Basic properties
| Modulus: | \(3724\) | |
| Conductor: | \(3724\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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 3724.en
\(\chi_{3724}(47,\cdot)\) \(\chi_{3724}(283,\cdot)\) \(\chi_{3724}(327,\cdot)\) \(\chi_{3724}(339,\cdot)\) \(\chi_{3724}(579,\cdot)\) \(\chi_{3724}(747,\cdot)\) \(\chi_{3724}(859,\cdot)\) \(\chi_{3724}(871,\cdot)\) \(\chi_{3724}(955,\cdot)\) \(\chi_{3724}(1111,\cdot)\) \(\chi_{3724}(1279,\cdot)\) \(\chi_{3724}(1347,\cdot)\) \(\chi_{3724}(1487,\cdot)\) \(\chi_{3724}(1643,\cdot)\) \(\chi_{3724}(1811,\cdot)\) \(\chi_{3724}(1879,\cdot)\) \(\chi_{3724}(1923,\cdot)\) \(\chi_{3724}(1935,\cdot)\) \(\chi_{3724}(2019,\cdot)\) \(\chi_{3724}(2343,\cdot)\) \(\chi_{3724}(2411,\cdot)\) \(\chi_{3724}(2455,\cdot)\) \(\chi_{3724}(2467,\cdot)\) \(\chi_{3724}(2551,\cdot)\) \(\chi_{3724}(2707,\cdot)\) \(\chi_{3724}(2875,\cdot)\) \(\chi_{3724}(2943,\cdot)\) \(\chi_{3724}(2987,\cdot)\) \(\chi_{3724}(2999,\cdot)\) \(\chi_{3724}(3083,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((-1,e\left(\frac{5}{42}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3724 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{121}{126}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) |