Basic properties
| Modulus: | \(33327\) | |
| Conductor: | \(33327\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1518\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 33327.gc
\(\chi_{33327}(52,\cdot)\) \(\chi_{33327}(292,\cdot)\) \(\chi_{33327}(418,\cdot)\) \(\chi_{33327}(430,\cdot)\) \(\chi_{33327}(556,\cdot)\) \(\chi_{33327}(607,\cdot)\) \(\chi_{33327}(670,\cdot)\) \(\chi_{33327}(745,\cdot)\) \(\chi_{33327}(808,\cdot)\) \(\chi_{33327}(859,\cdot)\) \(\chi_{33327}(922,\cdot)\) \(\chi_{33327}(997,\cdot)\) \(\chi_{33327}(1048,\cdot)\) \(\chi_{33327}(1060,\cdot)\) \(\chi_{33327}(1186,\cdot)\) \(\chi_{33327}(1237,\cdot)\) \(\chi_{33327}(1300,\cdot)\) \(\chi_{33327}(1363,\cdot)\) \(\chi_{33327}(1375,\cdot)\) \(\chi_{33327}(1438,\cdot)\) \(\chi_{33327}(1501,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{759})$ |
| Fixed field: | Number field defined by a degree 1518 polynomial (not computed) |
Values on generators
\((25922,9523,10585)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{5}{6}\right),e\left(\frac{43}{253}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 33327 }(1300, a) \) | \(-1\) | \(1\) | \(e\left(\frac{251}{253}\right)\) | \(e\left(\frac{249}{253}\right)\) | \(e\left(\frac{5}{1518}\right)\) | \(e\left(\frac{247}{253}\right)\) | \(e\left(\frac{1511}{1518}\right)\) | \(e\left(\frac{743}{759}\right)\) | \(e\left(\frac{697}{1518}\right)\) | \(e\left(\frac{245}{253}\right)\) | \(e\left(\frac{1157}{1518}\right)\) | \(e\left(\frac{1483}{1518}\right)\) |