Basic properties
| Modulus: | \(4056\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(48,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4056.cm
\(\chi_{4056}(217,\cdot)\) \(\chi_{4056}(289,\cdot)\) \(\chi_{4056}(601,\cdot)\) \(\chi_{4056}(841,\cdot)\) \(\chi_{4056}(913,\cdot)\) \(\chi_{4056}(1153,\cdot)\) \(\chi_{4056}(1225,\cdot)\) \(\chi_{4056}(1465,\cdot)\) \(\chi_{4056}(1537,\cdot)\) \(\chi_{4056}(1777,\cdot)\) \(\chi_{4056}(1849,\cdot)\) \(\chi_{4056}(2089,\cdot)\) \(\chi_{4056}(2161,\cdot)\) \(\chi_{4056}(2401,\cdot)\) \(\chi_{4056}(2473,\cdot)\) \(\chi_{4056}(2713,\cdot)\) \(\chi_{4056}(2785,\cdot)\) \(\chi_{4056}(3025,\cdot)\) \(\chi_{4056}(3097,\cdot)\) \(\chi_{4056}(3337,\cdot)\) \(\chi_{4056}(3409,\cdot)\) \(\chi_{4056}(3649,\cdot)\) \(\chi_{4056}(3721,\cdot)\) \(\chi_{4056}(3961,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((1015,2029,2705,3889)\) → \((1,1,1,e\left(\frac{32}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4056 }(217, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) |