Basic properties
| Modulus: | \(2183\) | |
| Conductor: | \(2183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(261\) | 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 2183.bc
\(\chi_{2183}(7,\cdot)\) \(\chi_{2183}(9,\cdot)\) \(\chi_{2183}(12,\cdot)\) \(\chi_{2183}(16,\cdot)\) \(\chi_{2183}(46,\cdot)\) \(\chi_{2183}(49,\cdot)\) \(\chi_{2183}(53,\cdot)\) \(\chi_{2183}(71,\cdot)\) \(\chi_{2183}(81,\cdot)\) \(\chi_{2183}(86,\cdot)\) \(\chi_{2183}(107,\cdot)\) \(\chi_{2183}(108,\cdot)\) \(\chi_{2183}(123,\cdot)\) \(\chi_{2183}(127,\cdot)\) \(\chi_{2183}(144,\cdot)\) \(\chi_{2183}(145,\cdot)\) \(\chi_{2183}(164,\cdot)\) \(\chi_{2183}(181,\cdot)\) \(\chi_{2183}(182,\cdot)\) \(\chi_{2183}(192,\cdot)\) \(\chi_{2183}(194,\cdot)\) \(\chi_{2183}(197,\cdot)\) \(\chi_{2183}(218,\cdot)\) \(\chi_{2183}(234,\cdot)\) \(\chi_{2183}(255,\cdot)\) \(\chi_{2183}(256,\cdot)\) \(\chi_{2183}(271,\cdot)\) \(\chi_{2183}(293,\cdot)\) \(\chi_{2183}(312,\cdot)\) \(\chi_{2183}(330,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{261})$ |
| Fixed field: | Number field defined by a degree 261 polynomial (not computed) |
Values on generators
\((1889,297)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{21}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2183 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{44}{261}\right)\) | \(e\left(\frac{199}{261}\right)\) | \(e\left(\frac{88}{261}\right)\) | \(e\left(\frac{148}{261}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{67}{261}\right)\) | \(e\left(\frac{44}{87}\right)\) | \(e\left(\frac{137}{261}\right)\) | \(e\left(\frac{64}{87}\right)\) | \(e\left(\frac{38}{87}\right)\) |