Basic properties
| Modulus: | \(166410\) | |
| Conductor: | \(16641\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1806\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{16641}(7981,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 166410.hw
\(\chi_{166410}(61,\cdot)\) \(\chi_{166410}(241,\cdot)\) \(\chi_{166410}(331,\cdot)\) \(\chi_{166410}(421,\cdot)\) \(\chi_{166410}(571,\cdot)\) \(\chi_{166410}(751,\cdot)\) \(\chi_{166410}(1381,\cdot)\) \(\chi_{166410}(2011,\cdot)\) \(\chi_{166410}(2221,\cdot)\) \(\chi_{166410}(3211,\cdot)\) \(\chi_{166410}(3271,\cdot)\) \(\chi_{166410}(3631,\cdot)\) \(\chi_{166410}(3931,\cdot)\) \(\chi_{166410}(4111,\cdot)\) \(\chi_{166410}(4201,\cdot)\) \(\chi_{166410}(4291,\cdot)\) \(\chi_{166410}(4441,\cdot)\) \(\chi_{166410}(4621,\cdot)\) \(\chi_{166410}(5251,\cdot)\) \(\chi_{166410}(5881,\cdot)\) \(\chi_{166410}(6091,\cdot)\) \(\chi_{166410}(7081,\cdot)\) \(\chi_{166410}(7141,\cdot)\) \(\chi_{166410}(7501,\cdot)\) \(\chi_{166410}(7801,\cdot)\) \(\chi_{166410}(7981,\cdot)\) \(\chi_{166410}(8071,\cdot)\) \(\chi_{166410}(8161,\cdot)\) \(\chi_{166410}(8311,\cdot)\) \(\chi_{166410}(8491,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{903})$ |
| Fixed field: | Number field defined by a degree 1806 polynomial (not computed) |
Values on generators
\((129431,99847,40681)\) → \((e\left(\frac{2}{3}\right),1,e\left(\frac{1235}{1806}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 166410 }(7981, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{258}\right)\) | \(e\left(\frac{626}{903}\right)\) | \(e\left(\frac{156}{301}\right)\) | \(e\left(\frac{722}{903}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{500}{903}\right)\) | \(e\left(\frac{1271}{1806}\right)\) | \(e\left(\frac{779}{903}\right)\) | \(e\left(\frac{161}{258}\right)\) | \(e\left(\frac{289}{903}\right)\) |