Dirichlet character \(\chi_{42237}(20641,\cdot)\)

• Label: 42237.20641
• Modulus: $42237$
• Conductor: $42237$
• Order: $114$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(42237\)
Conductor:	\(42237\)
Order:	\(114\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 42237.pb

\(\chi_{42237}(277,\cdot)\) \(\chi_{42237}(634,\cdot)\) \(\chi_{42237}(2500,\cdot)\) \(\chi_{42237}(2857,\cdot)\) \(\chi_{42237}(4723,\cdot)\) \(\chi_{42237}(5080,\cdot)\) \(\chi_{42237}(6946,\cdot)\) \(\chi_{42237}(7303,\cdot)\) \(\chi_{42237}(9169,\cdot)\) \(\chi_{42237}(9526,\cdot)\) \(\chi_{42237}(11392,\cdot)\) \(\chi_{42237}(11749,\cdot)\) \(\chi_{42237}(13615,\cdot)\) \(\chi_{42237}(13972,\cdot)\) \(\chi_{42237}(15838,\cdot)\) \(\chi_{42237}(16195,\cdot)\) \(\chi_{42237}(18061,\cdot)\) \(\chi_{42237}(18418,\cdot)\) \(\chi_{42237}(20641,\cdot)\) \(\chi_{42237}(22507,\cdot)\) \(\chi_{42237}(22864,\cdot)\) \(\chi_{42237}(24730,\cdot)\) \(\chi_{42237}(25087,\cdot)\) \(\chi_{42237}(26953,\cdot)\) \(\chi_{42237}(27310,\cdot)\) \(\chi_{42237}(29176,\cdot)\) \(\chi_{42237}(31399,\cdot)\) \(\chi_{42237}(31756,\cdot)\) \(\chi_{42237}(33622,\cdot)\) \(\chi_{42237}(33979,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{57})$
Fixed field:	Number field defined by a degree 114 polynomial (not computed)

Values on generators

\((32852,38989,12637)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{5}{6}\right),e\left(\frac{1}{57}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 42237 }(20641, a) \)	\(1\)	\(1\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)