Basic properties
| Modulus: | \(4056\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4056.cx
\(\chi_{4056}(17,\cdot)\) \(\chi_{4056}(257,\cdot)\) \(\chi_{4056}(329,\cdot)\) \(\chi_{4056}(569,\cdot)\) \(\chi_{4056}(641,\cdot)\) \(\chi_{4056}(881,\cdot)\) \(\chi_{4056}(953,\cdot)\) \(\chi_{4056}(1193,\cdot)\) \(\chi_{4056}(1265,\cdot)\) \(\chi_{4056}(1505,\cdot)\) \(\chi_{4056}(1577,\cdot)\) \(\chi_{4056}(1817,\cdot)\) \(\chi_{4056}(1889,\cdot)\) \(\chi_{4056}(2129,\cdot)\) \(\chi_{4056}(2201,\cdot)\) \(\chi_{4056}(2441,\cdot)\) \(\chi_{4056}(2753,\cdot)\) \(\chi_{4056}(2825,\cdot)\) \(\chi_{4056}(3137,\cdot)\) \(\chi_{4056}(3377,\cdot)\) \(\chi_{4056}(3449,\cdot)\) \(\chi_{4056}(3689,\cdot)\) \(\chi_{4056}(3761,\cdot)\) \(\chi_{4056}(4001,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,2029,2705,3889)\) → \((1,1,-1,e\left(\frac{73}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4056 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{5}{78}\right)\) |