Basic properties
| Modulus: | \(625\) | |
| Conductor: | \(625\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(125\) | 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 625.j
\(\chi_{625}(6,\cdot)\) \(\chi_{625}(11,\cdot)\) \(\chi_{625}(16,\cdot)\) \(\chi_{625}(21,\cdot)\) \(\chi_{625}(31,\cdot)\) \(\chi_{625}(36,\cdot)\) \(\chi_{625}(41,\cdot)\) \(\chi_{625}(46,\cdot)\) \(\chi_{625}(56,\cdot)\) \(\chi_{625}(61,\cdot)\) \(\chi_{625}(66,\cdot)\) \(\chi_{625}(71,\cdot)\) \(\chi_{625}(81,\cdot)\) \(\chi_{625}(86,\cdot)\) \(\chi_{625}(91,\cdot)\) \(\chi_{625}(96,\cdot)\) \(\chi_{625}(106,\cdot)\) \(\chi_{625}(111,\cdot)\) \(\chi_{625}(116,\cdot)\) \(\chi_{625}(121,\cdot)\) \(\chi_{625}(131,\cdot)\) \(\chi_{625}(136,\cdot)\) \(\chi_{625}(141,\cdot)\) \(\chi_{625}(146,\cdot)\) \(\chi_{625}(156,\cdot)\) \(\chi_{625}(161,\cdot)\) \(\chi_{625}(166,\cdot)\) \(\chi_{625}(171,\cdot)\) \(\chi_{625}(181,\cdot)\) \(\chi_{625}(186,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 125 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{23}{125}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 625 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{125}\right)\) | \(e\left(\frac{86}{125}\right)\) | \(e\left(\frac{46}{125}\right)\) | \(e\left(\frac{109}{125}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{69}{125}\right)\) | \(e\left(\frac{47}{125}\right)\) | \(e\left(\frac{73}{125}\right)\) | \(e\left(\frac{7}{125}\right)\) | \(e\left(\frac{72}{125}\right)\) |