Basic properties
| Modulus: | \(10053\) | |
| Conductor: | \(10053\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(558\) | 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 10053.dl
\(\chi_{10053}(38,\cdot)\) \(\chi_{10053}(92,\cdot)\) \(\chi_{10053}(227,\cdot)\) \(\chi_{10053}(302,\cdot)\) \(\chi_{10053}(452,\cdot)\) \(\chi_{10053}(470,\cdot)\) \(\chi_{10053}(473,\cdot)\) \(\chi_{10053}(515,\cdot)\) \(\chi_{10053}(533,\cdot)\) \(\chi_{10053}(581,\cdot)\) \(\chi_{10053}(608,\cdot)\) \(\chi_{10053}(626,\cdot)\) \(\chi_{10053}(707,\cdot)\) \(\chi_{10053}(761,\cdot)\) \(\chi_{10053}(803,\cdot)\) \(\chi_{10053}(851,\cdot)\) \(\chi_{10053}(1004,\cdot)\) \(\chi_{10053}(1064,\cdot)\) \(\chi_{10053}(1166,\cdot)\) \(\chi_{10053}(1202,\cdot)\) \(\chi_{10053}(1265,\cdot)\) \(\chi_{10053}(1325,\cdot)\) \(\chi_{10053}(1337,\cdot)\) \(\chi_{10053}(1373,\cdot)\) \(\chi_{10053}(1415,\cdot)\) \(\chi_{10053}(1424,\cdot)\) \(\chi_{10053}(1436,\cdot)\) \(\chi_{10053}(1472,\cdot)\) \(\chi_{10053}(1487,\cdot)\) \(\chi_{10053}(1640,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{279})$ |
| Fixed field: | Number field defined by a degree 558 polynomial (not computed) |
Values on generators
\((1118,8938)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{109}{279}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 10053 }(38, a) \) | \(-1\) | \(1\) | \(e\left(\frac{311}{558}\right)\) | \(e\left(\frac{32}{279}\right)\) | \(e\left(\frac{1}{62}\right)\) | \(e\left(\frac{235}{279}\right)\) | \(e\left(\frac{125}{186}\right)\) | \(e\left(\frac{160}{279}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{40}{93}\right)\) | \(e\left(\frac{223}{558}\right)\) | \(e\left(\frac{64}{279}\right)\) |