Dirichlet character \(\chi_{3136}(1835,\cdot)\)

• Label: 3136.1835
• Modulus: $3136$
• Conductor: $3136$
• Order: $112$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(3136\)
Conductor:	\(3136\)
Order:	\(112\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 3136.ct

\(\chi_{3136}(43,\cdot)\) \(\chi_{3136}(155,\cdot)\) \(\chi_{3136}(211,\cdot)\) \(\chi_{3136}(267,\cdot)\) \(\chi_{3136}(323,\cdot)\) \(\chi_{3136}(379,\cdot)\) \(\chi_{3136}(435,\cdot)\) \(\chi_{3136}(547,\cdot)\) \(\chi_{3136}(603,\cdot)\) \(\chi_{3136}(659,\cdot)\) \(\chi_{3136}(715,\cdot)\) \(\chi_{3136}(771,\cdot)\) \(\chi_{3136}(827,\cdot)\) \(\chi_{3136}(939,\cdot)\) \(\chi_{3136}(995,\cdot)\) \(\chi_{3136}(1051,\cdot)\) \(\chi_{3136}(1107,\cdot)\) \(\chi_{3136}(1163,\cdot)\) \(\chi_{3136}(1219,\cdot)\) \(\chi_{3136}(1331,\cdot)\) \(\chi_{3136}(1387,\cdot)\) \(\chi_{3136}(1443,\cdot)\) \(\chi_{3136}(1499,\cdot)\) \(\chi_{3136}(1555,\cdot)\) \(\chi_{3136}(1611,\cdot)\) \(\chi_{3136}(1723,\cdot)\) \(\chi_{3136}(1779,\cdot)\) \(\chi_{3136}(1835,\cdot)\) \(\chi_{3136}(1891,\cdot)\) \(\chi_{3136}(1947,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{112})$
Fixed field:	Number field defined by a degree 112 polynomial (not computed)

Values on generators

\((1471,197,1473)\) → \((-1,e\left(\frac{13}{16}\right),e\left(\frac{4}{7}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\( \chi_{ 3136 }(1835, a) \)	\(-1\)	\(1\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)