Basic properties
| Modulus: | \(10000\) | |
| Conductor: | \(2500\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(500\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2500}(1567,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 10000.cy
\(\chi_{10000}(47,\cdot)\) \(\chi_{10000}(63,\cdot)\) \(\chi_{10000}(127,\cdot)\) \(\chi_{10000}(223,\cdot)\) \(\chi_{10000}(287,\cdot)\) \(\chi_{10000}(303,\cdot)\) \(\chi_{10000}(367,\cdot)\) \(\chi_{10000}(383,\cdot)\) \(\chi_{10000}(447,\cdot)\) \(\chi_{10000}(463,\cdot)\) \(\chi_{10000}(527,\cdot)\) \(\chi_{10000}(623,\cdot)\) \(\chi_{10000}(687,\cdot)\) \(\chi_{10000}(703,\cdot)\) \(\chi_{10000}(767,\cdot)\) \(\chi_{10000}(783,\cdot)\) \(\chi_{10000}(847,\cdot)\) \(\chi_{10000}(863,\cdot)\) \(\chi_{10000}(927,\cdot)\) \(\chi_{10000}(1023,\cdot)\) \(\chi_{10000}(1087,\cdot)\) \(\chi_{10000}(1103,\cdot)\) \(\chi_{10000}(1167,\cdot)\) \(\chi_{10000}(1183,\cdot)\) \(\chi_{10000}(1247,\cdot)\) \(\chi_{10000}(1263,\cdot)\) \(\chi_{10000}(1327,\cdot)\) \(\chi_{10000}(1423,\cdot)\) \(\chi_{10000}(1487,\cdot)\) \(\chi_{10000}(1503,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{500})$ |
| Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\((8751,2501,9377)\) → \((-1,1,e\left(\frac{213}{500}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 10000 }(1567, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{500}\right)\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{41}{250}\right)\) | \(e\left(\frac{69}{250}\right)\) | \(e\left(\frac{107}{500}\right)\) | \(e\left(\frac{349}{500}\right)\) | \(e\left(\frac{71}{125}\right)\) | \(e\left(\frac{24}{125}\right)\) | \(e\left(\frac{53}{500}\right)\) | \(e\left(\frac{123}{500}\right)\) |