Basic properties
Modulus: | \(61731\) | |
Conductor: | \(61731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1083\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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
\((6860,54874)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{923}{1083}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 61731 }(562, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{361}\right)\) | \(e\left(\frac{134}{361}\right)\) | \(e\left(\frac{25}{1083}\right)\) | \(e\left(\frac{700}{1083}\right)\) | \(e\left(\frac{201}{361}\right)\) | \(e\left(\frac{226}{1083}\right)\) | \(e\left(\frac{343}{1083}\right)\) | \(e\left(\frac{60}{361}\right)\) | \(e\left(\frac{901}{1083}\right)\) | \(e\left(\frac{268}{361}\right)\) |