Basic properties
| Modulus: | \(6004\) | |
| Conductor: | \(1501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(117\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1501}(101,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.ec
\(\chi_{6004}(101,\cdot)\) \(\chi_{6004}(225,\cdot)\) \(\chi_{6004}(245,\cdot)\) \(\chi_{6004}(289,\cdot)\) \(\chi_{6004}(301,\cdot)\) \(\chi_{6004}(405,\cdot)\) \(\chi_{6004}(441,\cdot)\) \(\chi_{6004}(541,\cdot)\) \(\chi_{6004}(605,\cdot)\) \(\chi_{6004}(617,\cdot)\) \(\chi_{6004}(757,\cdot)\) \(\chi_{6004}(921,\cdot)\) \(\chi_{6004}(1013,\cdot)\) \(\chi_{6004}(1049,\cdot)\) \(\chi_{6004}(1073,\cdot)\) \(\chi_{6004}(1089,\cdot)\) \(\chi_{6004}(1353,\cdot)\) \(\chi_{6004}(1365,\cdot)\) \(\chi_{6004}(1601,\cdot)\) \(\chi_{6004}(1669,\cdot)\) \(\chi_{6004}(1677,\cdot)\) \(\chi_{6004}(1681,\cdot)\) \(\chi_{6004}(1697,\cdot)\) \(\chi_{6004}(1917,\cdot)\) \(\chi_{6004}(1961,\cdot)\) \(\chi_{6004}(1985,\cdot)\) \(\chi_{6004}(1993,\cdot)\) \(\chi_{6004}(2037,\cdot)\) \(\chi_{6004}(2277,\cdot)\) \(\chi_{6004}(2353,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 117 polynomial (not computed) |
Values on generators
\((3003,2529,3953)\) → \((1,e\left(\frac{7}{9}\right),e\left(\frac{12}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{117}\right)\) | \(e\left(\frac{79}{117}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{8}{117}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{32}{117}\right)\) | \(e\left(\frac{83}{117}\right)\) | \(e\left(\frac{19}{117}\right)\) | \(e\left(\frac{73}{117}\right)\) | \(e\left(\frac{5}{9}\right)\) |