Basic properties
| Modulus: | \(1343\) | |
| Conductor: | \(1343\) | 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 1343.ba
\(\chi_{1343}(21,\cdot)\) \(\chi_{1343}(38,\cdot)\) \(\chi_{1343}(64,\cdot)\) \(\chi_{1343}(89,\cdot)\) \(\chi_{1343}(166,\cdot)\) \(\chi_{1343}(225,\cdot)\) \(\chi_{1343}(259,\cdot)\) \(\chi_{1343}(302,\cdot)\) \(\chi_{1343}(378,\cdot)\) \(\chi_{1343}(574,\cdot)\) \(\chi_{1343}(591,\cdot)\) \(\chi_{1343}(599,\cdot)\) \(\chi_{1343}(642,\cdot)\) \(\chi_{1343}(650,\cdot)\) \(\chi_{1343}(684,\cdot)\) \(\chi_{1343}(778,\cdot)\) \(\chi_{1343}(812,\cdot)\) \(\chi_{1343}(854,\cdot)\) \(\chi_{1343}(931,\cdot)\) \(\chi_{1343}(956,\cdot)\) \(\chi_{1343}(1092,\cdot)\) \(\chi_{1343}(1152,\cdot)\) \(\chi_{1343}(1203,\cdot)\) \(\chi_{1343}(1237,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((870,477)\) → \((-i,e\left(\frac{9}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1343 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{17}{52}\right)\) |