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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4028.cc
\(\chi_{4028}(7,\cdot)\) \(\chi_{4028}(11,\cdot)\) \(\chi_{4028}(163,\cdot)\) \(\chi_{4028}(467,\cdot)\) \(\chi_{4028}(539,\cdot)\) \(\chi_{4028}(695,\cdot)\) \(\chi_{4028}(767,\cdot)\) \(\chi_{4028}(771,\cdot)\) \(\chi_{4028}(1071,\cdot)\) \(\chi_{4028}(1151,\cdot)\) \(\chi_{4028}(1223,\cdot)\) \(\chi_{4028}(1527,\cdot)\) \(\chi_{4028}(1607,\cdot)\) \(\chi_{4028}(1683,\cdot)\) \(\chi_{4028}(1755,\cdot)\) \(\chi_{4028}(1831,\cdot)\) \(\chi_{4028}(2211,\cdot)\) \(\chi_{4028}(2667,\cdot)\) \(\chi_{4028}(2743,\cdot)\) \(\chi_{4028}(2899,\cdot)\) \(\chi_{4028}(2975,\cdot)\) \(\chi_{4028}(3507,\cdot)\) \(\chi_{4028}(3735,\cdot)\) \(\chi_{4028}(3959,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2015,2757,2281)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{7}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4028 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) |