Basic properties
Modulus: | \(3969\) | |
Conductor: | \(3969\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(189\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3969.cy
\(\chi_{3969}(25,\cdot)\) \(\chi_{3969}(58,\cdot)\) \(\chi_{3969}(88,\cdot)\) \(\chi_{3969}(121,\cdot)\) \(\chi_{3969}(151,\cdot)\) \(\chi_{3969}(184,\cdot)\) \(\chi_{3969}(247,\cdot)\) \(\chi_{3969}(277,\cdot)\) \(\chi_{3969}(310,\cdot)\) \(\chi_{3969}(340,\cdot)\) \(\chi_{3969}(403,\cdot)\) \(\chi_{3969}(436,\cdot)\) \(\chi_{3969}(466,\cdot)\) \(\chi_{3969}(499,\cdot)\) \(\chi_{3969}(529,\cdot)\) \(\chi_{3969}(562,\cdot)\) \(\chi_{3969}(592,\cdot)\) \(\chi_{3969}(625,\cdot)\) \(\chi_{3969}(688,\cdot)\) \(\chi_{3969}(718,\cdot)\) \(\chi_{3969}(751,\cdot)\) \(\chi_{3969}(781,\cdot)\) \(\chi_{3969}(844,\cdot)\) \(\chi_{3969}(877,\cdot)\) \(\chi_{3969}(907,\cdot)\) \(\chi_{3969}(940,\cdot)\) \(\chi_{3969}(970,\cdot)\) \(\chi_{3969}(1003,\cdot)\) \(\chi_{3969}(1033,\cdot)\) \(\chi_{3969}(1066,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{189})$ |
Fixed field: | Number field defined by a degree 189 polynomial (not computed) |
Values on generators
\((2108,3727)\) → \((e\left(\frac{23}{27}\right),e\left(\frac{8}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3969 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{143}{189}\right)\) | \(e\left(\frac{97}{189}\right)\) | \(e\left(\frac{121}{189}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{59}{189}\right)\) | \(e\left(\frac{73}{189}\right)\) | \(e\left(\frac{5}{189}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{2}{9}\right)\) |