Basic properties
Modulus: | \(8015\) | |
Conductor: | \(1603\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(228\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1603}(101,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.gi
\(\chi_{8015}(101,\cdot)\) \(\chi_{8015}(136,\cdot)\) \(\chi_{8015}(551,\cdot)\) \(\chi_{8015}(586,\cdot)\) \(\chi_{8015}(796,\cdot)\) \(\chi_{8015}(801,\cdot)\) \(\chi_{8015}(1111,\cdot)\) \(\chi_{8015}(1251,\cdot)\) \(\chi_{8015}(1286,\cdot)\) \(\chi_{8015}(1361,\cdot)\) \(\chi_{8015}(1396,\cdot)\) \(\chi_{8015}(1426,\cdot)\) \(\chi_{8015}(1571,\cdot)\) \(\chi_{8015}(1601,\cdot)\) \(\chi_{8015}(1746,\cdot)\) \(\chi_{8015}(1811,\cdot)\) \(\chi_{8015}(1886,\cdot)\) \(\chi_{8015}(1916,\cdot)\) \(\chi_{8015}(2091,\cdot)\) \(\chi_{8015}(2236,\cdot)\) \(\chi_{8015}(2376,\cdot)\) \(\chi_{8015}(2511,\cdot)\) \(\chi_{8015}(2551,\cdot)\) \(\chi_{8015}(2726,\cdot)\) \(\chi_{8015}(2756,\cdot)\) \(\chi_{8015}(2761,\cdot)\) \(\chi_{8015}(3176,\cdot)\) \(\chi_{8015}(3321,\cdot)\) \(\chi_{8015}(3351,\cdot)\) \(\chi_{8015}(3456,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{228})$ |
Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{11}{76}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 8015 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{228}\right)\) | \(e\left(\frac{31}{114}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{49}{76}\right)\) | \(e\left(\frac{9}{76}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{13}{114}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{33}{76}\right)\) | \(e\left(\frac{28}{57}\right)\) |