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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.fc
\(\chi_{8015}(144,\cdot)\) \(\chi_{8015}(184,\cdot)\) \(\chi_{8015}(249,\cdot)\) \(\chi_{8015}(254,\cdot)\) \(\chi_{8015}(284,\cdot)\) \(\chi_{8015}(919,\cdot)\) \(\chi_{8015}(1089,\cdot)\) \(\chi_{8015}(1159,\cdot)\) \(\chi_{8015}(1304,\cdot)\) \(\chi_{8015}(1369,\cdot)\) \(\chi_{8015}(1654,\cdot)\) \(\chi_{8015}(1999,\cdot)\) \(\chi_{8015}(2109,\cdot)\) \(\chi_{8015}(2144,\cdot)\) \(\chi_{8015}(2594,\cdot)\) \(\chi_{8015}(2839,\cdot)\) \(\chi_{8015}(3194,\cdot)\) \(\chi_{8015}(3364,\cdot)\) \(\chi_{8015}(3399,\cdot)\) \(\chi_{8015}(4204,\cdot)\) \(\chi_{8015}(4589,\cdot)\) \(\chi_{8015}(4729,\cdot)\) \(\chi_{8015}(4939,\cdot)\) \(\chi_{8015}(5119,\cdot)\) \(\chi_{8015}(5149,\cdot)\) \(\chi_{8015}(5189,\cdot)\) \(\chi_{8015}(5399,\cdot)\) \(\chi_{8015}(5679,\cdot)\) \(\chi_{8015}(5744,\cdot)\) \(\chi_{8015}(5854,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{37}{57}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 8015 }(5119, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{114}\right)\) | \(e\left(\frac{97}{114}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{11}{57}\right)\) |