Basic properties
| Modulus: | \(8820\) | |
| Conductor: | \(2205\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2205}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8820.ja
\(\chi_{8820}(13,\cdot)\) \(\chi_{8820}(517,\cdot)\) \(\chi_{8820}(853,\cdot)\) \(\chi_{8820}(1357,\cdot)\) \(\chi_{8820}(1777,\cdot)\) \(\chi_{8820}(2113,\cdot)\) \(\chi_{8820}(2533,\cdot)\) \(\chi_{8820}(2617,\cdot)\) \(\chi_{8820}(3373,\cdot)\) \(\chi_{8820}(3793,\cdot)\) \(\chi_{8820}(3877,\cdot)\) \(\chi_{8820}(4297,\cdot)\) \(\chi_{8820}(4633,\cdot)\) \(\chi_{8820}(5053,\cdot)\) \(\chi_{8820}(5137,\cdot)\) \(\chi_{8820}(5557,\cdot)\) \(\chi_{8820}(5893,\cdot)\) \(\chi_{8820}(6313,\cdot)\) \(\chi_{8820}(6397,\cdot)\) \(\chi_{8820}(6817,\cdot)\) \(\chi_{8820}(7573,\cdot)\) \(\chi_{8820}(7657,\cdot)\) \(\chi_{8820}(8077,\cdot)\) \(\chi_{8820}(8413,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4411,7841,7057,1081)\) → \((1,e\left(\frac{1}{3}\right),-i,e\left(\frac{11}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8820 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(1\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{25}{84}\right)\) |