Dirichlet character \(\chi_{8036}(37,\cdot)\)

• Label: 8036.37
• Modulus: $8036$
• Conductor: $2009$
• Order: $105$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8036\)
Conductor:	\(2009\)
Order:	\(105\)
Real:	no
Primitive:	no, induced from \(\chi_{2009}(37,\cdot)\)
Minimal:	yes
Parity:	even

Galois orbit 8036.ds

\(\chi_{8036}(37,\cdot)\) \(\chi_{8036}(221,\cdot)\) \(\chi_{8036}(305,\cdot)\) \(\chi_{8036}(529,\cdot)\) \(\chi_{8036}(625,\cdot)\) \(\chi_{8036}(877,\cdot)\) \(\chi_{8036}(1117,\cdot)\) \(\chi_{8036}(1185,\cdot)\) \(\chi_{8036}(1369,\cdot)\) \(\chi_{8036}(1453,\cdot)\) \(\chi_{8036}(1677,\cdot)\) \(\chi_{8036}(1773,\cdot)\) \(\chi_{8036}(2025,\cdot)\) \(\chi_{8036}(2109,\cdot)\) \(\chi_{8036}(2265,\cdot)\) \(\chi_{8036}(2601,\cdot)\) \(\chi_{8036}(2825,\cdot)\) \(\chi_{8036}(3173,\cdot)\) \(\chi_{8036}(3257,\cdot)\) \(\chi_{8036}(3413,\cdot)\) \(\chi_{8036}(3481,\cdot)\) \(\chi_{8036}(3665,\cdot)\) \(\chi_{8036}(3749,\cdot)\) \(\chi_{8036}(3973,\cdot)\) \(\chi_{8036}(4069,\cdot)\) \(\chi_{8036}(4321,\cdot)\) \(\chi_{8036}(4405,\cdot)\) \(\chi_{8036}(4561,\cdot)\) \(\chi_{8036}(4629,\cdot)\) \(\chi_{8036}(4813,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{105})$
Fixed field:	Number field defined by a degree 105 polynomial (not computed)

Values on generators

\((4019,493,785)\) → \((1,e\left(\frac{16}{21}\right),e\left(\frac{4}{5}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\( \chi_{ 8036 }(37, a) \)	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)