Basic properties
Modulus: | \(3969\) | |
Conductor: | \(3969\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(378\) | 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.db
\(\chi_{3969}(5,\cdot)\) \(\chi_{3969}(38,\cdot)\) \(\chi_{3969}(101,\cdot)\) \(\chi_{3969}(131,\cdot)\) \(\chi_{3969}(164,\cdot)\) \(\chi_{3969}(194,\cdot)\) \(\chi_{3969}(257,\cdot)\) \(\chi_{3969}(290,\cdot)\) \(\chi_{3969}(320,\cdot)\) \(\chi_{3969}(353,\cdot)\) \(\chi_{3969}(383,\cdot)\) \(\chi_{3969}(416,\cdot)\) \(\chi_{3969}(446,\cdot)\) \(\chi_{3969}(479,\cdot)\) \(\chi_{3969}(542,\cdot)\) \(\chi_{3969}(572,\cdot)\) \(\chi_{3969}(605,\cdot)\) \(\chi_{3969}(635,\cdot)\) \(\chi_{3969}(698,\cdot)\) \(\chi_{3969}(731,\cdot)\) \(\chi_{3969}(761,\cdot)\) \(\chi_{3969}(794,\cdot)\) \(\chi_{3969}(824,\cdot)\) \(\chi_{3969}(857,\cdot)\) \(\chi_{3969}(887,\cdot)\) \(\chi_{3969}(920,\cdot)\) \(\chi_{3969}(983,\cdot)\) \(\chi_{3969}(1013,\cdot)\) \(\chi_{3969}(1046,\cdot)\) \(\chi_{3969}(1076,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{189})$ |
Fixed field: | Number field defined by a degree 378 polynomial (not computed) |
Values on generators
\((2108,3727)\) → \((e\left(\frac{23}{54}\right),e\left(\frac{29}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3969 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{143}{378}\right)\) | \(e\left(\frac{143}{189}\right)\) | \(e\left(\frac{155}{189}\right)\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{59}{378}\right)\) | \(e\left(\frac{73}{378}\right)\) | \(e\left(\frac{97}{189}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{11}{18}\right)\) |