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 \(\chi_{931}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3724.ef
\(\chi_{3724}(33,\cdot)\) \(\chi_{3724}(173,\cdot)\) \(\chi_{3724}(241,\cdot)\) \(\chi_{3724}(409,\cdot)\) \(\chi_{3724}(565,\cdot)\) \(\chi_{3724}(649,\cdot)\) \(\chi_{3724}(661,\cdot)\) \(\chi_{3724}(773,\cdot)\) \(\chi_{3724}(941,\cdot)\) \(\chi_{3724}(1181,\cdot)\) \(\chi_{3724}(1193,\cdot)\) \(\chi_{3724}(1237,\cdot)\) \(\chi_{3724}(1473,\cdot)\) \(\chi_{3724}(1629,\cdot)\) \(\chi_{3724}(1713,\cdot)\) \(\chi_{3724}(1725,\cdot)\) \(\chi_{3724}(1769,\cdot)\) \(\chi_{3724}(1837,\cdot)\) \(\chi_{3724}(2005,\cdot)\) \(\chi_{3724}(2161,\cdot)\) \(\chi_{3724}(2245,\cdot)\) \(\chi_{3724}(2257,\cdot)\) \(\chi_{3724}(2301,\cdot)\) \(\chi_{3724}(2369,\cdot)\) \(\chi_{3724}(2537,\cdot)\) \(\chi_{3724}(2693,\cdot)\) \(\chi_{3724}(2777,\cdot)\) \(\chi_{3724}(2789,\cdot)\) \(\chi_{3724}(2833,\cdot)\) \(\chi_{3724}(2901,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((1,e\left(\frac{41}{42}\right),e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3724 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{37}{126}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{2}{21}\right)\) |