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.hp
\(\chi_{8015}(67,\cdot)\) \(\chi_{8015}(72,\cdot)\) \(\chi_{8015}(142,\cdot)\) \(\chi_{8015}(368,\cdot)\) \(\chi_{8015}(452,\cdot)\) \(\chi_{8015}(508,\cdot)\) \(\chi_{8015}(1003,\cdot)\) \(\chi_{8015}(1073,\cdot)\) \(\chi_{8015}(1192,\cdot)\) \(\chi_{8015}(1297,\cdot)\) \(\chi_{8015}(1682,\cdot)\) \(\chi_{8015}(1782,\cdot)\) \(\chi_{8015}(1838,\cdot)\) \(\chi_{8015}(1922,\cdot)\) \(\chi_{8015}(2102,\cdot)\) \(\chi_{8015}(2223,\cdot)\) \(\chi_{8015}(2363,\cdot)\) \(\chi_{8015}(2578,\cdot)\) \(\chi_{8015}(2683,\cdot)\) \(\chi_{8015}(2783,\cdot)\) \(\chi_{8015}(2788,\cdot)\) \(\chi_{8015}(2858,\cdot)\) \(\chi_{8015}(2872,\cdot)\) \(\chi_{8015}(3308,\cdot)\) \(\chi_{8015}(3322,\cdot)\) \(\chi_{8015}(3343,\cdot)\) \(\chi_{8015}(3397,\cdot)\) \(\chi_{8015}(3693,\cdot)\) \(\chi_{8015}(3733,\cdot)\) \(\chi_{8015}(3917,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{228})$ |
Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((i,e\left(\frac{2}{3}\right),e\left(\frac{55}{228}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 8015 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{45}{76}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{55}{228}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{203}{228}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{34}{57}\right)\) |