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 \(\chi_{2205}(338,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8820.im
\(\chi_{8820}(137,\cdot)\) \(\chi_{8820}(653,\cdot)\) \(\chi_{8820}(893,\cdot)\) \(\chi_{8820}(1397,\cdot)\) \(\chi_{8820}(1913,\cdot)\) \(\chi_{8820}(2153,\cdot)\) \(\chi_{8820}(2417,\cdot)\) \(\chi_{8820}(2657,\cdot)\) \(\chi_{8820}(3173,\cdot)\) \(\chi_{8820}(3413,\cdot)\) \(\chi_{8820}(3677,\cdot)\) \(\chi_{8820}(3917,\cdot)\) \(\chi_{8820}(4433,\cdot)\) \(\chi_{8820}(4937,\cdot)\) \(\chi_{8820}(5177,\cdot)\) \(\chi_{8820}(5693,\cdot)\) \(\chi_{8820}(5933,\cdot)\) \(\chi_{8820}(6197,\cdot)\) \(\chi_{8820}(6953,\cdot)\) \(\chi_{8820}(7193,\cdot)\) \(\chi_{8820}(7457,\cdot)\) \(\chi_{8820}(7697,\cdot)\) \(\chi_{8820}(8453,\cdot)\) \(\chi_{8820}(8717,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4411,7841,7057,1081)\) → \((1,e\left(\frac{5}{6}\right),-i,e\left(\frac{4}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8820 }(6953, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(1\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{61}{84}\right)\) |