Basic properties
| Modulus: | \(6008\) | |
| Conductor: | \(3004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3004}(1135,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6008.bz
\(\chi_{6008}(7,\cdot)\) \(\chi_{6008}(111,\cdot)\) \(\chi_{6008}(183,\cdot)\) \(\chi_{6008}(239,\cdot)\) \(\chi_{6008}(327,\cdot)\) \(\chi_{6008}(343,\cdot)\) \(\chi_{6008}(383,\cdot)\) \(\chi_{6008}(391,\cdot)\) \(\chi_{6008}(407,\cdot)\) \(\chi_{6008}(415,\cdot)\) \(\chi_{6008}(447,\cdot)\) \(\chi_{6008}(463,\cdot)\) \(\chi_{6008}(543,\cdot)\) \(\chi_{6008}(687,\cdot)\) \(\chi_{6008}(743,\cdot)\) \(\chi_{6008}(807,\cdot)\) \(\chi_{6008}(927,\cdot)\) \(\chi_{6008}(967,\cdot)\) \(\chi_{6008}(1079,\cdot)\) \(\chi_{6008}(1135,\cdot)\) \(\chi_{6008}(1199,\cdot)\) \(\chi_{6008}(1215,\cdot)\) \(\chi_{6008}(1231,\cdot)\) \(\chi_{6008}(1295,\cdot)\) \(\chi_{6008}(1311,\cdot)\) \(\chi_{6008}(1351,\cdot)\) \(\chi_{6008}(1431,\cdot)\) \(\chi_{6008}(1639,\cdot)\) \(\chi_{6008}(1743,\cdot)\) \(\chi_{6008}(1823,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((1503,3005,1505)\) → \((-1,1,e\left(\frac{221}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6008 }(1135, a) \) | \(1\) | \(1\) | \(e\left(\frac{48}{125}\right)\) | \(e\left(\frac{78}{125}\right)\) | \(e\left(\frac{123}{125}\right)\) | \(e\left(\frac{96}{125}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{9}{125}\right)\) | \(e\left(\frac{1}{125}\right)\) | \(e\left(\frac{209}{250}\right)\) | \(e\left(\frac{103}{250}\right)\) | \(e\left(\frac{46}{125}\right)\) |