Dirichlet character \(\chi_{42237}(27758,\cdot)\)

• Label: 42237.27758
• 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.lv

\(\chi_{42237}(113,\cdot)\) \(\chi_{42237}(2336,\cdot)\) \(\chi_{42237}(3305,\cdot)\) \(\chi_{42237}(4559,\cdot)\) \(\chi_{42237}(5528,\cdot)\) \(\chi_{42237}(6782,\cdot)\) \(\chi_{42237}(7751,\cdot)\) \(\chi_{42237}(9005,\cdot)\) \(\chi_{42237}(9974,\cdot)\) \(\chi_{42237}(11228,\cdot)\) \(\chi_{42237}(12197,\cdot)\) \(\chi_{42237}(13451,\cdot)\) \(\chi_{42237}(14420,\cdot)\) \(\chi_{42237}(15674,\cdot)\) \(\chi_{42237}(16643,\cdot)\) \(\chi_{42237}(17897,\cdot)\) \(\chi_{42237}(18866,\cdot)\) \(\chi_{42237}(20120,\cdot)\) \(\chi_{42237}(21089,\cdot)\) \(\chi_{42237}(22343,\cdot)\) \(\chi_{42237}(23312,\cdot)\) \(\chi_{42237}(24566,\cdot)\) \(\chi_{42237}(25535,\cdot)\) \(\chi_{42237}(26789,\cdot)\) \(\chi_{42237}(27758,\cdot)\) \(\chi_{42237}(29012,\cdot)\) \(\chi_{42237}(29981,\cdot)\) \(\chi_{42237}(31235,\cdot)\) \(\chi_{42237}(32204,\cdot)\) \(\chi_{42237}(33458,\cdot)\) ...

Related number fields

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

Values on generators

\((32852,38989,12637)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{1}{3}\right),e\left(\frac{33}{38}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 42237 }(27758, a) \)	\(1\)	\(1\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{49}{114}\right)\)