Basic properties
| Modulus: | \(8281\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(30,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8281.cl
\(\chi_{8281}(30,\cdot)\) \(\chi_{8281}(667,\cdot)\) \(\chi_{8281}(998,\cdot)\) \(\chi_{8281}(1304,\cdot)\) \(\chi_{8281}(1635,\cdot)\) \(\chi_{8281}(1941,\cdot)\) \(\chi_{8281}(2272,\cdot)\) \(\chi_{8281}(2578,\cdot)\) \(\chi_{8281}(2909,\cdot)\) \(\chi_{8281}(3215,\cdot)\) \(\chi_{8281}(3546,\cdot)\) \(\chi_{8281}(3852,\cdot)\) \(\chi_{8281}(4183,\cdot)\) \(\chi_{8281}(4489,\cdot)\) \(\chi_{8281}(4820,\cdot)\) \(\chi_{8281}(5126,\cdot)\) \(\chi_{8281}(5457,\cdot)\) \(\chi_{8281}(5763,\cdot)\) \(\chi_{8281}(6094,\cdot)\) \(\chi_{8281}(6731,\cdot)\) \(\chi_{8281}(7037,\cdot)\) \(\chi_{8281}(7368,\cdot)\) \(\chi_{8281}(7674,\cdot)\) \(\chi_{8281}(8005,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1522,3382)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{67}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(30, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{35}{39}\right)\) |