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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 980.bt
\(\chi_{980}(3,\cdot)\) \(\chi_{980}(47,\cdot)\) \(\chi_{980}(87,\cdot)\) \(\chi_{980}(103,\cdot)\) \(\chi_{980}(143,\cdot)\) \(\chi_{980}(187,\cdot)\) \(\chi_{980}(243,\cdot)\) \(\chi_{980}(283,\cdot)\) \(\chi_{980}(327,\cdot)\) \(\chi_{980}(367,\cdot)\) \(\chi_{980}(383,\cdot)\) \(\chi_{980}(467,\cdot)\) \(\chi_{980}(507,\cdot)\) \(\chi_{980}(523,\cdot)\) \(\chi_{980}(563,\cdot)\) \(\chi_{980}(647,\cdot)\) \(\chi_{980}(663,\cdot)\) \(\chi_{980}(703,\cdot)\) \(\chi_{980}(747,\cdot)\) \(\chi_{980}(787,\cdot)\) \(\chi_{980}(843,\cdot)\) \(\chi_{980}(887,\cdot)\) \(\chi_{980}(927,\cdot)\) \(\chi_{980}(943,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((491,197,101)\) → \((-1,-i,e\left(\frac{41}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 980 }(523, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{3}\right)\) |