Basic properties
| Modulus: | \(8820\) | |
| Conductor: | \(8820\) | 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 8820.iy
\(\chi_{8820}(383,\cdot)\) \(\chi_{8820}(887,\cdot)\) \(\chi_{8820}(983,\cdot)\) \(\chi_{8820}(1487,\cdot)\) \(\chi_{8820}(1643,\cdot)\) \(\chi_{8820}(2147,\cdot)\) \(\chi_{8820}(2243,\cdot)\) \(\chi_{8820}(2747,\cdot)\) \(\chi_{8820}(2903,\cdot)\) \(\chi_{8820}(3407,\cdot)\) \(\chi_{8820}(3503,\cdot)\) \(\chi_{8820}(4007,\cdot)\) \(\chi_{8820}(4163,\cdot)\) \(\chi_{8820}(4667,\cdot)\) \(\chi_{8820}(4763,\cdot)\) \(\chi_{8820}(5267,\cdot)\) \(\chi_{8820}(5423,\cdot)\) \(\chi_{8820}(5927,\cdot)\) \(\chi_{8820}(6023,\cdot)\) \(\chi_{8820}(6527,\cdot)\) \(\chi_{8820}(7187,\cdot)\) \(\chi_{8820}(7787,\cdot)\) \(\chi_{8820}(7943,\cdot)\) \(\chi_{8820}(8543,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4411,7841,7057,1081)\) → \((-1,e\left(\frac{5}{6}\right),-i,e\left(\frac{23}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8820 }(383, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(1\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{31}{84}\right)\) |