Basic properties
| Modulus: | \(1343\) | |
| Conductor: | \(1343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(312\) | 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.bk
\(\chi_{1343}(2,\cdot)\) \(\chi_{1343}(9,\cdot)\) \(\chi_{1343}(19,\cdot)\) \(\chi_{1343}(25,\cdot)\) \(\chi_{1343}(26,\cdot)\) \(\chi_{1343}(32,\cdot)\) \(\chi_{1343}(36,\cdot)\) \(\chi_{1343}(42,\cdot)\) \(\chi_{1343}(49,\cdot)\) \(\chi_{1343}(76,\cdot)\) \(\chi_{1343}(83,\cdot)\) \(\chi_{1343}(104,\cdot)\) \(\chi_{1343}(110,\cdot)\) \(\chi_{1343}(111,\cdot)\) \(\chi_{1343}(121,\cdot)\) \(\chi_{1343}(128,\cdot)\) \(\chi_{1343}(151,\cdot)\) \(\chi_{1343}(155,\cdot)\) \(\chi_{1343}(162,\cdot)\) \(\chi_{1343}(178,\cdot)\) \(\chi_{1343}(189,\cdot)\) \(\chi_{1343}(202,\cdot)\) \(\chi_{1343}(230,\cdot)\) \(\chi_{1343}(246,\cdot)\) \(\chi_{1343}(253,\cdot)\) \(\chi_{1343}(257,\cdot)\) \(\chi_{1343}(263,\cdot)\) \(\chi_{1343}(281,\cdot)\) \(\chi_{1343}(287,\cdot)\) \(\chi_{1343}(321,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{312})$ |
| Fixed field: | Number field defined by a degree 312 polynomial (not computed) |
Values on generators
\((870,477)\) → \((e\left(\frac{5}{8}\right),e\left(\frac{5}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1343 }(1300, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{156}\right)\) | \(e\left(\frac{235}{312}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{23}{312}\right)\) | \(e\left(\frac{5}{312}\right)\) | \(e\left(\frac{209}{312}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{35}{104}\right)\) | \(e\left(\frac{29}{312}\right)\) |