Basic properties
| Modulus: | \(6004\) | |
| Conductor: | \(1501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1501}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.eh
\(\chi_{6004}(29,\cdot)\) \(\chi_{6004}(53,\cdot)\) \(\chi_{6004}(109,\cdot)\) \(\chi_{6004}(165,\cdot)\) \(\chi_{6004}(193,\cdot)\) \(\chi_{6004}(205,\cdot)\) \(\chi_{6004}(469,\cdot)\) \(\chi_{6004}(477,\cdot)\) \(\chi_{6004}(621,\cdot)\) \(\chi_{6004}(661,\cdot)\) \(\chi_{6004}(793,\cdot)\) \(\chi_{6004}(865,\cdot)\) \(\chi_{6004}(1001,\cdot)\) \(\chi_{6004}(1153,\cdot)\) \(\chi_{6004}(1245,\cdot)\) \(\chi_{6004}(1409,\cdot)\) \(\chi_{6004}(1465,\cdot)\) \(\chi_{6004}(1485,\cdot)\) \(\chi_{6004}(1497,\cdot)\) \(\chi_{6004}(1549,\cdot)\) \(\chi_{6004}(1609,\cdot)\) \(\chi_{6004}(1617,\cdot)\) \(\chi_{6004}(1693,\cdot)\) \(\chi_{6004}(1713,\cdot)\) \(\chi_{6004}(1777,\cdot)\) \(\chi_{6004}(1781,\cdot)\) \(\chi_{6004}(1845,\cdot)\) \(\chi_{6004}(1877,\cdot)\) \(\chi_{6004}(1933,\cdot)\) \(\chi_{6004}(2009,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((3003,2529,3953)\) → \((1,e\left(\frac{11}{18}\right),e\left(\frac{77}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{117}\right)\) | \(e\left(\frac{115}{117}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{101}{117}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{145}{234}\right)\) | \(e\left(\frac{107}{117}\right)\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{215}{234}\right)\) | \(e\left(\frac{8}{9}\right)\) |