Dirichlet character \(\chi_{373527}(61,\cdot)\)

• Label: 373527.61
• Modulus: $373527$
• Conductor: $373527$
• Order: $16170$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(373527\)
Conductor:	\(373527\)
Order:	\(16170\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 373527.rq

\(\chi_{373527}(61,\cdot)\) \(\chi_{373527}(250,\cdot)\) \(\chi_{373527}(283,\cdot)\) \(\chi_{373527}(376,\cdot)\) \(\chi_{373527}(409,\cdot)\) \(\chi_{373527}(502,\cdot)\) \(\chi_{373527}(535,\cdot)\) \(\chi_{373527}(787,\cdot)\) \(\chi_{373527}(943,\cdot)\) \(\chi_{373527}(976,\cdot)\) \(\chi_{373527}(1069,\cdot)\) \(\chi_{373527}(1102,\cdot)\) \(\chi_{373527}(1228,\cdot)\) \(\chi_{373527}(1447,\cdot)\) \(\chi_{373527}(1480,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{8085})$
Fixed field:	Number field defined by a degree 16170 polynomial (not computed)

Values on generators

\((290522,286408,126568)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{263}{294}\right),e\left(\frac{109}{110}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\( \chi_{ 373527 }(61, a) \)	\(1\)	\(1\)	\(e\left(\frac{3263}{16170}\right)\)	\(e\left(\frac{3263}{8085}\right)\)	\(e\left(\frac{3249}{5390}\right)\)	\(e\left(\frac{3263}{5390}\right)\)	\(e\left(\frac{1301}{1617}\right)\)	\(e\left(\frac{2944}{8085}\right)\)	\(e\left(\frac{6526}{8085}\right)\)	\(e\left(\frac{7426}{8085}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{103}{16170}\right)\)