Basic properties
| Modulus: | \(7938\) | |
| Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1323}(1301,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7938.cv
\(\chi_{7938}(125,\cdot)\) \(\chi_{7938}(251,\cdot)\) \(\chi_{7938}(503,\cdot)\) \(\chi_{7938}(629,\cdot)\) \(\chi_{7938}(1007,\cdot)\) \(\chi_{7938}(1259,\cdot)\) \(\chi_{7938}(1385,\cdot)\) \(\chi_{7938}(1637,\cdot)\) \(\chi_{7938}(2015,\cdot)\) \(\chi_{7938}(2141,\cdot)\) \(\chi_{7938}(2393,\cdot)\) \(\chi_{7938}(2519,\cdot)\) \(\chi_{7938}(2771,\cdot)\) \(\chi_{7938}(2897,\cdot)\) \(\chi_{7938}(3149,\cdot)\) \(\chi_{7938}(3275,\cdot)\) \(\chi_{7938}(3653,\cdot)\) \(\chi_{7938}(3905,\cdot)\) \(\chi_{7938}(4031,\cdot)\) \(\chi_{7938}(4283,\cdot)\) \(\chi_{7938}(4661,\cdot)\) \(\chi_{7938}(4787,\cdot)\) \(\chi_{7938}(5039,\cdot)\) \(\chi_{7938}(5165,\cdot)\) \(\chi_{7938}(5417,\cdot)\) \(\chi_{7938}(5543,\cdot)\) \(\chi_{7938}(5795,\cdot)\) \(\chi_{7938}(5921,\cdot)\) \(\chi_{7938}(6299,\cdot)\) \(\chi_{7938}(6551,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((6077,3727)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{1}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7938 }(125, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{73}{126}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{20}{21}\right)\) |