Basic properties
| Modulus: | \(2535\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(86,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2535.cd
\(\chi_{2535}(86,\cdot)\) \(\chi_{2535}(161,\cdot)\) \(\chi_{2535}(281,\cdot)\) \(\chi_{2535}(356,\cdot)\) \(\chi_{2535}(476,\cdot)\) \(\chi_{2535}(551,\cdot)\) \(\chi_{2535}(671,\cdot)\) \(\chi_{2535}(866,\cdot)\) \(\chi_{2535}(941,\cdot)\) \(\chi_{2535}(1061,\cdot)\) \(\chi_{2535}(1136,\cdot)\) \(\chi_{2535}(1256,\cdot)\) \(\chi_{2535}(1331,\cdot)\) \(\chi_{2535}(1526,\cdot)\) \(\chi_{2535}(1646,\cdot)\) \(\chi_{2535}(1721,\cdot)\) \(\chi_{2535}(1841,\cdot)\) \(\chi_{2535}(1916,\cdot)\) \(\chi_{2535}(2036,\cdot)\) \(\chi_{2535}(2111,\cdot)\) \(\chi_{2535}(2231,\cdot)\) \(\chi_{2535}(2306,\cdot)\) \(\chi_{2535}(2426,\cdot)\) \(\chi_{2535}(2501,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1691,1522,1861)\) → \((-1,1,e\left(\frac{41}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 2535 }(86, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(i\) | \(1\) |