Basic properties
| Modulus: | \(8281\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(126,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8281.bu
\(\chi_{8281}(295,\cdot)\) \(\chi_{8281}(393,\cdot)\) \(\chi_{8281}(932,\cdot)\) \(\chi_{8281}(1030,\cdot)\) \(\chi_{8281}(1569,\cdot)\) \(\chi_{8281}(2206,\cdot)\) \(\chi_{8281}(2304,\cdot)\) \(\chi_{8281}(2843,\cdot)\) \(\chi_{8281}(2941,\cdot)\) \(\chi_{8281}(3480,\cdot)\) \(\chi_{8281}(3578,\cdot)\) \(\chi_{8281}(4117,\cdot)\) \(\chi_{8281}(4215,\cdot)\) \(\chi_{8281}(4852,\cdot)\) \(\chi_{8281}(5391,\cdot)\) \(\chi_{8281}(5489,\cdot)\) \(\chi_{8281}(6028,\cdot)\) \(\chi_{8281}(6126,\cdot)\) \(\chi_{8281}(6665,\cdot)\) \(\chi_{8281}(6763,\cdot)\) \(\chi_{8281}(7302,\cdot)\) \(\chi_{8281}(7400,\cdot)\) \(\chi_{8281}(7939,\cdot)\) \(\chi_{8281}(8037,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((1522,3382)\) → \((1,e\left(\frac{11}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(295, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) |