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 \(\chi_{637}(188,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8281.cx
\(\chi_{8281}(188,\cdot)\) \(\chi_{8281}(258,\cdot)\) \(\chi_{8281}(657,\cdot)\) \(\chi_{8281}(1441,\cdot)\) \(\chi_{8281}(1770,\cdot)\) \(\chi_{8281}(1840,\cdot)\) \(\chi_{8281}(2554,\cdot)\) \(\chi_{8281}(2624,\cdot)\) \(\chi_{8281}(2953,\cdot)\) \(\chi_{8281}(3023,\cdot)\) \(\chi_{8281}(3737,\cdot)\) \(\chi_{8281}(3807,\cdot)\) \(\chi_{8281}(4136,\cdot)\) \(\chi_{8281}(4206,\cdot)\) \(\chi_{8281}(4920,\cdot)\) \(\chi_{8281}(4990,\cdot)\) \(\chi_{8281}(5319,\cdot)\) \(\chi_{8281}(6103,\cdot)\) \(\chi_{8281}(6502,\cdot)\) \(\chi_{8281}(6572,\cdot)\) \(\chi_{8281}(7286,\cdot)\) \(\chi_{8281}(7356,\cdot)\) \(\chi_{8281}(7685,\cdot)\) \(\chi_{8281}(7755,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1522,3382)\) → \((e\left(\frac{5}{14}\right),e\left(\frac{5}{12}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 8281 }(188, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{3}{7}\right)\) |