Basic properties
| Modulus: | \(4028\) | |
| Conductor: | \(4028\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4028.cd
\(\chi_{4028}(183,\cdot)\) \(\chi_{4028}(259,\cdot)\) \(\chi_{4028}(331,\cdot)\) \(\chi_{4028}(407,\cdot)\) \(\chi_{4028}(487,\cdot)\) \(\chi_{4028}(791,\cdot)\) \(\chi_{4028}(863,\cdot)\) \(\chi_{4028}(943,\cdot)\) \(\chi_{4028}(1243,\cdot)\) \(\chi_{4028}(1247,\cdot)\) \(\chi_{4028}(1319,\cdot)\) \(\chi_{4028}(1475,\cdot)\) \(\chi_{4028}(1547,\cdot)\) \(\chi_{4028}(1851,\cdot)\) \(\chi_{4028}(2003,\cdot)\) \(\chi_{4028}(2007,\cdot)\) \(\chi_{4028}(2083,\cdot)\) \(\chi_{4028}(2307,\cdot)\) \(\chi_{4028}(2535,\cdot)\) \(\chi_{4028}(3067,\cdot)\) \(\chi_{4028}(3143,\cdot)\) \(\chi_{4028}(3299,\cdot)\) \(\chi_{4028}(3375,\cdot)\) \(\chi_{4028}(3831,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2015,2757,2281)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{5}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4028 }(183, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) |