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.ee
\(\chi_{6004}(63,\cdot)\) \(\chi_{6004}(187,\cdot)\) \(\chi_{6004}(291,\cdot)\) \(\chi_{6004}(351,\cdot)\) \(\chi_{6004}(899,\cdot)\) \(\chi_{6004}(935,\cdot)\) \(\chi_{6004}(955,\cdot)\) \(\chi_{6004}(1011,\cdot)\) \(\chi_{6004}(1023,\cdot)\) \(\chi_{6004}(1239,\cdot)\) \(\chi_{6004}(1259,\cdot)\) \(\chi_{6004}(1271,\cdot)\) \(\chi_{6004}(1403,\cdot)\) \(\chi_{6004}(1411,\cdot)\) \(\chi_{6004}(1567,\cdot)\) \(\chi_{6004}(1575,\cdot)\) \(\chi_{6004}(1583,\cdot)\) \(\chi_{6004}(1643,\cdot)\) \(\chi_{6004}(1707,\cdot)\) \(\chi_{6004}(1727,\cdot)\) \(\chi_{6004}(1791,\cdot)\) \(\chi_{6004}(1847,\cdot)\) \(\chi_{6004}(1871,\cdot)\) \(\chi_{6004}(1935,\cdot)\) \(\chi_{6004}(1943,\cdot)\) \(\chi_{6004}(2107,\cdot)\) \(\chi_{6004}(2259,\cdot)\) \(\chi_{6004}(2399,\cdot)\) \(\chi_{6004}(2479,\cdot)\) \(\chi_{6004}(2531,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{117})$ |
Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((3003,2529,3953)\) → \((-1,e\left(\frac{8}{9}\right),e\left(\frac{23}{78}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 6004 }(1259, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{117}\right)\) | \(e\left(\frac{59}{117}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{82}{117}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{55}{117}\right)\) | \(e\left(\frac{100}{117}\right)\) | \(e\left(\frac{19}{234}\right)\) | \(e\left(\frac{95}{117}\right)\) | \(e\left(\frac{17}{18}\right)\) |