Basic properties
Modulus: | \(8015\) | |
Conductor: | \(1603\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1603}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.fg
\(\chi_{8015}(11,\cdot)\) \(\chi_{8015}(186,\cdot)\) \(\chi_{8015}(401,\cdot)\) \(\chi_{8015}(431,\cdot)\) \(\chi_{8015}(751,\cdot)\) \(\chi_{8015}(856,\cdot)\) \(\chi_{8015}(1101,\cdot)\) \(\chi_{8015}(1171,\cdot)\) \(\chi_{8015}(1586,\cdot)\) \(\chi_{8015}(1836,\cdot)\) \(\chi_{8015}(2076,\cdot)\) \(\chi_{8015}(2186,\cdot)\) \(\chi_{8015}(2466,\cdot)\) \(\chi_{8015}(2706,\cdot)\) \(\chi_{8015}(2816,\cdot)\) \(\chi_{8015}(2916,\cdot)\) \(\chi_{8015}(3446,\cdot)\) \(\chi_{8015}(3621,\cdot)\) \(\chi_{8015}(3866,\cdot)\) \(\chi_{8015}(4001,\cdot)\) \(\chi_{8015}(4106,\cdot)\) \(\chi_{8015}(4981,\cdot)\) \(\chi_{8015}(5021,\cdot)\) \(\chi_{8015}(5331,\cdot)\) \(\chi_{8015}(5436,\cdot)\) \(\chi_{8015}(5511,\cdot)\) \(\chi_{8015}(5681,\cdot)\) \(\chi_{8015}(5751,\cdot)\) \(\chi_{8015}(6141,\cdot)\) \(\chi_{8015}(6351,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{27}{38}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 8015 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{114}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{1}{57}\right)\) |