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 \(\chi_{1501}(21,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.er
\(\chi_{6004}(21,\cdot)\) \(\chi_{6004}(89,\cdot)\) \(\chi_{6004}(97,\cdot)\) \(\chi_{6004}(117,\cdot)\) \(\chi_{6004}(337,\cdot)\) \(\chi_{6004}(413,\cdot)\) \(\chi_{6004}(433,\cdot)\) \(\chi_{6004}(561,\cdot)\) \(\chi_{6004}(697,\cdot)\) \(\chi_{6004}(773,\cdot)\) \(\chi_{6004}(857,\cdot)\) \(\chi_{6004}(877,\cdot)\) \(\chi_{6004}(933,\cdot)\) \(\chi_{6004}(1173,\cdot)\) \(\chi_{6004}(1193,\cdot)\) \(\chi_{6004}(1237,\cdot)\) \(\chi_{6004}(1249,\cdot)\) \(\chi_{6004}(1381,\cdot)\) \(\chi_{6004}(1389,\cdot)\) \(\chi_{6004}(1553,\cdot)\) \(\chi_{6004}(1705,\cdot)\) \(\chi_{6004}(1997,\cdot)\) \(\chi_{6004}(2141,\cdot)\) \(\chi_{6004}(2233,\cdot)\) \(\chi_{6004}(2301,\cdot)\) \(\chi_{6004}(2309,\cdot)\) \(\chi_{6004}(2313,\cdot)\) \(\chi_{6004}(2549,\cdot)\) \(\chi_{6004}(2617,\cdot)\) \(\chi_{6004}(2625,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((3003,2529,3953)\) → \((1,e\left(\frac{1}{18}\right),e\left(\frac{9}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(21, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{234}\right)\) | \(e\left(\frac{95}{117}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{97}{117}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{191}{234}\right)\) | \(e\left(\frac{53}{234}\right)\) | \(e\left(\frac{11}{117}\right)\) | \(e\left(\frac{103}{234}\right)\) | \(e\left(\frac{1}{9}\right)\) |