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 \(\chi_{1323}(421,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7938.co
\(\chi_{7938}(127,\cdot)\) \(\chi_{7938}(253,\cdot)\) \(\chi_{7938}(505,\cdot)\) \(\chi_{7938}(631,\cdot)\) \(\chi_{7938}(1009,\cdot)\) \(\chi_{7938}(1261,\cdot)\) \(\chi_{7938}(1387,\cdot)\) \(\chi_{7938}(1639,\cdot)\) \(\chi_{7938}(2017,\cdot)\) \(\chi_{7938}(2143,\cdot)\) \(\chi_{7938}(2395,\cdot)\) \(\chi_{7938}(2521,\cdot)\) \(\chi_{7938}(2773,\cdot)\) \(\chi_{7938}(2899,\cdot)\) \(\chi_{7938}(3151,\cdot)\) \(\chi_{7938}(3277,\cdot)\) \(\chi_{7938}(3655,\cdot)\) \(\chi_{7938}(3907,\cdot)\) \(\chi_{7938}(4033,\cdot)\) \(\chi_{7938}(4285,\cdot)\) \(\chi_{7938}(4663,\cdot)\) \(\chi_{7938}(4789,\cdot)\) \(\chi_{7938}(5041,\cdot)\) \(\chi_{7938}(5167,\cdot)\) \(\chi_{7938}(5419,\cdot)\) \(\chi_{7938}(5545,\cdot)\) \(\chi_{7938}(5797,\cdot)\) \(\chi_{7938}(5923,\cdot)\) \(\chi_{7938}(6301,\cdot)\) \(\chi_{7938}(6553,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((6077,3727)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{3}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7938 }(127, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{21}\right)\) |