Basic properties
Modulus: | \(8015\) | |
Conductor: | \(1145\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(76\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1145}(8,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.es
\(\chi_{8015}(8,\cdot)\) \(\chi_{8015}(512,\cdot)\) \(\chi_{8015}(603,\cdot)\) \(\chi_{8015}(708,\cdot)\) \(\chi_{8015}(1002,\cdot)\) \(\chi_{8015}(1177,\cdot)\) \(\chi_{8015}(1268,\cdot)\) \(\chi_{8015}(1352,\cdot)\) \(\chi_{8015}(1387,\cdot)\) \(\chi_{8015}(1968,\cdot)\) \(\chi_{8015}(2612,\cdot)\) \(\chi_{8015}(3193,\cdot)\) \(\chi_{8015}(3228,\cdot)\) \(\chi_{8015}(3312,\cdot)\) \(\chi_{8015}(3403,\cdot)\) \(\chi_{8015}(3578,\cdot)\) \(\chi_{8015}(3872,\cdot)\) \(\chi_{8015}(3977,\cdot)\) \(\chi_{8015}(4068,\cdot)\) \(\chi_{8015}(4572,\cdot)\) \(\chi_{8015}(5153,\cdot)\) \(\chi_{8015}(5237,\cdot)\) \(\chi_{8015}(5727,\cdot)\) \(\chi_{8015}(5853,\cdot)\) \(\chi_{8015}(5902,\cdot)\) \(\chi_{8015}(6042,\cdot)\) \(\chi_{8015}(6063,\cdot)\) \(\chi_{8015}(6217,\cdot)\) \(\chi_{8015}(6378,\cdot)\) \(\chi_{8015}(6532,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{76})$ |
Fixed field: | Number field defined by a degree 76 polynomial |
Values on generators
\((3207,4581,4586)\) → \((-i,1,e\left(\frac{21}{76}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 8015 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{55}{76}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{21}{76}\right)\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{63}{76}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{4}{19}\right)\) |