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 \(\chi_{169}(73,\cdot)\) | 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
\((1015,2029,2705,3889)\) → \((1,1,1,e\left(\frac{17}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 4056 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(i\) | \(-1\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{12}{13}\right)\) |