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.by
\(\chi_{4028}(255,\cdot)\) \(\chi_{4028}(335,\cdot)\) \(\chi_{4028}(411,\cdot)\) \(\chi_{4028}(483,\cdot)\) \(\chi_{4028}(559,\cdot)\) \(\chi_{4028}(939,\cdot)\) \(\chi_{4028}(1395,\cdot)\) \(\chi_{4028}(1471,\cdot)\) \(\chi_{4028}(1627,\cdot)\) \(\chi_{4028}(1703,\cdot)\) \(\chi_{4028}(2235,\cdot)\) \(\chi_{4028}(2463,\cdot)\) \(\chi_{4028}(2687,\cdot)\) \(\chi_{4028}(2763,\cdot)\) \(\chi_{4028}(2767,\cdot)\) \(\chi_{4028}(2919,\cdot)\) \(\chi_{4028}(3223,\cdot)\) \(\chi_{4028}(3295,\cdot)\) \(\chi_{4028}(3451,\cdot)\) \(\chi_{4028}(3523,\cdot)\) \(\chi_{4028}(3527,\cdot)\) \(\chi_{4028}(3827,\cdot)\) \(\chi_{4028}(3907,\cdot)\) \(\chi_{4028}(3979,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2015,2757,2281)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{11}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4028 }(255, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) |