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 \(\chi_{1323}(290,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7938.cp
\(\chi_{7938}(143,\cdot)\) \(\chi_{7938}(341,\cdot)\) \(\chi_{7938}(719,\cdot)\) \(\chi_{7938}(899,\cdot)\) \(\chi_{7938}(1277,\cdot)\) \(\chi_{7938}(1475,\cdot)\) \(\chi_{7938}(1655,\cdot)\) \(\chi_{7938}(1853,\cdot)\) \(\chi_{7938}(2033,\cdot)\) \(\chi_{7938}(2231,\cdot)\) \(\chi_{7938}(2411,\cdot)\) \(\chi_{7938}(2609,\cdot)\) \(\chi_{7938}(2789,\cdot)\) \(\chi_{7938}(2987,\cdot)\) \(\chi_{7938}(3365,\cdot)\) \(\chi_{7938}(3545,\cdot)\) \(\chi_{7938}(3923,\cdot)\) \(\chi_{7938}(4121,\cdot)\) \(\chi_{7938}(4301,\cdot)\) \(\chi_{7938}(4499,\cdot)\) \(\chi_{7938}(4679,\cdot)\) \(\chi_{7938}(4877,\cdot)\) \(\chi_{7938}(5057,\cdot)\) \(\chi_{7938}(5255,\cdot)\) \(\chi_{7938}(5435,\cdot)\) \(\chi_{7938}(5633,\cdot)\) \(\chi_{7938}(6011,\cdot)\) \(\chi_{7938}(6191,\cdot)\) \(\chi_{7938}(6569,\cdot)\) \(\chi_{7938}(6767,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((6077,3727)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{31}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7938 }(143, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{73}{126}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(-1\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{20}{21}\right)\) |