Basic properties
| Modulus: | \(2500\) | |
| Conductor: | \(2500\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2500.x
\(\chi_{2500}(3,\cdot)\) \(\chi_{2500}(23,\cdot)\) \(\chi_{2500}(27,\cdot)\) \(\chi_{2500}(47,\cdot)\) \(\chi_{2500}(63,\cdot)\) \(\chi_{2500}(67,\cdot)\) \(\chi_{2500}(83,\cdot)\) \(\chi_{2500}(87,\cdot)\) \(\chi_{2500}(103,\cdot)\) \(\chi_{2500}(123,\cdot)\) \(\chi_{2500}(127,\cdot)\) \(\chi_{2500}(147,\cdot)\) \(\chi_{2500}(163,\cdot)\) \(\chi_{2500}(167,\cdot)\) \(\chi_{2500}(183,\cdot)\) \(\chi_{2500}(187,\cdot)\) \(\chi_{2500}(203,\cdot)\) \(\chi_{2500}(223,\cdot)\) \(\chi_{2500}(227,\cdot)\) \(\chi_{2500}(247,\cdot)\) \(\chi_{2500}(263,\cdot)\) \(\chi_{2500}(267,\cdot)\) \(\chi_{2500}(283,\cdot)\) \(\chi_{2500}(287,\cdot)\) \(\chi_{2500}(303,\cdot)\) \(\chi_{2500}(323,\cdot)\) \(\chi_{2500}(327,\cdot)\) \(\chi_{2500}(347,\cdot)\) \(\chi_{2500}(363,\cdot)\) \(\chi_{2500}(367,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{500})$ |
| Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\((1251,1877)\) → \((-1,e\left(\frac{431}{500}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2500 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{367}{500}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{117}{250}\right)\) | \(e\left(\frac{203}{250}\right)\) | \(e\left(\frac{409}{500}\right)\) | \(e\left(\frac{63}{500}\right)\) | \(e\left(\frac{102}{125}\right)\) | \(e\left(\frac{38}{125}\right)\) | \(e\left(\frac{11}{500}\right)\) | \(e\left(\frac{101}{500}\right)\) |