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.fz
\(\chi_{8015}(408,\cdot)\) \(\chi_{8015}(417,\cdot)\) \(\chi_{8015}(548,\cdot)\) \(\chi_{8015}(597,\cdot)\) \(\chi_{8015}(737,\cdot)\) \(\chi_{8015}(837,\cdot)\) \(\chi_{8015}(963,\cdot)\) \(\chi_{8015}(1068,\cdot)\) \(\chi_{8015}(1222,\cdot)\) \(\chi_{8015}(1327,\cdot)\) \(\chi_{8015}(1453,\cdot)\) \(\chi_{8015}(1873,\cdot)\) \(\chi_{8015}(1948,\cdot)\) \(\chi_{8015}(2067,\cdot)\) \(\chi_{8015}(2377,\cdot)\) \(\chi_{8015}(2447,\cdot)\) \(\chi_{8015}(2452,\cdot)\) \(\chi_{8015}(2543,\cdot)\) \(\chi_{8015}(2592,\cdot)\) \(\chi_{8015}(2643,\cdot)\) \(\chi_{8015}(3012,\cdot)\) \(\chi_{8015}(3168,\cdot)\) \(\chi_{8015}(3537,\cdot)\) \(\chi_{8015}(3572,\cdot)\) \(\chi_{8015}(3903,\cdot)\) \(\chi_{8015}(3922,\cdot)\) \(\chi_{8015}(3952,\cdot)\) \(\chi_{8015}(4048,\cdot)\) \(\chi_{8015}(4057,\cdot)\) \(\chi_{8015}(4083,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{228})$ |
Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-i,e\left(\frac{1}{3}\right),e\left(\frac{103}{228}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 8015 }(408, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{125}{228}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{103}{228}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{11}{114}\right)\) | \(e\left(\frac{59}{114}\right)\) | \(e\left(\frac{27}{76}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{35}{57}\right)\) |