Dirichlet character \(\chi_{508288}(8853,\cdot)\)

• Label: 508288.8853
• Modulus: $508288$
• Conductor: $508288$
• Order: $3040$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(508288\)
Conductor:	\(508288\)
Order:	\(3040\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 508288.tt

\(\chi_{508288}(37,\cdot)\) \(\chi_{508288}(493,\cdot)\) \(\chi_{508288}(797,\cdot)\) \(\chi_{508288}(949,\cdot)\) \(\chi_{508288}(1709,\cdot)\) \(\chi_{508288}(2469,\cdot)\) \(\chi_{508288}(2621,\cdot)\) \(\chi_{508288}(3381,\cdot)\) \(\chi_{508288}(3837,\cdot)\) \(\chi_{508288}(4141,\cdot)\) \(\chi_{508288}(4293,\cdot)\) \(\chi_{508288}(5509,\cdot)\) \(\chi_{508288}(5813,\cdot)\) \(\chi_{508288}(5965,\cdot)\) \(\chi_{508288}(6725,\cdot)\) \(\chi_{508288}(7181,\cdot)\) \(\chi_{508288}(7485,\cdot)\) \(\chi_{508288}(7637,\cdot)\) \(\chi_{508288}(8397,\cdot)\) \(\chi_{508288}(8853,\cdot)\) \(\chi_{508288}(9157,\cdot)\) \(\chi_{508288}(9309,\cdot)\) \(\chi_{508288}(10069,\cdot)\) \(\chi_{508288}(10525,\cdot)\) \(\chi_{508288}(10981,\cdot)\) \(\chi_{508288}(11741,\cdot)\) \(\chi_{508288}(12197,\cdot)\) \(\chi_{508288}(12501,\cdot)\) \(\chi_{508288}(12653,\cdot)\) \(\chi_{508288}(13413,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{3040})$
Fixed field:	Number field defined by a degree 3040 polynomial (not computed)

Values on generators

\((166783,174725,323457,14081)\) → \((1,e\left(\frac{13}{32}\right),e\left(\frac{3}{5}\right),e\left(\frac{25}{38}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\( \chi_{ 508288 }(8853, a) \)	\(-1\)	\(1\)	\(e\left(\frac{1417}{3040}\right)\)	\(e\left(\frac{1331}{3040}\right)\)	\(e\left(\frac{1439}{1520}\right)\)	\(e\left(\frac{1417}{1520}\right)\)	\(e\left(\frac{429}{3040}\right)\)	\(e\left(\frac{687}{760}\right)\)	\(e\left(\frac{349}{760}\right)\)	\(e\left(\frac{251}{608}\right)\)	\(e\left(\frac{225}{304}\right)\)	\(e\left(\frac{1331}{1520}\right)\)