Dirichlet character \(\chi_{38025}(31,\cdot)\)

• Label: 38025.31
• Modulus: $38025$
• Conductor: $38025$
• Order: $780$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(38025\)
Conductor:	\(38025\)
Order:	\(780\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 38025.om

\(\chi_{38025}(31,\cdot)\) \(\chi_{38025}(346,\cdot)\) \(\chi_{38025}(421,\cdot)\) \(\chi_{38025}(616,\cdot)\) \(\chi_{38025}(736,\cdot)\) \(\chi_{38025}(931,\cdot)\) \(\chi_{38025}(1006,\cdot)\) \(\chi_{38025}(1321,\cdot)\) \(\chi_{38025}(1516,\cdot)\) \(\chi_{38025}(1786,\cdot)\) \(\chi_{38025}(1906,\cdot)\) \(\chi_{38025}(2371,\cdot)\) \(\chi_{38025}(2491,\cdot)\) \(\chi_{38025}(2686,\cdot)\) \(\chi_{38025}(2761,\cdot)\) \(\chi_{38025}(2956,\cdot)\) \(\chi_{38025}(3271,\cdot)\) \(\chi_{38025}(3346,\cdot)\) \(\chi_{38025}(3541,\cdot)\) \(\chi_{38025}(3661,\cdot)\) \(\chi_{38025}(3856,\cdot)\) \(\chi_{38025}(3931,\cdot)\) \(\chi_{38025}(4246,\cdot)\) \(\chi_{38025}(4441,\cdot)\) \(\chi_{38025}(4516,\cdot)\) \(\chi_{38025}(4711,\cdot)\) \(\chi_{38025}(5296,\cdot)\) \(\chi_{38025}(5416,\cdot)\) \(\chi_{38025}(5611,\cdot)\) \(\chi_{38025}(5686,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{780})$
Fixed field:	Number field defined by a degree 780 polynomial (not computed)

Values on generators

\((29576,9127,37351)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{2}{5}\right),e\left(\frac{7}{52}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(14\)	\(16\)	\(17\)	\(19\)	\(22\)
\( \chi_{ 38025 }(31, a) \)	\(-1\)	\(1\)	\(e\left(\frac{677}{780}\right)\)	\(e\left(\frac{287}{390}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{157}{260}\right)\)	\(e\left(\frac{467}{780}\right)\)	\(e\left(\frac{118}{195}\right)\)	\(e\left(\frac{92}{195}\right)\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)