Basic properties
| Modulus: | \(8281\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(153,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8281.cp
\(\chi_{8281}(491,\cdot)\) \(\chi_{8281}(589,\cdot)\) \(\chi_{8281}(1128,\cdot)\) \(\chi_{8281}(1226,\cdot)\) \(\chi_{8281}(1765,\cdot)\) \(\chi_{8281}(1863,\cdot)\) \(\chi_{8281}(2402,\cdot)\) \(\chi_{8281}(2500,\cdot)\) \(\chi_{8281}(3039,\cdot)\) \(\chi_{8281}(3137,\cdot)\) \(\chi_{8281}(3676,\cdot)\) \(\chi_{8281}(3774,\cdot)\) \(\chi_{8281}(4313,\cdot)\) \(\chi_{8281}(4411,\cdot)\) \(\chi_{8281}(4950,\cdot)\) \(\chi_{8281}(5587,\cdot)\) \(\chi_{8281}(5685,\cdot)\) \(\chi_{8281}(6224,\cdot)\) \(\chi_{8281}(6322,\cdot)\) \(\chi_{8281}(6861,\cdot)\) \(\chi_{8281}(6959,\cdot)\) \(\chi_{8281}(7498,\cdot)\) \(\chi_{8281}(7596,\cdot)\) \(\chi_{8281}(8233,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1522,3382)\) → \((1,e\left(\frac{41}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(491, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) |