Basic properties
| Modulus: | \(3724\) | |
| Conductor: | \(931\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{931}(86,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3724.eo
\(\chi_{3724}(109,\cdot)\) \(\chi_{3724}(193,\cdot)\) \(\chi_{3724}(205,\cdot)\) \(\chi_{3724}(249,\cdot)\) \(\chi_{3724}(317,\cdot)\) \(\chi_{3724}(485,\cdot)\) \(\chi_{3724}(641,\cdot)\) \(\chi_{3724}(725,\cdot)\) \(\chi_{3724}(737,\cdot)\) \(\chi_{3724}(781,\cdot)\) \(\chi_{3724}(849,\cdot)\) \(\chi_{3724}(1017,\cdot)\) \(\chi_{3724}(1173,\cdot)\) \(\chi_{3724}(1257,\cdot)\) \(\chi_{3724}(1269,\cdot)\) \(\chi_{3724}(1313,\cdot)\) \(\chi_{3724}(1381,\cdot)\) \(\chi_{3724}(1705,\cdot)\) \(\chi_{3724}(1789,\cdot)\) \(\chi_{3724}(1801,\cdot)\) \(\chi_{3724}(1845,\cdot)\) \(\chi_{3724}(1913,\cdot)\) \(\chi_{3724}(2081,\cdot)\) \(\chi_{3724}(2237,\cdot)\) \(\chi_{3724}(2377,\cdot)\) \(\chi_{3724}(2445,\cdot)\) \(\chi_{3724}(2613,\cdot)\) \(\chi_{3724}(2769,\cdot)\) \(\chi_{3724}(2853,\cdot)\) \(\chi_{3724}(2865,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((1,e\left(\frac{16}{21}\right),e\left(\frac{17}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3724 }(1017, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{126}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{5}{42}\right)\) |