Dirichlet character \(\chi_{9800}(5333,\cdot)\)

• Label: 9800.5333
• Modulus: $9800$
• Conductor: $9800$
• Order: $140$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(9800\)
Conductor:	\(9800\)
Order:	\(140\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 9800.gi

\(\chi_{9800}(13,\cdot)\) \(\chi_{9800}(237,\cdot)\) \(\chi_{9800}(517,\cdot)\) \(\chi_{9800}(573,\cdot)\) \(\chi_{9800}(797,\cdot)\) \(\chi_{9800}(853,\cdot)\) \(\chi_{9800}(1133,\cdot)\) \(\chi_{9800}(1413,\cdot)\) \(\chi_{9800}(1637,\cdot)\) \(\chi_{9800}(1917,\cdot)\) \(\chi_{9800}(1973,\cdot)\) \(\chi_{9800}(2197,\cdot)\) \(\chi_{9800}(2477,\cdot)\) \(\chi_{9800}(2533,\cdot)\) \(\chi_{9800}(2813,\cdot)\) \(\chi_{9800}(3317,\cdot)\) \(\chi_{9800}(3373,\cdot)\) \(\chi_{9800}(3597,\cdot)\) \(\chi_{9800}(3653,\cdot)\) \(\chi_{9800}(3877,\cdot)\) \(\chi_{9800}(3933,\cdot)\) \(\chi_{9800}(4437,\cdot)\) \(\chi_{9800}(4717,\cdot)\) \(\chi_{9800}(4773,\cdot)\) \(\chi_{9800}(5053,\cdot)\) \(\chi_{9800}(5277,\cdot)\) \(\chi_{9800}(5333,\cdot)\) \(\chi_{9800}(5613,\cdot)\) \(\chi_{9800}(5837,\cdot)\) \(\chi_{9800}(6117,\cdot)\) ...

Related number fields

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

Values on generators

\((7351,4901,1177,5001)\) → \((1,-1,e\left(\frac{3}{20}\right),e\left(\frac{5}{14}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\( \chi_{ 9800 }(5333, a) \)	\(1\)	\(1\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)