Basic properties
| Modulus: | \(8820\) | |
| Conductor: | \(2940\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2940}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8820.is
\(\chi_{8820}(107,\cdot)\) \(\chi_{8820}(683,\cdot)\) \(\chi_{8820}(1187,\cdot)\) \(\chi_{8820}(1367,\cdot)\) \(\chi_{8820}(1943,\cdot)\) \(\chi_{8820}(2123,\cdot)\) \(\chi_{8820}(2447,\cdot)\) \(\chi_{8820}(3383,\cdot)\) \(\chi_{8820}(3707,\cdot)\) \(\chi_{8820}(3887,\cdot)\) \(\chi_{8820}(4463,\cdot)\) \(\chi_{8820}(4643,\cdot)\) \(\chi_{8820}(5147,\cdot)\) \(\chi_{8820}(5723,\cdot)\) \(\chi_{8820}(5903,\cdot)\) \(\chi_{8820}(6227,\cdot)\) \(\chi_{8820}(6407,\cdot)\) \(\chi_{8820}(6983,\cdot)\) \(\chi_{8820}(7163,\cdot)\) \(\chi_{8820}(7487,\cdot)\) \(\chi_{8820}(7667,\cdot)\) \(\chi_{8820}(8243,\cdot)\) \(\chi_{8820}(8423,\cdot)\) \(\chi_{8820}(8747,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4411,7841,7057,1081)\) → \((-1,-1,i,e\left(\frac{1}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8820 }(107, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{15}{28}\right)\) |