Basic properties
| Modulus: | \(4056\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4056.cr
\(\chi_{4056}(73,\cdot)\) \(\chi_{4056}(265,\cdot)\) \(\chi_{4056}(385,\cdot)\) \(\chi_{4056}(697,\cdot)\) \(\chi_{4056}(889,\cdot)\) \(\chi_{4056}(1009,\cdot)\) \(\chi_{4056}(1201,\cdot)\) \(\chi_{4056}(1321,\cdot)\) \(\chi_{4056}(1513,\cdot)\) \(\chi_{4056}(1633,\cdot)\) \(\chi_{4056}(1825,\cdot)\) \(\chi_{4056}(1945,\cdot)\) \(\chi_{4056}(2137,\cdot)\) \(\chi_{4056}(2257,\cdot)\) \(\chi_{4056}(2449,\cdot)\) \(\chi_{4056}(2569,\cdot)\) \(\chi_{4056}(2761,\cdot)\) \(\chi_{4056}(2881,\cdot)\) \(\chi_{4056}(3073,\cdot)\) \(\chi_{4056}(3193,\cdot)\) \(\chi_{4056}(3385,\cdot)\) \(\chi_{4056}(3505,\cdot)\) \(\chi_{4056}(3697,\cdot)\) \(\chi_{4056}(4009,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1015,2029,2705,3889)\) → \((1,1,1,e\left(\frac{21}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4056 }(385, a) \) | \(-1\) | \(1\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(i\) | \(-1\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{11}{13}\right)\) |