Basic properties
| Modulus: | \(8015\) | |
| Conductor: | \(1145\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(76\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1145}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.en
\(\chi_{8015}(43,\cdot)\) \(\chi_{8015}(57,\cdot)\) \(\chi_{8015}(218,\cdot)\) \(\chi_{8015}(848,\cdot)\) \(\chi_{8015}(932,\cdot)\) \(\chi_{8015}(1037,\cdot)\) \(\chi_{8015}(1198,\cdot)\) \(\chi_{8015}(1478,\cdot)\) \(\chi_{8015}(1828,\cdot)\) \(\chi_{8015}(2122,\cdot)\) \(\chi_{8015}(2332,\cdot)\) \(\chi_{8015}(2493,\cdot)\) \(\chi_{8015}(2563,\cdot)\) \(\chi_{8015}(2808,\cdot)\) \(\chi_{8015}(2913,\cdot)\) \(\chi_{8015}(2962,\cdot)\) \(\chi_{8015}(3263,\cdot)\) \(\chi_{8015}(3452,\cdot)\) \(\chi_{8015}(4138,\cdot)\) \(\chi_{8015}(4243,\cdot)\) \(\chi_{8015}(4607,\cdot)\) \(\chi_{8015}(4852,\cdot)\) \(\chi_{8015}(5027,\cdot)\) \(\chi_{8015}(5328,\cdot)\) \(\chi_{8015}(5538,\cdot)\) \(\chi_{8015}(5657,\cdot)\) \(\chi_{8015}(6007,\cdot)\) \(\chi_{8015}(6168,\cdot)\) \(\chi_{8015}(6287,\cdot)\) \(\chi_{8015}(6637,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{76})$ |
| Fixed field: | Number field defined by a degree 76 polynomial |
Values on generators
\((3207,4581,4586)\) → \((-i,1,e\left(\frac{12}{19}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{76}\right)\) | \(e\left(\frac{47}{76}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{3}{76}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{49}{76}\right)\) | \(e\left(\frac{11}{76}\right)\) | \(e\left(\frac{1}{19}\right)\) |