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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.hi
\(\chi_{8015}(39,\cdot)\) \(\chi_{8015}(74,\cdot)\) \(\chi_{8015}(79,\cdot)\) \(\chi_{8015}(179,\cdot)\) \(\chi_{8015}(219,\cdot)\) \(\chi_{8015}(319,\cdot)\) \(\chi_{8015}(499,\cdot)\) \(\chi_{8015}(954,\cdot)\) \(\chi_{8015}(1269,\cdot)\) \(\chi_{8015}(1479,\cdot)\) \(\chi_{8015}(1579,\cdot)\) \(\chi_{8015}(1719,\cdot)\) \(\chi_{8015}(1794,\cdot)\) \(\chi_{8015}(2174,\cdot)\) \(\chi_{8015}(2249,\cdot)\) \(\chi_{8015}(2314,\cdot)\) \(\chi_{8015}(2529,\cdot)\) \(\chi_{8015}(2669,\cdot)\) \(\chi_{8015}(2949,\cdot)\) \(\chi_{8015}(2984,\cdot)\) \(\chi_{8015}(3054,\cdot)\) \(\chi_{8015}(3089,\cdot)\) \(\chi_{8015}(3159,\cdot)\) \(\chi_{8015}(3404,\cdot)\) \(\chi_{8015}(3574,\cdot)\) \(\chi_{8015}(3714,\cdot)\) \(\chi_{8015}(3819,\cdot)\) \(\chi_{8015}(3824,\cdot)\) \(\chi_{8015}(3854,\cdot)\) \(\chi_{8015}(3959,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{228})$ |
Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{97}{228}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 8015 }(39, a) \) | \(-1\) | \(1\) | \(e\left(\frac{175}{228}\right)\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{97}{228}\right)\) | \(e\left(\frac{23}{76}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{67}{114}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{21}{76}\right)\) | \(e\left(\frac{4}{57}\right)\) |