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 \(\chi_{1501}(345,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.ex
\(\chi_{6004}(345,\cdot)\) \(\chi_{6004}(393,\cdot)\) \(\chi_{6004}(401,\cdot)\) \(\chi_{6004}(509,\cdot)\) \(\chi_{6004}(717,\cdot)\) \(\chi_{6004}(781,\cdot)\) \(\chi_{6004}(849,\cdot)\) \(\chi_{6004}(1093,\cdot)\) \(\chi_{6004}(1097,\cdot)\) \(\chi_{6004}(1169,\cdot)\) \(\chi_{6004}(1181,\cdot)\) \(\chi_{6004}(1397,\cdot)\) \(\chi_{6004}(1457,\cdot)\) \(\chi_{6004}(1561,\cdot)\) \(\chi_{6004}(1725,\cdot)\) \(\chi_{6004}(1801,\cdot)\) \(\chi_{6004}(1865,\cdot)\) \(\chi_{6004}(2005,\cdot)\) \(\chi_{6004}(2029,\cdot)\) \(\chi_{6004}(2093,\cdot)\) \(\chi_{6004}(2377,\cdot)\) \(\chi_{6004}(2637,\cdot)\) \(\chi_{6004}(2673,\cdot)\) \(\chi_{6004}(2681,\cdot)\) \(\chi_{6004}(2689,\cdot)\) \(\chi_{6004}(2693,\cdot)\) \(\chi_{6004}(2749,\cdot)\) \(\chi_{6004}(2833,\cdot)\) \(\chi_{6004}(2929,\cdot)\) \(\chi_{6004}(2977,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((3003,2529,3953)\) → \((1,e\left(\frac{13}{18}\right),e\left(\frac{11}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(345, a) \) | \(1\) | \(1\) | \(e\left(\frac{62}{117}\right)\) | \(e\left(\frac{35}{117}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{7}{117}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{95}{234}\right)\) | \(e\left(\frac{97}{117}\right)\) | \(e\left(\frac{43}{234}\right)\) | \(e\left(\frac{79}{234}\right)\) | \(e\left(\frac{1}{9}\right)\) |