Basic properties
Modulus: | \(6031\) | |
Conductor: | \(6031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(162\) | 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.gm
\(\chi_{6031}(225,\cdot)\) \(\chi_{6031}(336,\cdot)\) \(\chi_{6031}(395,\cdot)\) \(\chi_{6031}(522,\cdot)\) \(\chi_{6031}(620,\cdot)\) \(\chi_{6031}(706,\cdot)\) \(\chi_{6031}(743,\cdot)\) \(\chi_{6031}(770,\cdot)\) \(\chi_{6031}(966,\cdot)\) \(\chi_{6031}(1262,\cdot)\) \(\chi_{6031}(1286,\cdot)\) \(\chi_{6031}(1394,\cdot)\) \(\chi_{6031}(1723,\cdot)\) \(\chi_{6031}(1730,\cdot)\) \(\chi_{6031}(1743,\cdot)\) \(\chi_{6031}(1880,\cdot)\) \(\chi_{6031}(1954,\cdot)\) \(\chi_{6031}(1965,\cdot)\) \(\chi_{6031}(2176,\cdot)\) \(\chi_{6031}(2298,\cdot)\) \(\chi_{6031}(2426,\cdot)\) \(\chi_{6031}(2500,\cdot)\) \(\chi_{6031}(2519,\cdot)\) \(\chi_{6031}(2692,\cdot)\) \(\chi_{6031}(2704,\cdot)\) \(\chi_{6031}(2890,\cdot)\) \(\chi_{6031}(2948,\cdot)\) \(\chi_{6031}(3240,\cdot)\) \(\chi_{6031}(3284,\cdot)\) \(\chi_{6031}(3462,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{81})$ |
Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{35}{81}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6031 }(225, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{162}\right)\) | \(e\left(\frac{34}{81}\right)\) | \(e\left(\frac{25}{81}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{53}{81}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{68}{81}\right)\) | \(e\left(\frac{20}{81}\right)\) | \(e\left(\frac{79}{81}\right)\) |