Dirichlet character \(\chi_{42237}(400,\cdot)\)

• Label: 42237.400
• 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.mr

\(\chi_{42237}(400,\cdot)\) \(\chi_{42237}(628,\cdot)\) \(\chi_{42237}(2623,\cdot)\) \(\chi_{42237}(2851,\cdot)\) \(\chi_{42237}(4846,\cdot)\) \(\chi_{42237}(5074,\cdot)\) \(\chi_{42237}(7069,\cdot)\) \(\chi_{42237}(7297,\cdot)\) \(\chi_{42237}(9292,\cdot)\) \(\chi_{42237}(9520,\cdot)\) \(\chi_{42237}(11515,\cdot)\) \(\chi_{42237}(11743,\cdot)\) \(\chi_{42237}(13738,\cdot)\) \(\chi_{42237}(13966,\cdot)\) \(\chi_{42237}(15961,\cdot)\) \(\chi_{42237}(16189,\cdot)\) \(\chi_{42237}(18184,\cdot)\) \(\chi_{42237}(20407,\cdot)\) \(\chi_{42237}(20635,\cdot)\) \(\chi_{42237}(22630,\cdot)\) \(\chi_{42237}(22858,\cdot)\) \(\chi_{42237}(24853,\cdot)\) \(\chi_{42237}(25081,\cdot)\) \(\chi_{42237}(27304,\cdot)\) \(\chi_{42237}(29299,\cdot)\) \(\chi_{42237}(29527,\cdot)\) \(\chi_{42237}(31522,\cdot)\) \(\chi_{42237}(31750,\cdot)\) \(\chi_{42237}(33745,\cdot)\) \(\chi_{42237}(33973,\cdot)\) ...

Related number fields

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

Values on generators

\((32852,38989,12637)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{5}{6}\right),e\left(\frac{7}{19}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 42237 }(400, a) \)	\(1\)	\(1\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{53}{57}\right)\)