Basic properties
| Modulus: | \(3015\) | |
| Conductor: | \(3015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 3015.ee
\(\chi_{3015}(92,\cdot)\) \(\chi_{3015}(158,\cdot)\) \(\chi_{3015}(263,\cdot)\) \(\chi_{3015}(293,\cdot)\) \(\chi_{3015}(308,\cdot)\) \(\chi_{3015}(533,\cdot)\) \(\chi_{3015}(617,\cdot)\) \(\chi_{3015}(662,\cdot)\) \(\chi_{3015}(752,\cdot)\) \(\chi_{3015}(893,\cdot)\) \(\chi_{3015}(947,\cdot)\) \(\chi_{3015}(1067,\cdot)\) \(\chi_{3015}(1112,\cdot)\) \(\chi_{3015}(1148,\cdot)\) \(\chi_{3015}(1163,\cdot)\) \(\chi_{3015}(1298,\cdot)\) \(\chi_{3015}(1337,\cdot)\) \(\chi_{3015}(1622,\cdot)\) \(\chi_{3015}(1667,\cdot)\) \(\chi_{3015}(1697,\cdot)\) \(\chi_{3015}(1757,\cdot)\) \(\chi_{3015}(1823,\cdot)\) \(\chi_{3015}(1868,\cdot)\) \(\chi_{3015}(1958,\cdot)\) \(\chi_{3015}(1967,\cdot)\) \(\chi_{3015}(2072,\cdot)\) \(\chi_{3015}(2102,\cdot)\) \(\chi_{3015}(2117,\cdot)\) \(\chi_{3015}(2153,\cdot)\) \(\chi_{3015}(2273,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((1676,1207,136)\) → \((e\left(\frac{1}{6}\right),-i,e\left(\frac{8}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3015 }(263, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{132}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{19}{132}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{53}{132}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) |