Dirichlet character \(\chi_{44100}(10687,\cdot)\)

• Label: 44100.10687
• Modulus: $44100$
• Conductor: $44100$
• Order: $420$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(44100\)
Conductor:	\(44100\)
Order:	\(420\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 44100.sa

\(\chi_{44100}(103,\cdot)\) \(\chi_{44100}(367,\cdot)\) \(\chi_{44100}(1123,\cdot)\) \(\chi_{44100}(1363,\cdot)\) \(\chi_{44100}(1627,\cdot)\) \(\chi_{44100}(1867,\cdot)\) \(\chi_{44100}(2623,\cdot)\) \(\chi_{44100}(2887,\cdot)\) \(\chi_{44100}(3127,\cdot)\) \(\chi_{44100}(3883,\cdot)\) \(\chi_{44100}(4387,\cdot)\) \(\chi_{44100}(4903,\cdot)\) \(\chi_{44100}(5647,\cdot)\) \(\chi_{44100}(6163,\cdot)\) \(\chi_{44100}(6403,\cdot)\) \(\chi_{44100}(6667,\cdot)\) \(\chi_{44100}(7423,\cdot)\) \(\chi_{44100}(7927,\cdot)\) \(\chi_{44100}(8167,\cdot)\) \(\chi_{44100}(8683,\cdot)\) \(\chi_{44100}(8923,\cdot)\) \(\chi_{44100}(9187,\cdot)\) \(\chi_{44100}(10183,\cdot)\) \(\chi_{44100}(10447,\cdot)\) \(\chi_{44100}(10687,\cdot)\) \(\chi_{44100}(11947,\cdot)\) \(\chi_{44100}(12463,\cdot)\) \(\chi_{44100}(12703,\cdot)\) \(\chi_{44100}(13723,\cdot)\) \(\chi_{44100}(13963,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{420})$
Fixed field:	Number field defined by a degree 420 polynomial (not computed)

Values on generators

\((22051,34301,15877,9901)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{9}{20}\right),e\left(\frac{29}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 44100 }(10687, a) \)	\(-1\)	\(1\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{1}{420}\right)\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{149}{420}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{61}{84}\right)\)