Basic properties
| Modulus: | \(625\) | |
| Conductor: | \(625\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 625.l
\(\chi_{625}(2,\cdot)\) \(\chi_{625}(3,\cdot)\) \(\chi_{625}(8,\cdot)\) \(\chi_{625}(12,\cdot)\) \(\chi_{625}(13,\cdot)\) \(\chi_{625}(17,\cdot)\) \(\chi_{625}(22,\cdot)\) \(\chi_{625}(23,\cdot)\) \(\chi_{625}(27,\cdot)\) \(\chi_{625}(28,\cdot)\) \(\chi_{625}(33,\cdot)\) \(\chi_{625}(37,\cdot)\) \(\chi_{625}(38,\cdot)\) \(\chi_{625}(42,\cdot)\) \(\chi_{625}(47,\cdot)\) \(\chi_{625}(48,\cdot)\) \(\chi_{625}(52,\cdot)\) \(\chi_{625}(53,\cdot)\) \(\chi_{625}(58,\cdot)\) \(\chi_{625}(62,\cdot)\) \(\chi_{625}(63,\cdot)\) \(\chi_{625}(67,\cdot)\) \(\chi_{625}(72,\cdot)\) \(\chi_{625}(73,\cdot)\) \(\chi_{625}(77,\cdot)\) \(\chi_{625}(78,\cdot)\) \(\chi_{625}(83,\cdot)\) \(\chi_{625}(87,\cdot)\) \(\chi_{625}(88,\cdot)\) \(\chi_{625}(92,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{500})$ |
| Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{319}{500}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 625 }(163, a) \) | \(-1\) | \(1\) | \(e\left(\frac{319}{500}\right)\) | \(e\left(\frac{133}{500}\right)\) | \(e\left(\frac{69}{250}\right)\) | \(e\left(\frac{113}{125}\right)\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{457}{500}\right)\) | \(e\left(\frac{133}{250}\right)\) | \(e\left(\frac{86}{125}\right)\) | \(e\left(\frac{271}{500}\right)\) | \(e\left(\frac{341}{500}\right)\) |