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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4056.db
\(\chi_{4056}(29,\cdot)\) \(\chi_{4056}(269,\cdot)\) \(\chi_{4056}(341,\cdot)\) \(\chi_{4056}(581,\cdot)\) \(\chi_{4056}(893,\cdot)\) \(\chi_{4056}(965,\cdot)\) \(\chi_{4056}(1277,\cdot)\) \(\chi_{4056}(1517,\cdot)\) \(\chi_{4056}(1589,\cdot)\) \(\chi_{4056}(1829,\cdot)\) \(\chi_{4056}(1901,\cdot)\) \(\chi_{4056}(2141,\cdot)\) \(\chi_{4056}(2213,\cdot)\) \(\chi_{4056}(2453,\cdot)\) \(\chi_{4056}(2525,\cdot)\) \(\chi_{4056}(2765,\cdot)\) \(\chi_{4056}(2837,\cdot)\) \(\chi_{4056}(3077,\cdot)\) \(\chi_{4056}(3149,\cdot)\) \(\chi_{4056}(3389,\cdot)\) \(\chi_{4056}(3461,\cdot)\) \(\chi_{4056}(3701,\cdot)\) \(\chi_{4056}(3773,\cdot)\) \(\chi_{4056}(4013,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,2029,2705,3889)\) → \((1,-1,-1,e\left(\frac{10}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4056 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{29}{39}\right)\) |