Dirichlet character \(\chi_{127072}(37507,\cdot)\)

• Label: 127072.37507
• Modulus: $127072$
• Conductor: $127072$
• Order: $760$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(127072\)
Conductor:	\(127072\)
Order:	\(760\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 127072.mp

\(\chi_{127072}(875,\cdot)\) \(\chi_{127072}(1179,\cdot)\) \(\chi_{127072}(1635,\cdot)\) \(\chi_{127072}(2395,\cdot)\) \(\chi_{127072}(2547,\cdot)\) \(\chi_{127072}(2851,\cdot)\) \(\chi_{127072}(3307,\cdot)\) \(\chi_{127072}(4067,\cdot)\) \(\chi_{127072}(4219,\cdot)\) \(\chi_{127072}(4523,\cdot)\) \(\chi_{127072}(4979,\cdot)\) \(\chi_{127072}(5739,\cdot)\) \(\chi_{127072}(5891,\cdot)\) \(\chi_{127072}(6195,\cdot)\) \(\chi_{127072}(6651,\cdot)\) \(\chi_{127072}(7411,\cdot)\) \(\chi_{127072}(7563,\cdot)\) \(\chi_{127072}(7867,\cdot)\) \(\chi_{127072}(8323,\cdot)\) \(\chi_{127072}(9083,\cdot)\) \(\chi_{127072}(9235,\cdot)\) \(\chi_{127072}(9539,\cdot)\) \(\chi_{127072}(9995,\cdot)\) \(\chi_{127072}(10755,\cdot)\) \(\chi_{127072}(10907,\cdot)\) \(\chi_{127072}(11211,\cdot)\) \(\chi_{127072}(11667,\cdot)\) \(\chi_{127072}(12427,\cdot)\) \(\chi_{127072}(12579,\cdot)\) \(\chi_{127072}(12883,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{760})$
Fixed field:	Number field defined by a degree 760 polynomial (not computed)

Values on generators

\((39711,47653,69313,14081)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{3}{10}\right),e\left(\frac{12}{19}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\( \chi_{ 127072 }(37507, a) \)	\(1\)	\(1\)	\(e\left(\frac{619}{760}\right)\)	\(e\left(\frac{77}{760}\right)\)	\(e\left(\frac{33}{380}\right)\)	\(e\left(\frac{239}{380}\right)\)	\(e\left(\frac{543}{760}\right)\)	\(e\left(\frac{87}{95}\right)\)	\(e\left(\frac{89}{95}\right)\)	\(e\left(\frac{137}{152}\right)\)	\(e\left(\frac{73}{76}\right)\)	\(e\left(\frac{77}{380}\right)\)