Basic properties
Modulus: | \(6004\) | |
Conductor: | \(6004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(234\) | 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 6004.et
\(\chi_{6004}(35,\cdot)\) \(\chi_{6004}(43,\cdot)\) \(\chi_{6004}(47,\cdot)\) \(\chi_{6004}(139,\cdot)\) \(\chi_{6004}(195,\cdot)\) \(\chi_{6004}(271,\cdot)\) \(\chi_{6004}(359,\cdot)\) \(\chi_{6004}(423,\cdot)\) \(\chi_{6004}(443,\cdot)\) \(\chi_{6004}(503,\cdot)\) \(\chi_{6004}(511,\cdot)\) \(\chi_{6004}(587,\cdot)\) \(\chi_{6004}(671,\cdot)\) \(\chi_{6004}(707,\cdot)\) \(\chi_{6004}(739,\cdot)\) \(\chi_{6004}(1087,\cdot)\) \(\chi_{6004}(1183,\cdot)\) \(\chi_{6004}(1251,\cdot)\) \(\chi_{6004}(1327,\cdot)\) \(\chi_{6004}(1339,\cdot)\) \(\chi_{6004}(1391,\cdot)\) \(\chi_{6004}(1499,\cdot)\) \(\chi_{6004}(1507,\cdot)\) \(\chi_{6004}(1555,\cdot)\) \(\chi_{6004}(1619,\cdot)\) \(\chi_{6004}(1639,\cdot)\) \(\chi_{6004}(1719,\cdot)\) \(\chi_{6004}(1887,\cdot)\) \(\chi_{6004}(1955,\cdot)\) \(\chi_{6004}(2023,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{117})$ |
Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((3003,2529,3953)\) → \((-1,e\left(\frac{8}{9}\right),e\left(\frac{25}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 6004 }(271, a) \) | \(1\) | \(1\) | \(e\left(\frac{44}{117}\right)\) | \(e\left(\frac{11}{117}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{88}{117}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{40}{117}\right)\) | \(e\left(\frac{55}{117}\right)\) | \(e\left(\frac{145}{234}\right)\) | \(e\left(\frac{23}{117}\right)\) | \(e\left(\frac{11}{18}\right)\) |