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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3724.ej
\(\chi_{3724}(167,\cdot)\) \(\chi_{3724}(223,\cdot)\) \(\chi_{3724}(279,\cdot)\) \(\chi_{3724}(307,\cdot)\) \(\chi_{3724}(363,\cdot)\) \(\chi_{3724}(447,\cdot)\) \(\chi_{3724}(699,\cdot)\) \(\chi_{3724}(755,\cdot)\) \(\chi_{3724}(811,\cdot)\) \(\chi_{3724}(839,\cdot)\) \(\chi_{3724}(895,\cdot)\) \(\chi_{3724}(1231,\cdot)\) \(\chi_{3724}(1287,\cdot)\) \(\chi_{3724}(1343,\cdot)\) \(\chi_{3724}(1427,\cdot)\) \(\chi_{3724}(1511,\cdot)\) \(\chi_{3724}(1819,\cdot)\) \(\chi_{3724}(1875,\cdot)\) \(\chi_{3724}(1903,\cdot)\) \(\chi_{3724}(2043,\cdot)\) \(\chi_{3724}(2295,\cdot)\) \(\chi_{3724}(2407,\cdot)\) \(\chi_{3724}(2435,\cdot)\) \(\chi_{3724}(2491,\cdot)\) \(\chi_{3724}(2575,\cdot)\) \(\chi_{3724}(2827,\cdot)\) \(\chi_{3724}(2883,\cdot)\) \(\chi_{3724}(2967,\cdot)\) \(\chi_{3724}(3023,\cdot)\) \(\chi_{3724}(3107,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((-1,e\left(\frac{13}{14}\right),e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3724 }(755, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{13}{126}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{19}{42}\right)\) |