Basic properties
| Modulus: | \(1875\) | |
| Conductor: | \(625\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(500\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{625}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1875.w
\(\chi_{1875}(13,\cdot)\) \(\chi_{1875}(22,\cdot)\) \(\chi_{1875}(28,\cdot)\) \(\chi_{1875}(37,\cdot)\) \(\chi_{1875}(52,\cdot)\) \(\chi_{1875}(58,\cdot)\) \(\chi_{1875}(67,\cdot)\) \(\chi_{1875}(73,\cdot)\) \(\chi_{1875}(88,\cdot)\) \(\chi_{1875}(97,\cdot)\) \(\chi_{1875}(103,\cdot)\) \(\chi_{1875}(112,\cdot)\) \(\chi_{1875}(127,\cdot)\) \(\chi_{1875}(133,\cdot)\) \(\chi_{1875}(142,\cdot)\) \(\chi_{1875}(148,\cdot)\) \(\chi_{1875}(163,\cdot)\) \(\chi_{1875}(172,\cdot)\) \(\chi_{1875}(178,\cdot)\) \(\chi_{1875}(187,\cdot)\) \(\chi_{1875}(202,\cdot)\) \(\chi_{1875}(208,\cdot)\) \(\chi_{1875}(217,\cdot)\) \(\chi_{1875}(223,\cdot)\) \(\chi_{1875}(238,\cdot)\) \(\chi_{1875}(247,\cdot)\) \(\chi_{1875}(253,\cdot)\) \(\chi_{1875}(262,\cdot)\) \(\chi_{1875}(277,\cdot)\) \(\chi_{1875}(283,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{500})$ |
| Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\((626,1252)\) → \((1,e\left(\frac{139}{500}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1875 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{139}{500}\right)\) | \(e\left(\frac{139}{250}\right)\) | \(e\left(\frac{83}{100}\right)\) | \(e\left(\frac{417}{500}\right)\) | \(e\left(\frac{41}{125}\right)\) | \(e\left(\frac{321}{500}\right)\) | \(e\left(\frac{27}{250}\right)\) | \(e\left(\frac{14}{125}\right)\) | \(e\left(\frac{47}{500}\right)\) | \(e\left(\frac{51}{250}\right)\) |