Basic properties
| Modulus: | \(10000\) | |
| Conductor: | \(625\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(125\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{625}(366,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 10000.ci
\(\chi_{10000}(81,\cdot)\) \(\chi_{10000}(161,\cdot)\) \(\chi_{10000}(241,\cdot)\) \(\chi_{10000}(321,\cdot)\) \(\chi_{10000}(481,\cdot)\) \(\chi_{10000}(561,\cdot)\) \(\chi_{10000}(641,\cdot)\) \(\chi_{10000}(721,\cdot)\) \(\chi_{10000}(881,\cdot)\) \(\chi_{10000}(961,\cdot)\) \(\chi_{10000}(1041,\cdot)\) \(\chi_{10000}(1121,\cdot)\) \(\chi_{10000}(1281,\cdot)\) \(\chi_{10000}(1361,\cdot)\) \(\chi_{10000}(1441,\cdot)\) \(\chi_{10000}(1521,\cdot)\) \(\chi_{10000}(1681,\cdot)\) \(\chi_{10000}(1761,\cdot)\) \(\chi_{10000}(1841,\cdot)\) \(\chi_{10000}(1921,\cdot)\) \(\chi_{10000}(2081,\cdot)\) \(\chi_{10000}(2161,\cdot)\) \(\chi_{10000}(2241,\cdot)\) \(\chi_{10000}(2321,\cdot)\) \(\chi_{10000}(2481,\cdot)\) \(\chi_{10000}(2561,\cdot)\) \(\chi_{10000}(2641,\cdot)\) \(\chi_{10000}(2721,\cdot)\) \(\chi_{10000}(2881,\cdot)\) \(\chi_{10000}(2961,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 125 polynomial (not computed) |
Values on generators
\((8751,2501,9377)\) → \((1,1,e\left(\frac{16}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 10000 }(2241, a) \) | \(1\) | \(1\) | \(e\left(\frac{87}{125}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{49}{125}\right)\) | \(e\left(\frac{116}{125}\right)\) | \(e\left(\frac{99}{125}\right)\) | \(e\left(\frac{18}{125}\right)\) | \(e\left(\frac{63}{125}\right)\) | \(e\left(\frac{97}{125}\right)\) | \(e\left(\frac{21}{125}\right)\) | \(e\left(\frac{11}{125}\right)\) |