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 \(\chi_{1603}(51,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.eh
\(\chi_{8015}(51,\cdot)\) \(\chi_{8015}(396,\cdot)\) \(\chi_{8015}(506,\cdot)\) \(\chi_{8015}(541,\cdot)\) \(\chi_{8015}(991,\cdot)\) \(\chi_{8015}(1236,\cdot)\) \(\chi_{8015}(1591,\cdot)\) \(\chi_{8015}(1761,\cdot)\) \(\chi_{8015}(1796,\cdot)\) \(\chi_{8015}(2601,\cdot)\) \(\chi_{8015}(2986,\cdot)\) \(\chi_{8015}(3126,\cdot)\) \(\chi_{8015}(3336,\cdot)\) \(\chi_{8015}(3516,\cdot)\) \(\chi_{8015}(3546,\cdot)\) \(\chi_{8015}(3586,\cdot)\) \(\chi_{8015}(3796,\cdot)\) \(\chi_{8015}(4076,\cdot)\) \(\chi_{8015}(4141,\cdot)\) \(\chi_{8015}(4251,\cdot)\) \(\chi_{8015}(4531,\cdot)\) \(\chi_{8015}(4706,\cdot)\) \(\chi_{8015}(4776,\cdot)\) \(\chi_{8015}(4846,\cdot)\) \(\chi_{8015}(5191,\cdot)\) \(\chi_{8015}(5896,\cdot)\) \(\chi_{8015}(6556,\cdot)\) \(\chi_{8015}(6596,\cdot)\) \(\chi_{8015}(6661,\cdot)\) \(\chi_{8015}(6666,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((3207,4581,4586)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{10}{57}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 8015 }(51, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{23}{57}\right)\) |