Basic properties
| Modulus: | \(1343\) | |
| Conductor: | \(1343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(208\) | 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.bi
\(\chi_{1343}(12,\cdot)\) \(\chi_{1343}(14,\cdot)\) \(\chi_{1343}(27,\cdot)\) \(\chi_{1343}(41,\cdot)\) \(\chi_{1343}(57,\cdot)\) \(\chi_{1343}(58,\cdot)\) \(\chi_{1343}(61,\cdot)\) \(\chi_{1343}(71,\cdot)\) \(\chi_{1343}(91,\cdot)\) \(\chi_{1343}(96,\cdot)\) \(\chi_{1343}(112,\cdot)\) \(\chi_{1343}(148,\cdot)\) \(\chi_{1343}(150,\cdot)\) \(\chi_{1343}(173,\cdot)\) \(\chi_{1343}(175,\cdot)\) \(\chi_{1343}(199,\cdot)\) \(\chi_{1343}(215,\cdot)\) \(\chi_{1343}(216,\cdot)\) \(\chi_{1343}(227,\cdot)\) \(\chi_{1343}(249,\cdot)\) \(\chi_{1343}(252,\cdot)\) \(\chi_{1343}(278,\cdot)\) \(\chi_{1343}(294,\cdot)\) \(\chi_{1343}(295,\cdot)\) \(\chi_{1343}(328,\cdot)\) \(\chi_{1343}(330,\cdot)\) \(\chi_{1343}(333,\cdot)\) \(\chi_{1343}(343,\cdot)\) \(\chi_{1343}(377,\cdot)\) \(\chi_{1343}(385,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{208})$ |
| Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((870,477)\) → \((e\left(\frac{1}{16}\right),e\left(\frac{3}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1343 }(802, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{104}\right)\) | \(e\left(\frac{37}{208}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{97}{208}\right)\) | \(e\left(\frac{107}{208}\right)\) | \(e\left(\frac{167}{208}\right)\) | \(e\left(\frac{1}{104}\right)\) | \(e\left(\frac{37}{104}\right)\) | \(e\left(\frac{167}{208}\right)\) | \(e\left(\frac{59}{208}\right)\) |