Basic properties
| Modulus: | \(8281\) | |
| Conductor: | \(637\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{637}(437,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8281.cy
\(\chi_{8281}(437,\cdot)\) \(\chi_{8281}(577,\cdot)\) \(\chi_{8281}(775,\cdot)\) \(\chi_{8281}(915,\cdot)\) \(\chi_{8281}(1620,\cdot)\) \(\chi_{8281}(1760,\cdot)\) \(\chi_{8281}(1958,\cdot)\) \(\chi_{8281}(2098,\cdot)\) \(\chi_{8281}(2803,\cdot)\) \(\chi_{8281}(2943,\cdot)\) \(\chi_{8281}(3141,\cdot)\) \(\chi_{8281}(3281,\cdot)\) \(\chi_{8281}(3986,\cdot)\) \(\chi_{8281}(4126,\cdot)\) \(\chi_{8281}(4324,\cdot)\) \(\chi_{8281}(4464,\cdot)\) \(\chi_{8281}(5169,\cdot)\) \(\chi_{8281}(5309,\cdot)\) \(\chi_{8281}(5647,\cdot)\) \(\chi_{8281}(6492,\cdot)\) \(\chi_{8281}(6690,\cdot)\) \(\chi_{8281}(7535,\cdot)\) \(\chi_{8281}(7873,\cdot)\) \(\chi_{8281}(8013,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1522,3382)\) → \((e\left(\frac{31}{42}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 8281 }(437, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{13}{21}\right)\) |