Basic properties
Modulus: | \(10000\) | |
Conductor: | \(5000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(500\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{5000}(3947,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 10000.cx
\(\chi_{10000}(23,\cdot)\) \(\chi_{10000}(87,\cdot)\) \(\chi_{10000}(103,\cdot)\) \(\chi_{10000}(167,\cdot)\) \(\chi_{10000}(183,\cdot)\) \(\chi_{10000}(247,\cdot)\) \(\chi_{10000}(263,\cdot)\) \(\chi_{10000}(327,\cdot)\) \(\chi_{10000}(423,\cdot)\) \(\chi_{10000}(487,\cdot)\) \(\chi_{10000}(503,\cdot)\) \(\chi_{10000}(567,\cdot)\) \(\chi_{10000}(583,\cdot)\) \(\chi_{10000}(647,\cdot)\) \(\chi_{10000}(663,\cdot)\) \(\chi_{10000}(727,\cdot)\) \(\chi_{10000}(823,\cdot)\) \(\chi_{10000}(887,\cdot)\) \(\chi_{10000}(903,\cdot)\) \(\chi_{10000}(967,\cdot)\) \(\chi_{10000}(983,\cdot)\) \(\chi_{10000}(1047,\cdot)\) \(\chi_{10000}(1063,\cdot)\) \(\chi_{10000}(1127,\cdot)\) \(\chi_{10000}(1223,\cdot)\) \(\chi_{10000}(1287,\cdot)\) \(\chi_{10000}(1303,\cdot)\) \(\chi_{10000}(1367,\cdot)\) \(\chi_{10000}(1383,\cdot)\) \(\chi_{10000}(1447,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{500})$ |
Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\((8751,2501,9377)\) → \((-1,-1,e\left(\frac{317}{500}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 10000 }(1447, a) \) | \(1\) | \(1\) | \(e\left(\frac{419}{500}\right)\) | \(e\left(\frac{99}{100}\right)\) | \(e\left(\frac{169}{250}\right)\) | \(e\left(\frac{98}{125}\right)\) | \(e\left(\frac{313}{500}\right)\) | \(e\left(\frac{341}{500}\right)\) | \(e\left(\frac{3}{250}\right)\) | \(e\left(\frac{207}{250}\right)\) | \(e\left(\frac{377}{500}\right)\) | \(e\left(\frac{257}{500}\right)\) |