Dirichlet character \(\chi_{3503}(1800,\cdot)\)

• Label: 3503.1800
• Modulus: $3503$
• Conductor: $3503$
• Order: $140$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3503\)
Conductor:	\(3503\)
Order:	\(140\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3503.ch

\(\chi_{3503}(2,\cdot)\) \(\chi_{3503}(8,\cdot)\) \(\chi_{3503}(194,\cdot)\) \(\chi_{3503}(283,\cdot)\) \(\chi_{3503}(438,\cdot)\) \(\chi_{3503}(450,\cdot)\) \(\chi_{3503}(512,\cdot)\) \(\chi_{3503}(597,\cdot)\) \(\chi_{3503}(622,\cdot)\) \(\chi_{3503}(686,\cdot)\) \(\chi_{3503}(777,\cdot)\) \(\chi_{3503}(783,\cdot)\) \(\chi_{3503}(872,\cdot)\) \(\chi_{3503}(1025,\cdot)\) \(\chi_{3503}(1031,\cdot)\) \(\chi_{3503}(1070,\cdot)\) \(\chi_{3503}(1132,\cdot)\) \(\chi_{3503}(1186,\cdot)\) \(\chi_{3503}(1211,\cdot)\) \(\chi_{3503}(1275,\cdot)\) \(\chi_{3503}(1461,\cdot)\) \(\chi_{3503}(1614,\cdot)\) \(\chi_{3503}(1709,\cdot)\) \(\chi_{3503}(1752,\cdot)\) \(\chi_{3503}(1800,\cdot)\) \(\chi_{3503}(1806,\cdot)\) \(\chi_{3503}(1864,\cdot)\) \(\chi_{3503}(1868,\cdot)\) \(\chi_{3503}(1907,\cdot)\) \(\chi_{3503}(2048,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{140})$
Fixed field:	Number field defined by a degree 140 polynomial (not computed)

Values on generators

\((3165,342)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{23}{28}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 3503 }(1800, a) \)	\(1\)	\(1\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{13}{70}\right)\)