Basic properties
| Modulus: | \(4056\) | |
| Conductor: | \(1352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1352}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4056.da
\(\chi_{4056}(43,\cdot)\) \(\chi_{4056}(283,\cdot)\) \(\chi_{4056}(355,\cdot)\) \(\chi_{4056}(595,\cdot)\) \(\chi_{4056}(667,\cdot)\) \(\chi_{4056}(907,\cdot)\) \(\chi_{4056}(979,\cdot)\) \(\chi_{4056}(1219,\cdot)\) \(\chi_{4056}(1291,\cdot)\) \(\chi_{4056}(1531,\cdot)\) \(\chi_{4056}(1603,\cdot)\) \(\chi_{4056}(1843,\cdot)\) \(\chi_{4056}(1915,\cdot)\) \(\chi_{4056}(2155,\cdot)\) \(\chi_{4056}(2227,\cdot)\) \(\chi_{4056}(2467,\cdot)\) \(\chi_{4056}(2539,\cdot)\) \(\chi_{4056}(2779,\cdot)\) \(\chi_{4056}(3091,\cdot)\) \(\chi_{4056}(3163,\cdot)\) \(\chi_{4056}(3475,\cdot)\) \(\chi_{4056}(3715,\cdot)\) \(\chi_{4056}(3787,\cdot)\) \(\chi_{4056}(4027,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,2029,2705,3889)\) → \((-1,-1,1,e\left(\frac{61}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4056 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) |