Dirichlet character \(\chi_{42237}(16636,\cdot)\)

• Label: 42237.16636
• Modulus: $42237$
• Conductor: $42237$
• Order: $57$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(42237\)
Conductor:	\(42237\)
Order:	\(57\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 42237.li

\(\chi_{42237}(1075,\cdot)\) \(\chi_{42237}(1888,\cdot)\) \(\chi_{42237}(3298,\cdot)\) \(\chi_{42237}(4111,\cdot)\) \(\chi_{42237}(5521,\cdot)\) \(\chi_{42237}(6334,\cdot)\) \(\chi_{42237}(7744,\cdot)\) \(\chi_{42237}(8557,\cdot)\) \(\chi_{42237}(9967,\cdot)\) \(\chi_{42237}(10780,\cdot)\) \(\chi_{42237}(12190,\cdot)\) \(\chi_{42237}(13003,\cdot)\) \(\chi_{42237}(14413,\cdot)\) \(\chi_{42237}(15226,\cdot)\) \(\chi_{42237}(16636,\cdot)\) \(\chi_{42237}(17449,\cdot)\) \(\chi_{42237}(18859,\cdot)\) \(\chi_{42237}(19672,\cdot)\) \(\chi_{42237}(21082,\cdot)\) \(\chi_{42237}(21895,\cdot)\) \(\chi_{42237}(23305,\cdot)\) \(\chi_{42237}(25528,\cdot)\) \(\chi_{42237}(26341,\cdot)\) \(\chi_{42237}(27751,\cdot)\) \(\chi_{42237}(28564,\cdot)\) \(\chi_{42237}(29974,\cdot)\) \(\chi_{42237}(30787,\cdot)\) \(\chi_{42237}(33010,\cdot)\) \(\chi_{42237}(34420,\cdot)\) \(\chi_{42237}(35233,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{57})$
Fixed field:	Number field defined by a degree 57 polynomial

Values on generators

\((32852,38989,12637)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{2}{3}\right),e\left(\frac{5}{57}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 42237 }(16636, a) \)	\(1\)	\(1\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{3}{19}\right)\)