Basic properties
| Modulus: | \(4410\) | |
| 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 \(\chi_{2205}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4410.ei
\(\chi_{4410}(43,\cdot)\) \(\chi_{4410}(337,\cdot)\) \(\chi_{4410}(463,\cdot)\) \(\chi_{4410}(547,\cdot)\) \(\chi_{4410}(673,\cdot)\) \(\chi_{4410}(967,\cdot)\) \(\chi_{4410}(1093,\cdot)\) \(\chi_{4410}(1303,\cdot)\) \(\chi_{4410}(1597,\cdot)\) \(\chi_{4410}(1723,\cdot)\) \(\chi_{4410}(1807,\cdot)\) \(\chi_{4410}(1933,\cdot)\) \(\chi_{4410}(2227,\cdot)\) \(\chi_{4410}(2437,\cdot)\) \(\chi_{4410}(2563,\cdot)\) \(\chi_{4410}(2857,\cdot)\) \(\chi_{4410}(2983,\cdot)\) \(\chi_{4410}(3067,\cdot)\) \(\chi_{4410}(3193,\cdot)\) \(\chi_{4410}(3487,\cdot)\) \(\chi_{4410}(3613,\cdot)\) \(\chi_{4410}(3697,\cdot)\) \(\chi_{4410}(4243,\cdot)\) \(\chi_{4410}(4327,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((3431,2647,1081)\) → \((e\left(\frac{2}{3}\right),-i,e\left(\frac{1}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 4410 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(-1\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{65}{84}\right)\) |