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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8820.iu
\(\chi_{8820}(23,\cdot)\) \(\chi_{8820}(527,\cdot)\) \(\chi_{8820}(767,\cdot)\) \(\chi_{8820}(1283,\cdot)\) \(\chi_{8820}(1523,\cdot)\) \(\chi_{8820}(1787,\cdot)\) \(\chi_{8820}(2543,\cdot)\) \(\chi_{8820}(2783,\cdot)\) \(\chi_{8820}(3047,\cdot)\) \(\chi_{8820}(3287,\cdot)\) \(\chi_{8820}(4043,\cdot)\) \(\chi_{8820}(4307,\cdot)\) \(\chi_{8820}(4547,\cdot)\) \(\chi_{8820}(5063,\cdot)\) \(\chi_{8820}(5303,\cdot)\) \(\chi_{8820}(5807,\cdot)\) \(\chi_{8820}(6323,\cdot)\) \(\chi_{8820}(6563,\cdot)\) \(\chi_{8820}(6827,\cdot)\) \(\chi_{8820}(7067,\cdot)\) \(\chi_{8820}(7583,\cdot)\) \(\chi_{8820}(7823,\cdot)\) \(\chi_{8820}(8087,\cdot)\) \(\chi_{8820}(8327,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4411,7841,7057,1081)\) → \((-1,e\left(\frac{5}{6}\right),-i,e\left(\frac{19}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8820 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(-1\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{43}{84}\right)\) |