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 \(\chi_{1501}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.ek
\(\chi_{6004}(17,\cdot)\) \(\chi_{6004}(61,\cdot)\) \(\chi_{6004}(93,\cdot)\) \(\chi_{6004}(137,\cdot)\) \(\chi_{6004}(377,\cdot)\) \(\chi_{6004}(385,\cdot)\) \(\chi_{6004}(453,\cdot)\) \(\chi_{6004}(689,\cdot)\) \(\chi_{6004}(693,\cdot)\) \(\chi_{6004}(701,\cdot)\) \(\chi_{6004}(769,\cdot)\) \(\chi_{6004}(861,\cdot)\) \(\chi_{6004}(1005,\cdot)\) \(\chi_{6004}(1297,\cdot)\) \(\chi_{6004}(1449,\cdot)\) \(\chi_{6004}(1613,\cdot)\) \(\chi_{6004}(1621,\cdot)\) \(\chi_{6004}(1753,\cdot)\) \(\chi_{6004}(1765,\cdot)\) \(\chi_{6004}(1809,\cdot)\) \(\chi_{6004}(1829,\cdot)\) \(\chi_{6004}(2069,\cdot)\) \(\chi_{6004}(2125,\cdot)\) \(\chi_{6004}(2145,\cdot)\) \(\chi_{6004}(2229,\cdot)\) \(\chi_{6004}(2305,\cdot)\) \(\chi_{6004}(2441,\cdot)\) \(\chi_{6004}(2569,\cdot)\) \(\chi_{6004}(2589,\cdot)\) \(\chi_{6004}(2665,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((3003,2529,3953)\) → \((1,e\left(\frac{5}{9}\right),e\left(\frac{7}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{115}{234}\right)\) | \(e\left(\frac{68}{117}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{115}{117}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{109}{117}\right)\) | \(e\left(\frac{17}{234}\right)\) | \(e\left(\frac{49}{234}\right)\) | \(e\left(\frac{11}{117}\right)\) | \(e\left(\frac{1}{9}\right)\) |