Basic properties
Modulus: | \(8015\) | |
Conductor: | \(1603\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(57\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1603}(256,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.eg
\(\chi_{8015}(16,\cdot)\) \(\chi_{8015}(121,\cdot)\) \(\chi_{8015}(256,\cdot)\) \(\chi_{8015}(501,\cdot)\) \(\chi_{8015}(676,\cdot)\) \(\chi_{8015}(1206,\cdot)\) \(\chi_{8015}(1306,\cdot)\) \(\chi_{8015}(1416,\cdot)\) \(\chi_{8015}(1656,\cdot)\) \(\chi_{8015}(1936,\cdot)\) \(\chi_{8015}(2046,\cdot)\) \(\chi_{8015}(2286,\cdot)\) \(\chi_{8015}(2536,\cdot)\) \(\chi_{8015}(2951,\cdot)\) \(\chi_{8015}(3021,\cdot)\) \(\chi_{8015}(3266,\cdot)\) \(\chi_{8015}(3371,\cdot)\) \(\chi_{8015}(3691,\cdot)\) \(\chi_{8015}(3721,\cdot)\) \(\chi_{8015}(3936,\cdot)\) \(\chi_{8015}(4111,\cdot)\) \(\chi_{8015}(4596,\cdot)\) \(\chi_{8015}(4701,\cdot)\) \(\chi_{8015}(4741,\cdot)\) \(\chi_{8015}(5091,\cdot)\) \(\chi_{8015}(5371,\cdot)\) \(\chi_{8015}(5721,\cdot)\) \(\chi_{8015}(5786,\cdot)\) \(\chi_{8015}(5996,\cdot)\) \(\chi_{8015}(6386,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((3207,4581,4586)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{14}{19}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 8015 }(256, a) \) | \(1\) | \(1\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{13}{57}\right)\) |