Basic properties
| Modulus: | \(4056\) | |
| Conductor: | \(4056\) | 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 4056.cv
\(\chi_{4056}(35,\cdot)\) \(\chi_{4056}(107,\cdot)\) \(\chi_{4056}(347,\cdot)\) \(\chi_{4056}(419,\cdot)\) \(\chi_{4056}(659,\cdot)\) \(\chi_{4056}(731,\cdot)\) \(\chi_{4056}(971,\cdot)\) \(\chi_{4056}(1043,\cdot)\) \(\chi_{4056}(1283,\cdot)\) \(\chi_{4056}(1355,\cdot)\) \(\chi_{4056}(1595,\cdot)\) \(\chi_{4056}(1907,\cdot)\) \(\chi_{4056}(1979,\cdot)\) \(\chi_{4056}(2291,\cdot)\) \(\chi_{4056}(2531,\cdot)\) \(\chi_{4056}(2603,\cdot)\) \(\chi_{4056}(2843,\cdot)\) \(\chi_{4056}(2915,\cdot)\) \(\chi_{4056}(3155,\cdot)\) \(\chi_{4056}(3227,\cdot)\) \(\chi_{4056}(3467,\cdot)\) \(\chi_{4056}(3539,\cdot)\) \(\chi_{4056}(3779,\cdot)\) \(\chi_{4056}(3851,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,2029,2705,3889)\) → \((-1,-1,-1,e\left(\frac{29}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4056 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{59}{78}\right)\) |