Basic properties
| Modulus: | \(10000\) | |
| Conductor: | \(10000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(500\) | 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 10000.da
\(\chi_{10000}(21,\cdot)\) \(\chi_{10000}(61,\cdot)\) \(\chi_{10000}(141,\cdot)\) \(\chi_{10000}(181,\cdot)\) \(\chi_{10000}(221,\cdot)\) \(\chi_{10000}(261,\cdot)\) \(\chi_{10000}(341,\cdot)\) \(\chi_{10000}(381,\cdot)\) \(\chi_{10000}(421,\cdot)\) \(\chi_{10000}(461,\cdot)\) \(\chi_{10000}(541,\cdot)\) \(\chi_{10000}(581,\cdot)\) \(\chi_{10000}(621,\cdot)\) \(\chi_{10000}(661,\cdot)\) \(\chi_{10000}(741,\cdot)\) \(\chi_{10000}(781,\cdot)\) \(\chi_{10000}(821,\cdot)\) \(\chi_{10000}(861,\cdot)\) \(\chi_{10000}(941,\cdot)\) \(\chi_{10000}(981,\cdot)\) \(\chi_{10000}(1021,\cdot)\) \(\chi_{10000}(1061,\cdot)\) \(\chi_{10000}(1141,\cdot)\) \(\chi_{10000}(1181,\cdot)\) \(\chi_{10000}(1221,\cdot)\) \(\chi_{10000}(1261,\cdot)\) \(\chi_{10000}(1341,\cdot)\) \(\chi_{10000}(1381,\cdot)\) \(\chi_{10000}(1421,\cdot)\) \(\chi_{10000}(1461,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{500})$ |
| Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\((8751,2501,9377)\) → \((1,i,e\left(\frac{77}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 10000 }(1381, a) \) | \(1\) | \(1\) | \(e\left(\frac{331}{500}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{81}{250}\right)\) | \(e\left(\frac{233}{500}\right)\) | \(e\left(\frac{187}{500}\right)\) | \(e\left(\frac{71}{125}\right)\) | \(e\left(\frac{119}{500}\right)\) | \(e\left(\frac{461}{500}\right)\) | \(e\left(\frac{249}{250}\right)\) | \(e\left(\frac{493}{500}\right)\) |