Dirichlet character \(\chi_{33957}(2,\cdot)\)

• Label: 33957.2
• Modulus: $33957$
• Conductor: $33957$
• Order: $1470$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(33957\)
Conductor:	\(33957\)
Order:	\(1470\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 33957.ik

\(\chi_{33957}(2,\cdot)\) \(\chi_{33957}(95,\cdot)\) \(\chi_{33957}(347,\cdot)\) \(\chi_{33957}(380,\cdot)\) \(\chi_{33957}(536,\cdot)\) \(\chi_{33957}(662,\cdot)\) \(\chi_{33957}(695,\cdot)\) \(\chi_{33957}(788,\cdot)\) \(\chi_{33957}(821,\cdot)\) \(\chi_{33957}(1040,\cdot)\) \(\chi_{33957}(1073,\cdot)\) \(\chi_{33957}(1229,\cdot)\) \(\chi_{33957}(1262,\cdot)\) \(\chi_{33957}(1355,\cdot)\) \(\chi_{33957}(1388,\cdot)\) \(\chi_{33957}(1481,\cdot)\) \(\chi_{33957}(1514,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{735})$
Fixed field:	Number field defined by a degree 1470 polynomial (not computed)

Values on generators

\((18866,14752,24697)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{97}{147}\right),e\left(\frac{1}{10}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\( \chi_{ 33957 }(2, a) \)	\(1\)	\(1\)	\(e\left(\frac{206}{735}\right)\)	\(e\left(\frac{412}{735}\right)\)	\(e\left(\frac{181}{490}\right)\)	\(e\left(\frac{206}{245}\right)\)	\(e\left(\frac{191}{294}\right)\)	\(e\left(\frac{727}{1470}\right)\)	\(e\left(\frac{89}{735}\right)\)	\(e\left(\frac{659}{735}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1367}{1470}\right)\)