Basic properties
| Modulus: | \(166410\) | |
| Conductor: | \(1849\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1806\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1849}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 166410.ib
\(\chi_{166410}(91,\cdot)\) \(\chi_{166410}(631,\cdot)\) \(\chi_{166410}(721,\cdot)\) \(\chi_{166410}(1351,\cdot)\) \(\chi_{166410}(1531,\cdot)\) \(\chi_{166410}(1621,\cdot)\) \(\chi_{166410}(1711,\cdot)\) \(\chi_{166410}(1981,\cdot)\) \(\chi_{166410}(2341,\cdot)\) \(\chi_{166410}(3151,\cdot)\) \(\chi_{166410}(3511,\cdot)\) \(\chi_{166410}(3961,\cdot)\) \(\chi_{166410}(4501,\cdot)\) \(\chi_{166410}(4591,\cdot)\) \(\chi_{166410}(5221,\cdot)\) \(\chi_{166410}(5401,\cdot)\) \(\chi_{166410}(5491,\cdot)\) \(\chi_{166410}(5581,\cdot)\) \(\chi_{166410}(5851,\cdot)\) \(\chi_{166410}(6211,\cdot)\) \(\chi_{166410}(7021,\cdot)\) \(\chi_{166410}(7201,\cdot)\) \(\chi_{166410}(7381,\cdot)\) \(\chi_{166410}(7831,\cdot)\) \(\chi_{166410}(8371,\cdot)\) \(\chi_{166410}(8461,\cdot)\) \(\chi_{166410}(9091,\cdot)\) \(\chi_{166410}(9271,\cdot)\) \(\chi_{166410}(9361,\cdot)\) \(\chi_{166410}(9451,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{903})$ |
| Fixed field: | Number field defined by a degree 1806 polynomial (not computed) |
Values on generators
\((129431,99847,40681)\) → \((1,1,e\left(\frac{1}{1806}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 166410 }(40681, a) \) | \(-1\) | \(1\) | \(e\left(\frac{35}{258}\right)\) | \(e\left(\frac{243}{301}\right)\) | \(e\left(\frac{520}{903}\right)\) | \(e\left(\frac{334}{903}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{890}{903}\right)\) | \(e\left(\frac{41}{1806}\right)\) | \(e\left(\frac{899}{903}\right)\) | \(e\left(\frac{241}{258}\right)\) | \(e\left(\frac{29}{301}\right)\) |