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 \(\chi_{1323}(752,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7938.cu
\(\chi_{7938}(17,\cdot)\) \(\chi_{7938}(89,\cdot)\) \(\chi_{7938}(395,\cdot)\) \(\chi_{7938}(467,\cdot)\) \(\chi_{7938}(773,\cdot)\) \(\chi_{7938}(845,\cdot)\) \(\chi_{7938}(1151,\cdot)\) \(\chi_{7938}(1223,\cdot)\) \(\chi_{7938}(1529,\cdot)\) \(\chi_{7938}(1601,\cdot)\) \(\chi_{7938}(1907,\cdot)\) \(\chi_{7938}(2357,\cdot)\) \(\chi_{7938}(2663,\cdot)\) \(\chi_{7938}(2735,\cdot)\) \(\chi_{7938}(3041,\cdot)\) \(\chi_{7938}(3113,\cdot)\) \(\chi_{7938}(3419,\cdot)\) \(\chi_{7938}(3491,\cdot)\) \(\chi_{7938}(3797,\cdot)\) \(\chi_{7938}(3869,\cdot)\) \(\chi_{7938}(4175,\cdot)\) \(\chi_{7938}(4247,\cdot)\) \(\chi_{7938}(4553,\cdot)\) \(\chi_{7938}(5003,\cdot)\) \(\chi_{7938}(5309,\cdot)\) \(\chi_{7938}(5381,\cdot)\) \(\chi_{7938}(5687,\cdot)\) \(\chi_{7938}(5759,\cdot)\) \(\chi_{7938}(6065,\cdot)\) \(\chi_{7938}(6137,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((6077,3727)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{25}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7938 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{5}{7}\right)\) |