Basic properties
Modulus: | \(2535\) | |
Conductor: | \(2535\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2535.cf
\(\chi_{2535}(53,\cdot)\) \(\chi_{2535}(92,\cdot)\) \(\chi_{2535}(248,\cdot)\) \(\chi_{2535}(287,\cdot)\) \(\chi_{2535}(443,\cdot)\) \(\chi_{2535}(482,\cdot)\) \(\chi_{2535}(638,\cdot)\) \(\chi_{2535}(833,\cdot)\) \(\chi_{2535}(872,\cdot)\) \(\chi_{2535}(1028,\cdot)\) \(\chi_{2535}(1067,\cdot)\) \(\chi_{2535}(1223,\cdot)\) \(\chi_{2535}(1262,\cdot)\) \(\chi_{2535}(1418,\cdot)\) \(\chi_{2535}(1457,\cdot)\) \(\chi_{2535}(1613,\cdot)\) \(\chi_{2535}(1652,\cdot)\) \(\chi_{2535}(1808,\cdot)\) \(\chi_{2535}(1847,\cdot)\) \(\chi_{2535}(2003,\cdot)\) \(\chi_{2535}(2042,\cdot)\) \(\chi_{2535}(2237,\cdot)\) \(\chi_{2535}(2393,\cdot)\) \(\chi_{2535}(2432,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1691,1522,1861)\) → \((-1,-i,e\left(\frac{10}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 2535 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(-1\) | \(-i\) |