Basic properties
Modulus: | \(8015\) | |
Conductor: | \(8015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(228\) | 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.gt
\(\chi_{8015}(12,\cdot)\) \(\chi_{8015}(33,\cdot)\) \(\chi_{8015}(103,\cdot)\) \(\chi_{8015}(278,\cdot)\) \(\chi_{8015}(367,\cdot)\) \(\chi_{8015}(558,\cdot)\) \(\chi_{8015}(612,\cdot)\) \(\chi_{8015}(668,\cdot)\) \(\chi_{8015}(733,\cdot)\) \(\chi_{8015}(1013,\cdot)\) \(\chi_{8015}(1062,\cdot)\) \(\chi_{8015}(1097,\cdot)\) \(\chi_{8015}(1207,\cdot)\) \(\chi_{8015}(1223,\cdot)\) \(\chi_{8015}(1263,\cdot)\) \(\chi_{8015}(1293,\cdot)\) \(\chi_{8015}(1473,\cdot)\) \(\chi_{8015}(1552,\cdot)\) \(\chi_{8015}(1683,\cdot)\) \(\chi_{8015}(1823,\cdot)\) \(\chi_{8015}(1837,\cdot)\) \(\chi_{8015}(1902,\cdot)\) \(\chi_{8015}(2047,\cdot)\) \(\chi_{8015}(2117,\cdot)\) \(\chi_{8015}(2208,\cdot)\) \(\chi_{8015}(2287,\cdot)\) \(\chi_{8015}(2922,\cdot)\) \(\chi_{8015}(2952,\cdot)\) \(\chi_{8015}(2957,\cdot)\) \(\chi_{8015}(3013,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{228})$ |
Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-i,e\left(\frac{5}{6}\right),e\left(\frac{71}{114}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 8015 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{228}\right)\) | \(e\left(\frac{143}{228}\right)\) | \(e\left(\frac{113}{114}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{37}{76}\right)\) | \(e\left(\frac{29}{114}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{47}{76}\right)\) | \(e\left(\frac{47}{76}\right)\) | \(e\left(\frac{56}{57}\right)\) |