{34272}(10469,\cdot)\) \(\chi_{34272}(10733,\cdot)\) \(\chi_{34272}(12245,\cdot)\) \(\chi_{34272}(13493,\cdot)\) \(\chi_{34272}(13997,\cdot)\) \(\chi_{34272}(15269,\cdot)\) \(\chi_{34272}(15509,\cdot)\) \(\chi_{34272}(17789,\cdot)\) \(\chi_{34272}(18533,\cdot)\) \(\chi_{34272}(21053,\cdot)\) \(\chi_{34272}(21821,\cdot)\) \(\chi_{34272}(25085,\cdot)\) \(\chi_{34272}(28877,\cdot)\) \(\chi_{34272}(32141,\cdot)\)

Related number fields

Field of values:	\(\Q(\zeta_{48})\)
Fixed field:	Number field defined by a degree 48 polynomial

Values on generators

\((2143,29989,3809,14689,14113)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{1}{6}\right),e\left(\frac{2}{3}\right),e\left(\frac{11}{16}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\( \chi_{ 34272 }(21053, a) \)	\(1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)