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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 16245.gc
\(\chi_{16245}(88,\cdot)\) \(\chi_{16245}(103,\cdot)\) \(\chi_{16245}(772,\cdot)\) \(\chi_{16245}(787,\cdot)\) \(\chi_{16245}(943,\cdot)\) \(\chi_{16245}(958,\cdot)\) \(\chi_{16245}(1627,\cdot)\) \(\chi_{16245}(1642,\cdot)\) \(\chi_{16245}(1798,\cdot)\) \(\chi_{16245}(1813,\cdot)\) \(\chi_{16245}(2482,\cdot)\) \(\chi_{16245}(2497,\cdot)\) \(\chi_{16245}(2653,\cdot)\) \(\chi_{16245}(2668,\cdot)\) \(\chi_{16245}(3337,\cdot)\) \(\chi_{16245}(3352,\cdot)\) \(\chi_{16245}(3508,\cdot)\) \(\chi_{16245}(3523,\cdot)\) \(\chi_{16245}(4192,\cdot)\) \(\chi_{16245}(4207,\cdot)\) \(\chi_{16245}(4363,\cdot)\) \(\chi_{16245}(4378,\cdot)\) \(\chi_{16245}(5047,\cdot)\) \(\chi_{16245}(5062,\cdot)\) \(\chi_{16245}(5218,\cdot)\) \(\chi_{16245}(5233,\cdot)\) \(\chi_{16245}(5902,\cdot)\) \(\chi_{16245}(5917,\cdot)\) \(\chi_{16245}(6073,\cdot)\) \(\chi_{16245}(6088,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3611,12997,15886)\) → \((e\left(\frac{1}{3}\right),-i,e\left(\frac{55}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 16245 }(2668, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{76}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{103}{228}\right)\) | \(e\left(\frac{53}{76}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{49}{76}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{179}{228}\right)\) | \(e\left(\frac{25}{228}\right)\) |