Basic properties
Modulus: | \(6031\) | |
Conductor: | \(6031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(81\) | 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 6031.fo
\(\chi_{6031}(26,\cdot)\) \(\chi_{6031}(84,\cdot)\) \(\chi_{6031}(232,\cdot)\) \(\chi_{6031}(306,\cdot)\) \(\chi_{6031}(359,\cdot)\) \(\chi_{6031}(528,\cdot)\) \(\chi_{6031}(676,\cdot)\) \(\chi_{6031}(803,\cdot)\) \(\chi_{6031}(877,\cdot)\) \(\chi_{6031}(988,\cdot)\) \(\chi_{6031}(1025,\cdot)\) \(\chi_{6031}(1099,\cdot)\) \(\chi_{6031}(1231,\cdot)\) \(\chi_{6031}(1358,\cdot)\) \(\chi_{6031}(1395,\cdot)\) \(\chi_{6031}(1564,\cdot)\) \(\chi_{6031}(1580,\cdot)\) \(\chi_{6031}(1601,\cdot)\) \(\chi_{6031}(1802,\cdot)\) \(\chi_{6031}(1839,\cdot)\) \(\chi_{6031}(1876,\cdot)\) \(\chi_{6031}(1971,\cdot)\) \(\chi_{6031}(2135,\cdot)\) \(\chi_{6031}(2230,\cdot)\) \(\chi_{6031}(2505,\cdot)\) \(\chi_{6031}(2526,\cdot)\) \(\chi_{6031}(2727,\cdot)\) \(\chi_{6031}(2764,\cdot)\) \(\chi_{6031}(2785,\cdot)\) \(\chi_{6031}(2822,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{81})$ |
Fixed field: | Number field defined by a degree 81 polynomial |
Values on generators
\((816,5218)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{47}{81}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6031 }(1099, a) \) | \(1\) | \(1\) | \(e\left(\frac{74}{81}\right)\) | \(e\left(\frac{22}{81}\right)\) | \(e\left(\frac{67}{81}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{2}{81}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{44}{81}\right)\) | \(e\left(\frac{23}{81}\right)\) | \(e\left(\frac{22}{81}\right)\) |