Basic properties
Modulus: | \(8015\) | |
Conductor: | \(1603\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(57\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1603}(1558,\cdot)\) | 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)
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Galois orbit 8015.ef
\(\chi_{8015}(81,\cdot)\) \(\chi_{8015}(151,\cdot)\) \(\chi_{8015}(361,\cdot)\) \(\chi_{8015}(611,\cdot)\) \(\chi_{8015}(641,\cdot)\) \(\chi_{8015}(816,\cdot)\) \(\chi_{8015}(1096,\cdot)\) \(\chi_{8015}(1271,\cdot)\) \(\chi_{8015}(1341,\cdot)\) \(\chi_{8015}(1411,\cdot)\) \(\chi_{8015}(1976,\cdot)\) \(\chi_{8015}(2081,\cdot)\) \(\chi_{8015}(2116,\cdot)\) \(\chi_{8015}(2461,\cdot)\) \(\chi_{8015}(2921,\cdot)\) \(\chi_{8015}(2991,\cdot)\) \(\chi_{8015}(3161,\cdot)\) \(\chi_{8015}(3201,\cdot)\) \(\chi_{8015}(3231,\cdot)\) \(\chi_{8015}(3831,\cdot)\) \(\chi_{8015}(3896,\cdot)\) \(\chi_{8015}(4281,\cdot)\) \(\chi_{8015}(4426,\cdot)\) \(\chi_{8015}(4631,\cdot)\) \(\chi_{8015}(4671,\cdot)\) \(\chi_{8015}(5086,\cdot)\) \(\chi_{8015}(5121,\cdot)\) \(\chi_{8015}(5196,\cdot)\) \(\chi_{8015}(5231,\cdot)\) \(\chi_{8015}(6036,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((3207,4581,4586)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{43}{57}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 8015 }(3161, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{40}{57}\right)\) |