Basic properties
| Modulus: | \(2183\) | |
| Conductor: | \(2183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(116\) | 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.x
\(\chi_{2183}(68,\cdot)\) \(\chi_{2183}(80,\cdot)\) \(\chi_{2183}(105,\cdot)\) \(\chi_{2183}(154,\cdot)\) \(\chi_{2183}(228,\cdot)\) \(\chi_{2183}(253,\cdot)\) \(\chi_{2183}(265,\cdot)\) \(\chi_{2183}(302,\cdot)\) \(\chi_{2183}(376,\cdot)\) \(\chi_{2183}(438,\cdot)\) \(\chi_{2183}(475,\cdot)\) \(\chi_{2183}(487,\cdot)\) \(\chi_{2183}(635,\cdot)\) \(\chi_{2183}(697,\cdot)\) \(\chi_{2183}(734,\cdot)\) \(\chi_{2183}(771,\cdot)\) \(\chi_{2183}(783,\cdot)\) \(\chi_{2183}(808,\cdot)\) \(\chi_{2183}(820,\cdot)\) \(\chi_{2183}(845,\cdot)\) \(\chi_{2183}(894,\cdot)\) \(\chi_{2183}(931,\cdot)\) \(\chi_{2183}(956,\cdot)\) \(\chi_{2183}(993,\cdot)\) \(\chi_{2183}(1030,\cdot)\) \(\chi_{2183}(1067,\cdot)\) \(\chi_{2183}(1079,\cdot)\) \(\chi_{2183}(1141,\cdot)\) \(\chi_{2183}(1178,\cdot)\) \(\chi_{2183}(1215,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{116})$ |
| Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((1889,297)\) → \((i,e\left(\frac{6}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2183 }(438, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{116}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{115}{116}\right)\) | \(e\left(\frac{35}{116}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{43}{116}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{39}{58}\right)\) |