Basic properties
| Modulus: | \(2183\) | |
| Conductor: | \(2183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(174\) | 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.ba
\(\chi_{2183}(10,\cdot)\) \(\chi_{2183}(47,\cdot)\) \(\chi_{2183}(158,\cdot)\) \(\chi_{2183}(174,\cdot)\) \(\chi_{2183}(195,\cdot)\) \(\chi_{2183}(211,\cdot)\) \(\chi_{2183}(232,\cdot)\) \(\chi_{2183}(269,\cdot)\) \(\chi_{2183}(306,\cdot)\) \(\chi_{2183}(396,\cdot)\) \(\chi_{2183}(528,\cdot)\) \(\chi_{2183}(544,\cdot)\) \(\chi_{2183}(565,\cdot)\) \(\chi_{2183}(581,\cdot)\) \(\chi_{2183}(655,\cdot)\) \(\chi_{2183}(692,\cdot)\) \(\chi_{2183}(750,\cdot)\) \(\chi_{2183}(840,\cdot)\) \(\chi_{2183}(898,\cdot)\) \(\chi_{2183}(935,\cdot)\) \(\chi_{2183}(988,\cdot)\) \(\chi_{2183}(1009,\cdot)\) \(\chi_{2183}(1046,\cdot)\) \(\chi_{2183}(1099,\cdot)\) \(\chi_{2183}(1173,\cdot)\) \(\chi_{2183}(1194,\cdot)\) \(\chi_{2183}(1210,\cdot)\) \(\chi_{2183}(1247,\cdot)\) \(\chi_{2183}(1321,\cdot)\) \(\chi_{2183}(1342,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{87})$ |
| Fixed field: | Number field defined by a degree 174 polynomial (not computed) |
Values on generators
\((1889,297)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{7}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2183 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{137}{174}\right)\) | \(e\left(\frac{32}{87}\right)\) | \(e\left(\frac{50}{87}\right)\) | \(e\left(\frac{5}{87}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{44}{87}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{64}{87}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{1}{58}\right)\) |