Basic properties
| Modulus: | \(4056\) | |
| Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{676}(55,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4056.cw
\(\chi_{4056}(55,\cdot)\) \(\chi_{4056}(295,\cdot)\) \(\chi_{4056}(367,\cdot)\) \(\chi_{4056}(607,\cdot)\) \(\chi_{4056}(679,\cdot)\) \(\chi_{4056}(919,\cdot)\) \(\chi_{4056}(1231,\cdot)\) \(\chi_{4056}(1303,\cdot)\) \(\chi_{4056}(1615,\cdot)\) \(\chi_{4056}(1855,\cdot)\) \(\chi_{4056}(1927,\cdot)\) \(\chi_{4056}(2167,\cdot)\) \(\chi_{4056}(2239,\cdot)\) \(\chi_{4056}(2479,\cdot)\) \(\chi_{4056}(2551,\cdot)\) \(\chi_{4056}(2791,\cdot)\) \(\chi_{4056}(2863,\cdot)\) \(\chi_{4056}(3103,\cdot)\) \(\chi_{4056}(3175,\cdot)\) \(\chi_{4056}(3415,\cdot)\) \(\chi_{4056}(3487,\cdot)\) \(\chi_{4056}(3727,\cdot)\) \(\chi_{4056}(3799,\cdot)\) \(\chi_{4056}(4039,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1015,2029,2705,3889)\) → \((-1,1,1,e\left(\frac{28}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4056 }(55, a) \) | \(-1\) | \(1\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{61}{78}\right)\) |