Dirichlet character \(\chi_{34272}(29621,\cdot)\)

• Label: 34272.29621
• 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.bmp

\(\chi_{34272}(1661,\cdot)\) \(\chi_{34272}(1901,\cdot)\) \(\chi_{34272}(3173,\cdot)\) \(\chi_{34272}(3677,\cdot)\) \(\chi_{34272}(4925,\cdot)\) \(\chi_{34272}(6437,\cdot)\) \(\chi_{34272}(6701,\cdot)\) \(\chi_{34272}(6941,\cdot)\) \(\chi_{34272}(9965,\cdot)\) \(\chi_{34272}(19301,\cdot)\) \(\chi_{34272}(22565,\cdot)\) \(\chi_{34272}(26357,\cdot)\) \(\chi_{34272}(29621,\cdot)\) \(\chi_{34272}(30389,\cdot)\) \(\chi_{34272}(32909,\cdot)\) \(\chi_{34272}(33653,\cdot)\)

Related number fields

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

Values on generators

\((2143,29989,3809,14689,14113)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{1}{6}\right),e\left(\frac{2}{3}\right),e\left(\frac{11}{16}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\( \chi_{ 34272 }(29621, a) \)	\(1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)