Basic properties
| Modulus: | \(2028\) | |
| Conductor: | \(2028\) | 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 2028.bp
\(\chi_{2028}(35,\cdot)\) \(\chi_{2028}(107,\cdot)\) \(\chi_{2028}(263,\cdot)\) \(\chi_{2028}(347,\cdot)\) \(\chi_{2028}(419,\cdot)\) \(\chi_{2028}(503,\cdot)\) \(\chi_{2028}(575,\cdot)\) \(\chi_{2028}(659,\cdot)\) \(\chi_{2028}(731,\cdot)\) \(\chi_{2028}(815,\cdot)\) \(\chi_{2028}(887,\cdot)\) \(\chi_{2028}(971,\cdot)\) \(\chi_{2028}(1043,\cdot)\) \(\chi_{2028}(1127,\cdot)\) \(\chi_{2028}(1199,\cdot)\) \(\chi_{2028}(1283,\cdot)\) \(\chi_{2028}(1355,\cdot)\) \(\chi_{2028}(1439,\cdot)\) \(\chi_{2028}(1511,\cdot)\) \(\chi_{2028}(1595,\cdot)\) \(\chi_{2028}(1751,\cdot)\) \(\chi_{2028}(1823,\cdot)\) \(\chi_{2028}(1907,\cdot)\) \(\chi_{2028}(1979,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,677,1861)\) → \((-1,-1,e\left(\frac{29}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2028 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{10}{39}\right)\) |