Basic properties
Modulus: | \(980\) | |
Conductor: | \(980\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 980.bs
\(\chi_{980}(23,\cdot)\) \(\chi_{980}(107,\cdot)\) \(\chi_{980}(123,\cdot)\) \(\chi_{980}(163,\cdot)\) \(\chi_{980}(207,\cdot)\) \(\chi_{980}(247,\cdot)\) \(\chi_{980}(303,\cdot)\) \(\chi_{980}(347,\cdot)\) \(\chi_{980}(387,\cdot)\) \(\chi_{980}(403,\cdot)\) \(\chi_{980}(443,\cdot)\) \(\chi_{980}(487,\cdot)\) \(\chi_{980}(527,\cdot)\) \(\chi_{980}(543,\cdot)\) \(\chi_{980}(583,\cdot)\) \(\chi_{980}(627,\cdot)\) \(\chi_{980}(683,\cdot)\) \(\chi_{980}(723,\cdot)\) \(\chi_{980}(767,\cdot)\) \(\chi_{980}(807,\cdot)\) \(\chi_{980}(823,\cdot)\) \(\chi_{980}(907,\cdot)\) \(\chi_{980}(947,\cdot)\) \(\chi_{980}(963,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((491,197,101)\) → \((-1,i,e\left(\frac{11}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 980 }(487, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{6}\right)\) |