Basic properties
| Modulus: | \(6004\) | |
| Conductor: | \(1501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1501}(145,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.cz
\(\chi_{6004}(145,\cdot)\) \(\chi_{6004}(221,\cdot)\) \(\chi_{6004}(369,\cdot)\) \(\chi_{6004}(449,\cdot)\) \(\chi_{6004}(521,\cdot)\) \(\chi_{6004}(977,\cdot)\) \(\chi_{6004}(1057,\cdot)\) \(\chi_{6004}(1741,\cdot)\) \(\chi_{6004}(1813,\cdot)\) \(\chi_{6004}(2193,\cdot)\) \(\chi_{6004}(2497,\cdot)\) \(\chi_{6004}(2725,\cdot)\) \(\chi_{6004}(2729,\cdot)\) \(\chi_{6004}(2881,\cdot)\) \(\chi_{6004}(2957,\cdot)\) \(\chi_{6004}(3109,\cdot)\) \(\chi_{6004}(3561,\cdot)\) \(\chi_{6004}(3869,\cdot)\) \(\chi_{6004}(3941,\cdot)\) \(\chi_{6004}(4325,\cdot)\) \(\chi_{6004}(4933,\cdot)\) \(\chi_{6004}(5537,\cdot)\) \(\chi_{6004}(5841,\cdot)\) \(\chi_{6004}(5993,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3003,2529,3953)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{73}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 6004 }(145, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(1\) |