Basic properties
| Modulus: | \(16245\) | |
| Conductor: | \(16245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(228\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 16245.gb
\(\chi_{16245}(7,\cdot)\) \(\chi_{16245}(178,\cdot)\) \(\chi_{16245}(562,\cdot)\) \(\chi_{16245}(733,\cdot)\) \(\chi_{16245}(862,\cdot)\) \(\chi_{16245}(1033,\cdot)\) \(\chi_{16245}(1417,\cdot)\) \(\chi_{16245}(1588,\cdot)\) \(\chi_{16245}(1717,\cdot)\) \(\chi_{16245}(1888,\cdot)\) \(\chi_{16245}(2272,\cdot)\) \(\chi_{16245}(2443,\cdot)\) \(\chi_{16245}(2572,\cdot)\) \(\chi_{16245}(2743,\cdot)\) \(\chi_{16245}(3127,\cdot)\) \(\chi_{16245}(3298,\cdot)\) \(\chi_{16245}(3427,\cdot)\) \(\chi_{16245}(3598,\cdot)\) \(\chi_{16245}(3982,\cdot)\) \(\chi_{16245}(4153,\cdot)\) \(\chi_{16245}(4282,\cdot)\) \(\chi_{16245}(4453,\cdot)\) \(\chi_{16245}(4837,\cdot)\) \(\chi_{16245}(5008,\cdot)\) \(\chi_{16245}(5137,\cdot)\) \(\chi_{16245}(5308,\cdot)\) \(\chi_{16245}(5692,\cdot)\) \(\chi_{16245}(5863,\cdot)\) \(\chi_{16245}(5992,\cdot)\) \(\chi_{16245}(6163,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3611,12997,15886)\) → \((e\left(\frac{2}{3}\right),i,e\left(\frac{25}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 16245 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{27}{76}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{161}{228}\right)\) | \(e\left(\frac{5}{76}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{29}{76}\right)\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{85}{228}\right)\) | \(e\left(\frac{173}{228}\right)\) |