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 \(\chi_{931}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3724.ee
\(\chi_{3724}(5,\cdot)\) \(\chi_{3724}(101,\cdot)\) \(\chi_{3724}(213,\cdot)\) \(\chi_{3724}(397,\cdot)\) \(\chi_{3724}(453,\cdot)\) \(\chi_{3724}(465,\cdot)\) \(\chi_{3724}(537,\cdot)\) \(\chi_{3724}(633,\cdot)\) \(\chi_{3724}(745,\cdot)\) \(\chi_{3724}(929,\cdot)\) \(\chi_{3724}(985,\cdot)\) \(\chi_{3724}(997,\cdot)\) \(\chi_{3724}(1069,\cdot)\) \(\chi_{3724}(1165,\cdot)\) \(\chi_{3724}(1277,\cdot)\) \(\chi_{3724}(1461,\cdot)\) \(\chi_{3724}(1517,\cdot)\) \(\chi_{3724}(1529,\cdot)\) \(\chi_{3724}(1601,\cdot)\) \(\chi_{3724}(1809,\cdot)\) \(\chi_{3724}(1993,\cdot)\) \(\chi_{3724}(2049,\cdot)\) \(\chi_{3724}(2061,\cdot)\) \(\chi_{3724}(2133,\cdot)\) \(\chi_{3724}(2229,\cdot)\) \(\chi_{3724}(2341,\cdot)\) \(\chi_{3724}(2525,\cdot)\) \(\chi_{3724}(2581,\cdot)\) \(\chi_{3724}(2593,\cdot)\) \(\chi_{3724}(2761,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((1,e\left(\frac{29}{42}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3724 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{31}{42}\right)\) |