Basic properties
| Modulus: | \(1343\) | |
| Conductor: | \(1343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(624\) | 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.bm
\(\chi_{1343}(3,\cdot)\) \(\chi_{1343}(6,\cdot)\) \(\chi_{1343}(7,\cdot)\) \(\chi_{1343}(28,\cdot)\) \(\chi_{1343}(29,\cdot)\) \(\chi_{1343}(37,\cdot)\) \(\chi_{1343}(39,\cdot)\) \(\chi_{1343}(48,\cdot)\) \(\chi_{1343}(54,\cdot)\) \(\chi_{1343}(63,\cdot)\) \(\chi_{1343}(74,\cdot)\) \(\chi_{1343}(75,\cdot)\) \(\chi_{1343}(82,\cdot)\) \(\chi_{1343}(107,\cdot)\) \(\chi_{1343}(108,\cdot)\) \(\chi_{1343}(109,\cdot)\) \(\chi_{1343}(113,\cdot)\) \(\chi_{1343}(114,\cdot)\) \(\chi_{1343}(116,\cdot)\) \(\chi_{1343}(122,\cdot)\) \(\chi_{1343}(126,\cdot)\) \(\chi_{1343}(133,\cdot)\) \(\chi_{1343}(139,\cdot)\) \(\chi_{1343}(142,\cdot)\) \(\chi_{1343}(147,\cdot)\) \(\chi_{1343}(156,\cdot)\) \(\chi_{1343}(164,\cdot)\) \(\chi_{1343}(165,\cdot)\) \(\chi_{1343}(192,\cdot)\) \(\chi_{1343}(193,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{624})$ |
| Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((870,477)\) → \((e\left(\frac{15}{16}\right),e\left(\frac{53}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1343 }(244, a) \) | \(1\) | \(1\) | \(e\left(\frac{263}{312}\right)\) | \(e\left(\frac{385}{624}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{509}{624}\right)\) | \(e\left(\frac{287}{624}\right)\) | \(e\left(\frac{203}{624}\right)\) | \(e\left(\frac{55}{104}\right)\) | \(e\left(\frac{73}{312}\right)\) | \(e\left(\frac{137}{208}\right)\) | \(e\left(\frac{479}{624}\right)\) |