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.io
\(\chi_{8820}(43,\cdot)\) \(\chi_{8820}(463,\cdot)\) \(\chi_{8820}(547,\cdot)\) \(\chi_{8820}(967,\cdot)\) \(\chi_{8820}(1303,\cdot)\) \(\chi_{8820}(1723,\cdot)\) \(\chi_{8820}(1807,\cdot)\) \(\chi_{8820}(2227,\cdot)\) \(\chi_{8820}(2563,\cdot)\) \(\chi_{8820}(2983,\cdot)\) \(\chi_{8820}(3067,\cdot)\) \(\chi_{8820}(3487,\cdot)\) \(\chi_{8820}(4243,\cdot)\) \(\chi_{8820}(4327,\cdot)\) \(\chi_{8820}(4747,\cdot)\) \(\chi_{8820}(5083,\cdot)\) \(\chi_{8820}(5503,\cdot)\) \(\chi_{8820}(6007,\cdot)\) \(\chi_{8820}(6343,\cdot)\) \(\chi_{8820}(6847,\cdot)\) \(\chi_{8820}(7267,\cdot)\) \(\chi_{8820}(7603,\cdot)\) \(\chi_{8820}(8023,\cdot)\) \(\chi_{8820}(8107,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4411,7841,7057,1081)\) → \((-1,e\left(\frac{2}{3}\right),-i,e\left(\frac{4}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8820 }(6343, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(1\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{71}{84}\right)\) |