Basic properties
Modulus: | \(8041\) | |
Conductor: | \(731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(56\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{731}(355,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.dj
\(\chi_{8041}(342,\cdot)\) \(\chi_{8041}(661,\cdot)\) \(\chi_{8041}(1079,\cdot)\) \(\chi_{8041}(1607,\cdot)\) \(\chi_{8041}(1827,\cdot)\) \(\chi_{8041}(1970,\cdot)\) \(\chi_{8041}(2025,\cdot)\) \(\chi_{8041}(2773,\cdot)\) \(\chi_{8041}(2916,\cdot)\) \(\chi_{8041}(3279,\cdot)\) \(\chi_{8041}(3653,\cdot)\) \(\chi_{8041}(4225,\cdot)\) \(\chi_{8041}(4445,\cdot)\) \(\chi_{8041}(4599,\cdot)\) \(\chi_{8041}(5336,\cdot)\) \(\chi_{8041}(5391,\cdot)\) \(\chi_{8041}(5754,\cdot)\) \(\chi_{8041}(6084,\cdot)\) \(\chi_{8041}(6282,\cdot)\) \(\chi_{8041}(6700,\cdot)\) \(\chi_{8041}(7030,\cdot)\) \(\chi_{8041}(7063,\cdot)\) \(\chi_{8041}(7437,\cdot)\) \(\chi_{8041}(8009,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{56})$ |
Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((6580,2366,562)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{5}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(3279, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{41}{56}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{9}{56}\right)\) |