Basic properties
| Modulus: | \(61731\) | |
| Conductor: | \(61731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1083\) | 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 61731.cs
\(\chi_{61731}(7,\cdot)\) \(\chi_{61731}(49,\cdot)\) \(\chi_{61731}(178,\cdot)\) \(\chi_{61731}(220,\cdot)\) \(\chi_{61731}(349,\cdot)\) \(\chi_{61731}(391,\cdot)\) \(\chi_{61731}(520,\cdot)\) \(\chi_{61731}(562,\cdot)\) \(\chi_{61731}(691,\cdot)\) \(\chi_{61731}(733,\cdot)\) \(\chi_{61731}(862,\cdot)\) \(\chi_{61731}(904,\cdot)\) \(\chi_{61731}(1033,\cdot)\) \(\chi_{61731}(1075,\cdot)\) \(\chi_{61731}(1204,\cdot)\) \(\chi_{61731}(1246,\cdot)\) \(\chi_{61731}(1417,\cdot)\) \(\chi_{61731}(1546,\cdot)\) \(\chi_{61731}(1588,\cdot)\) \(\chi_{61731}(1717,\cdot)\) \(\chi_{61731}(1759,\cdot)\) \(\chi_{61731}(1888,\cdot)\) \(\chi_{61731}(1930,\cdot)\) \(\chi_{61731}(2059,\cdot)\) \(\chi_{61731}(2101,\cdot)\) \(\chi_{61731}(2230,\cdot)\) \(\chi_{61731}(2272,\cdot)\) \(\chi_{61731}(2401,\cdot)\) \(\chi_{61731}(2443,\cdot)\) \(\chi_{61731}(2572,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1083})$ |
| Fixed field: | Number field defined by a degree 1083 polynomial (not computed) |
Values on generators
\((6860,54874)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{328}{1083}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 61731 }(2401, a) \) | \(1\) | \(1\) | \(e\left(\frac{350}{361}\right)\) | \(e\left(\frac{339}{361}\right)\) | \(e\left(\frac{761}{1083}\right)\) | \(e\left(\frac{731}{1083}\right)\) | \(e\left(\frac{328}{361}\right)\) | \(e\left(\frac{728}{1083}\right)\) | \(e\left(\frac{434}{1083}\right)\) | \(e\left(\frac{238}{361}\right)\) | \(e\left(\frac{698}{1083}\right)\) | \(e\left(\frac{317}{361}\right)\) |