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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2183.z
\(\chi_{2183}(27,\cdot)\) \(\chi_{2183}(48,\cdot)\) \(\chi_{2183}(64,\cdot)\) \(\chi_{2183}(85,\cdot)\) \(\chi_{2183}(122,\cdot)\) \(\chi_{2183}(138,\cdot)\) \(\chi_{2183}(159,\cdot)\) \(\chi_{2183}(175,\cdot)\) \(\chi_{2183}(196,\cdot)\) \(\chi_{2183}(212,\cdot)\) \(\chi_{2183}(307,\cdot)\) \(\chi_{2183}(323,\cdot)\) \(\chi_{2183}(344,\cdot)\) \(\chi_{2183}(381,\cdot)\) \(\chi_{2183}(418,\cdot)\) \(\chi_{2183}(434,\cdot)\) \(\chi_{2183}(492,\cdot)\) \(\chi_{2183}(508,\cdot)\) \(\chi_{2183}(529,\cdot)\) \(\chi_{2183}(566,\cdot)\) \(\chi_{2183}(582,\cdot)\) \(\chi_{2183}(619,\cdot)\) \(\chi_{2183}(656,\cdot)\) \(\chi_{2183}(677,\cdot)\) \(\chi_{2183}(730,\cdot)\) \(\chi_{2183}(788,\cdot)\) \(\chi_{2183}(841,\cdot)\) \(\chi_{2183}(862,\cdot)\) \(\chi_{2183}(936,\cdot)\) \(\chi_{2183}(973,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{87})$ |
| Fixed field: | Number field defined by a degree 174 polynomial (not computed) |
Values on generators
\((1889,297)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{17}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2183 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{131}{174}\right)\) | \(e\left(\frac{56}{87}\right)\) | \(e\left(\frac{44}{87}\right)\) | \(e\left(\frac{61}{174}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{77}{87}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{25}{87}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) |