Basic properties
Modulus: | \(4056\) | |
Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{676}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4056.ct
\(\chi_{4056}(31,\cdot)\) \(\chi_{4056}(151,\cdot)\) \(\chi_{4056}(343,\cdot)\) \(\chi_{4056}(463,\cdot)\) \(\chi_{4056}(655,\cdot)\) \(\chi_{4056}(967,\cdot)\) \(\chi_{4056}(1087,\cdot)\) \(\chi_{4056}(1279,\cdot)\) \(\chi_{4056}(1399,\cdot)\) \(\chi_{4056}(1711,\cdot)\) \(\chi_{4056}(1903,\cdot)\) \(\chi_{4056}(2023,\cdot)\) \(\chi_{4056}(2215,\cdot)\) \(\chi_{4056}(2335,\cdot)\) \(\chi_{4056}(2527,\cdot)\) \(\chi_{4056}(2647,\cdot)\) \(\chi_{4056}(2839,\cdot)\) \(\chi_{4056}(2959,\cdot)\) \(\chi_{4056}(3151,\cdot)\) \(\chi_{4056}(3271,\cdot)\) \(\chi_{4056}(3463,\cdot)\) \(\chi_{4056}(3583,\cdot)\) \(\chi_{4056}(3775,\cdot)\) \(\chi_{4056}(3895,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1015,2029,2705,3889)\) → \((-1,1,1,e\left(\frac{7}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 4056 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(i\) | \(1\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{3}{26}\right)\) |