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 \(\chi_{1323}(583,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7938.cn
\(\chi_{7938}(289,\cdot)\) \(\chi_{7938}(739,\cdot)\) \(\chi_{7938}(1045,\cdot)\) \(\chi_{7938}(1117,\cdot)\) \(\chi_{7938}(1423,\cdot)\) \(\chi_{7938}(1495,\cdot)\) \(\chi_{7938}(1801,\cdot)\) \(\chi_{7938}(1873,\cdot)\) \(\chi_{7938}(2179,\cdot)\) \(\chi_{7938}(2251,\cdot)\) \(\chi_{7938}(2557,\cdot)\) \(\chi_{7938}(2629,\cdot)\) \(\chi_{7938}(2935,\cdot)\) \(\chi_{7938}(3385,\cdot)\) \(\chi_{7938}(3691,\cdot)\) \(\chi_{7938}(3763,\cdot)\) \(\chi_{7938}(4069,\cdot)\) \(\chi_{7938}(4141,\cdot)\) \(\chi_{7938}(4447,\cdot)\) \(\chi_{7938}(4519,\cdot)\) \(\chi_{7938}(4825,\cdot)\) \(\chi_{7938}(4897,\cdot)\) \(\chi_{7938}(5203,\cdot)\) \(\chi_{7938}(5275,\cdot)\) \(\chi_{7938}(5581,\cdot)\) \(\chi_{7938}(6031,\cdot)\) \(\chi_{7938}(6337,\cdot)\) \(\chi_{7938}(6409,\cdot)\) \(\chi_{7938}(6715,\cdot)\) \(\chi_{7938}(6787,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((6077,3727)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{4}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7938 }(289, a) \) | \(1\) | \(1\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{3}{7}\right)\) |