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.jc
\(\chi_{8820}(583,\cdot)\) \(\chi_{8820}(823,\cdot)\) \(\chi_{8820}(1087,\cdot)\) \(\chi_{8820}(1327,\cdot)\) \(\chi_{8820}(2083,\cdot)\) \(\chi_{8820}(2347,\cdot)\) \(\chi_{8820}(2587,\cdot)\) \(\chi_{8820}(3103,\cdot)\) \(\chi_{8820}(3343,\cdot)\) \(\chi_{8820}(3847,\cdot)\) \(\chi_{8820}(4363,\cdot)\) \(\chi_{8820}(4603,\cdot)\) \(\chi_{8820}(4867,\cdot)\) \(\chi_{8820}(5107,\cdot)\) \(\chi_{8820}(5623,\cdot)\) \(\chi_{8820}(5863,\cdot)\) \(\chi_{8820}(6127,\cdot)\) \(\chi_{8820}(6367,\cdot)\) \(\chi_{8820}(6883,\cdot)\) \(\chi_{8820}(7387,\cdot)\) \(\chi_{8820}(7627,\cdot)\) \(\chi_{8820}(8143,\cdot)\) \(\chi_{8820}(8383,\cdot)\) \(\chi_{8820}(8647,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4411,7841,7057,1081)\) → \((-1,e\left(\frac{2}{3}\right),-i,e\left(\frac{4}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8820 }(583, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{47}{84}\right)\) |