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 \(\chi_{1501}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.el
\(\chi_{6004}(33,\cdot)\) \(\chi_{6004}(41,\cdot)\) \(\chi_{6004}(173,\cdot)\) \(\chi_{6004}(185,\cdot)\) \(\chi_{6004}(249,\cdot)\) \(\chi_{6004}(333,\cdot)\) \(\chi_{6004}(357,\cdot)\) \(\chi_{6004}(409,\cdot)\) \(\chi_{6004}(489,\cdot)\) \(\chi_{6004}(545,\cdot)\) \(\chi_{6004}(565,\cdot)\) \(\chi_{6004}(649,\cdot)\) \(\chi_{6004}(725,\cdot)\) \(\chi_{6004}(965,\cdot)\) \(\chi_{6004}(1009,\cdot)\) \(\chi_{6004}(1017,\cdot)\) \(\chi_{6004}(1041,\cdot)\) \(\chi_{6004}(1085,\cdot)\) \(\chi_{6004}(1305,\cdot)\) \(\chi_{6004}(1321,\cdot)\) \(\chi_{6004}(1325,\cdot)\) \(\chi_{6004}(1333,\cdot)\) \(\chi_{6004}(1401,\cdot)\) \(\chi_{6004}(1637,\cdot)\) \(\chi_{6004}(1649,\cdot)\) \(\chi_{6004}(1913,\cdot)\) \(\chi_{6004}(1929,\cdot)\) \(\chi_{6004}(1953,\cdot)\) \(\chi_{6004}(1989,\cdot)\) \(\chi_{6004}(2081,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((3003,2529,3953)\) → \((1,e\left(\frac{7}{18}\right),e\left(\frac{23}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{110}{117}\right)\) | \(e\left(\frac{8}{117}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{103}{117}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{5}{234}\right)\) | \(e\left(\frac{1}{117}\right)\) | \(e\left(\frac{109}{234}\right)\) | \(e\left(\frac{37}{234}\right)\) | \(e\left(\frac{7}{9}\right)\) |