Basic properties
Modulus: | \(8015\) | |
Conductor: | \(8015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.fq
\(\chi_{8015}(534,\cdot)\) \(\chi_{8015}(879,\cdot)\) \(\chi_{8015}(949,\cdot)\) \(\chi_{8015}(1019,\cdot)\) \(\chi_{8015}(1194,\cdot)\) \(\chi_{8015}(1474,\cdot)\) \(\chi_{8015}(1584,\cdot)\) \(\chi_{8015}(1649,\cdot)\) \(\chi_{8015}(1929,\cdot)\) \(\chi_{8015}(2139,\cdot)\) \(\chi_{8015}(2179,\cdot)\) \(\chi_{8015}(2209,\cdot)\) \(\chi_{8015}(2389,\cdot)\) \(\chi_{8015}(2599,\cdot)\) \(\chi_{8015}(2739,\cdot)\) \(\chi_{8015}(3124,\cdot)\) \(\chi_{8015}(3929,\cdot)\) \(\chi_{8015}(3964,\cdot)\) \(\chi_{8015}(4134,\cdot)\) \(\chi_{8015}(4489,\cdot)\) \(\chi_{8015}(4734,\cdot)\) \(\chi_{8015}(5184,\cdot)\) \(\chi_{8015}(5219,\cdot)\) \(\chi_{8015}(5329,\cdot)\) \(\chi_{8015}(5674,\cdot)\) \(\chi_{8015}(5959,\cdot)\) \(\chi_{8015}(6024,\cdot)\) \(\chi_{8015}(6169,\cdot)\) \(\chi_{8015}(6239,\cdot)\) \(\chi_{8015}(6409,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{101}{114}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 8015 }(1019, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{37}{114}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{43}{57}\right)\) |