Basic properties
| Modulus: | \(4410\) | |
| Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{245}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4410.em
\(\chi_{4410}(37,\cdot)\) \(\chi_{4410}(163,\cdot)\) \(\chi_{4410}(487,\cdot)\) \(\chi_{4410}(613,\cdot)\) \(\chi_{4410}(793,\cdot)\) \(\chi_{4410}(1117,\cdot)\) \(\chi_{4410}(1297,\cdot)\) \(\chi_{4410}(1423,\cdot)\) \(\chi_{4410}(1747,\cdot)\) \(\chi_{4410}(1873,\cdot)\) \(\chi_{4410}(1927,\cdot)\) \(\chi_{4410}(2053,\cdot)\) \(\chi_{4410}(2377,\cdot)\) \(\chi_{4410}(2503,\cdot)\) \(\chi_{4410}(2557,\cdot)\) \(\chi_{4410}(2683,\cdot)\) \(\chi_{4410}(3133,\cdot)\) \(\chi_{4410}(3187,\cdot)\) \(\chi_{4410}(3637,\cdot)\) \(\chi_{4410}(3763,\cdot)\) \(\chi_{4410}(3817,\cdot)\) \(\chi_{4410}(3943,\cdot)\) \(\chi_{4410}(4267,\cdot)\) \(\chi_{4410}(4393,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((3431,2647,1081)\) → \((1,i,e\left(\frac{16}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 4410 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{9}{28}\right)\) |