Basic properties
| Modulus: | \(4056\) | |
| Conductor: | \(4056\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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.dr
\(\chi_{4056}(11,\cdot)\) \(\chi_{4056}(59,\cdot)\) \(\chi_{4056}(227,\cdot)\) \(\chi_{4056}(275,\cdot)\) \(\chi_{4056}(323,\cdot)\) \(\chi_{4056}(371,\cdot)\) \(\chi_{4056}(539,\cdot)\) \(\chi_{4056}(635,\cdot)\) \(\chi_{4056}(683,\cdot)\) \(\chi_{4056}(851,\cdot)\) \(\chi_{4056}(899,\cdot)\) \(\chi_{4056}(947,\cdot)\) \(\chi_{4056}(1163,\cdot)\) \(\chi_{4056}(1211,\cdot)\) \(\chi_{4056}(1259,\cdot)\) \(\chi_{4056}(1307,\cdot)\) \(\chi_{4056}(1475,\cdot)\) \(\chi_{4056}(1523,\cdot)\) \(\chi_{4056}(1571,\cdot)\) \(\chi_{4056}(1619,\cdot)\) \(\chi_{4056}(1787,\cdot)\) \(\chi_{4056}(1835,\cdot)\) \(\chi_{4056}(1883,\cdot)\) \(\chi_{4056}(1931,\cdot)\) \(\chi_{4056}(2099,\cdot)\) \(\chi_{4056}(2147,\cdot)\) \(\chi_{4056}(2195,\cdot)\) \(\chi_{4056}(2243,\cdot)\) \(\chi_{4056}(2411,\cdot)\) \(\chi_{4056}(2459,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1015,2029,2705,3889)\) → \((-1,-1,-1,e\left(\frac{35}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4056 }(59, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{41}{78}\right)\) |