Basic properties
| Modulus: | \(1352\) | |
| Conductor: | \(1352\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1352.bj
\(\chi_{1352}(5,\cdot)\) \(\chi_{1352}(21,\cdot)\) \(\chi_{1352}(109,\cdot)\) \(\chi_{1352}(125,\cdot)\) \(\chi_{1352}(213,\cdot)\) \(\chi_{1352}(229,\cdot)\) \(\chi_{1352}(317,\cdot)\) \(\chi_{1352}(333,\cdot)\) \(\chi_{1352}(421,\cdot)\) \(\chi_{1352}(525,\cdot)\) \(\chi_{1352}(541,\cdot)\) \(\chi_{1352}(629,\cdot)\) \(\chi_{1352}(645,\cdot)\) \(\chi_{1352}(733,\cdot)\) \(\chi_{1352}(749,\cdot)\) \(\chi_{1352}(837,\cdot)\) \(\chi_{1352}(853,\cdot)\) \(\chi_{1352}(941,\cdot)\) \(\chi_{1352}(957,\cdot)\) \(\chi_{1352}(1045,\cdot)\) \(\chi_{1352}(1061,\cdot)\) \(\chi_{1352}(1149,\cdot)\) \(\chi_{1352}(1165,\cdot)\) \(\chi_{1352}(1269,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1015,677,1185)\) → \((1,-1,e\left(\frac{17}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1352 }(749, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(-i\) | \(e\left(\frac{1}{52}\right)\) | \(-1\) |