Basic properties
| Modulus: | \(10000\) | |
| Conductor: | \(5000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{5000}(4381,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 10000.cl
\(\chi_{10000}(41,\cdot)\) \(\chi_{10000}(121,\cdot)\) \(\chi_{10000}(281,\cdot)\) \(\chi_{10000}(361,\cdot)\) \(\chi_{10000}(441,\cdot)\) \(\chi_{10000}(521,\cdot)\) \(\chi_{10000}(681,\cdot)\) \(\chi_{10000}(761,\cdot)\) \(\chi_{10000}(841,\cdot)\) \(\chi_{10000}(921,\cdot)\) \(\chi_{10000}(1081,\cdot)\) \(\chi_{10000}(1161,\cdot)\) \(\chi_{10000}(1241,\cdot)\) \(\chi_{10000}(1321,\cdot)\) \(\chi_{10000}(1481,\cdot)\) \(\chi_{10000}(1561,\cdot)\) \(\chi_{10000}(1641,\cdot)\) \(\chi_{10000}(1721,\cdot)\) \(\chi_{10000}(1881,\cdot)\) \(\chi_{10000}(1961,\cdot)\) \(\chi_{10000}(2041,\cdot)\) \(\chi_{10000}(2121,\cdot)\) \(\chi_{10000}(2281,\cdot)\) \(\chi_{10000}(2361,\cdot)\) \(\chi_{10000}(2441,\cdot)\) \(\chi_{10000}(2521,\cdot)\) \(\chi_{10000}(2681,\cdot)\) \(\chi_{10000}(2761,\cdot)\) \(\chi_{10000}(2841,\cdot)\) \(\chi_{10000}(2921,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((8751,2501,9377)\) → \((1,-1,e\left(\frac{27}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 10000 }(1881, a) \) | \(1\) | \(1\) | \(e\left(\frac{153}{250}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{28}{125}\right)\) | \(e\left(\frac{79}{250}\right)\) | \(e\left(\frac{131}{250}\right)\) | \(e\left(\frac{46}{125}\right)\) | \(e\left(\frac{197}{250}\right)\) | \(e\left(\frac{93}{250}\right)\) | \(e\left(\frac{12}{125}\right)\) | \(e\left(\frac{209}{250}\right)\) |