Basic properties
| Modulus: | \(2183\) | |
| Conductor: | \(2183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(348\) | 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 2183.bd
\(\chi_{2183}(29,\cdot)\) \(\chi_{2183}(45,\cdot)\) \(\chi_{2183}(51,\cdot)\) \(\chi_{2183}(66,\cdot)\) \(\chi_{2183}(88,\cdot)\) \(\chi_{2183}(125,\cdot)\) \(\chi_{2183}(134,\cdot)\) \(\chi_{2183}(140,\cdot)\) \(\chi_{2183}(171,\cdot)\) \(\chi_{2183}(193,\cdot)\) \(\chi_{2183}(199,\cdot)\) \(\chi_{2183}(230,\cdot)\) \(\chi_{2183}(245,\cdot)\) \(\chi_{2183}(251,\cdot)\) \(\chi_{2183}(282,\cdot)\) \(\chi_{2183}(304,\cdot)\) \(\chi_{2183}(310,\cdot)\) \(\chi_{2183}(341,\cdot)\) \(\chi_{2183}(399,\cdot)\) \(\chi_{2183}(430,\cdot)\) \(\chi_{2183}(458,\cdot)\) \(\chi_{2183}(489,\cdot)\) \(\chi_{2183}(547,\cdot)\) \(\chi_{2183}(584,\cdot)\) \(\chi_{2183}(606,\cdot)\) \(\chi_{2183}(615,\cdot)\) \(\chi_{2183}(643,\cdot)\) \(\chi_{2183}(652,\cdot)\) \(\chi_{2183}(658,\cdot)\) \(\chi_{2183}(674,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{348})$ |
| Fixed field: | Number field defined by a degree 348 polynomial (not computed) |
Values on generators
\((1889,297)\) → \((e\left(\frac{7}{12}\right),e\left(\frac{14}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2183 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{348}\right)\) | \(e\left(\frac{53}{174}\right)\) | \(e\left(\frac{23}{174}\right)\) | \(e\left(\frac{109}{348}\right)\) | \(e\left(\frac{43}{116}\right)\) | \(e\left(\frac{31}{87}\right)\) | \(e\left(\frac{23}{116}\right)\) | \(e\left(\frac{53}{87}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{33}{58}\right)\) |