Basic properties
| Modulus: | \(7938\) | |
| Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1323}(184,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7938.cm
\(\chi_{7938}(37,\cdot)\) \(\chi_{7938}(235,\cdot)\) \(\chi_{7938}(415,\cdot)\) \(\chi_{7938}(613,\cdot)\) \(\chi_{7938}(793,\cdot)\) \(\chi_{7938}(991,\cdot)\) \(\chi_{7938}(1171,\cdot)\) \(\chi_{7938}(1369,\cdot)\) \(\chi_{7938}(1747,\cdot)\) \(\chi_{7938}(1927,\cdot)\) \(\chi_{7938}(2305,\cdot)\) \(\chi_{7938}(2503,\cdot)\) \(\chi_{7938}(2683,\cdot)\) \(\chi_{7938}(2881,\cdot)\) \(\chi_{7938}(3061,\cdot)\) \(\chi_{7938}(3259,\cdot)\) \(\chi_{7938}(3439,\cdot)\) \(\chi_{7938}(3637,\cdot)\) \(\chi_{7938}(3817,\cdot)\) \(\chi_{7938}(4015,\cdot)\) \(\chi_{7938}(4393,\cdot)\) \(\chi_{7938}(4573,\cdot)\) \(\chi_{7938}(4951,\cdot)\) \(\chi_{7938}(5149,\cdot)\) \(\chi_{7938}(5329,\cdot)\) \(\chi_{7938}(5527,\cdot)\) \(\chi_{7938}(5707,\cdot)\) \(\chi_{7938}(5905,\cdot)\) \(\chi_{7938}(6085,\cdot)\) \(\chi_{7938}(6283,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((6077,3727)\) → \((e\left(\frac{7}{9}\right),e\left(\frac{16}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7938 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(1\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{21}\right)\) |