Dirichlet character \(\chi_{34272}(27715,\cdot)\)

• Label: 34272.27715
• 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.brz

\(\chi_{34272}(1915,\cdot)\) \(\chi_{34272}(3019,\cdot)\) \(\chi_{34272}(10075,\cdot)\) \(\chi_{34272}(14515,\cdot)\) \(\chi_{34272}(17539,\cdot)\) \(\chi_{34272}(18043,\cdot)\) \(\chi_{34272}(19555,\cdot)\) \(\chi_{34272}(22579,\cdot)\) \(\chi_{34272}(22675,\cdot)\) \(\chi_{34272}(25099,\cdot)\) \(\chi_{34272}(25699,\cdot)\) \(\chi_{34272}(26203,\cdot)\) \(\chi_{34272}(27715,\cdot)\) \(\chi_{34272}(29131,\cdot)\) \(\chi_{34272}(30739,\cdot)\) \(\chi_{34272}(33259,\cdot)\)

Related number fields

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

Values on generators

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

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\( \chi_{ 34272 }(27715, a) \)	\(1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)