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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3015.ep
\(\chi_{3015}(2,\cdot)\) \(\chi_{3015}(32,\cdot)\) \(\chi_{3015}(113,\cdot)\) \(\chi_{3015}(128,\cdot)\) \(\chi_{3015}(182,\cdot)\) \(\chi_{3015}(212,\cdot)\) \(\chi_{3015}(302,\cdot)\) \(\chi_{3015}(347,\cdot)\) \(\chi_{3015}(353,\cdot)\) \(\chi_{3015}(452,\cdot)\) \(\chi_{3015}(497,\cdot)\) \(\chi_{3015}(587,\cdot)\) \(\chi_{3015}(848,\cdot)\) \(\chi_{3015}(878,\cdot)\) \(\chi_{3015}(1103,\cdot)\) \(\chi_{3015}(1202,\cdot)\) \(\chi_{3015}(1208,\cdot)\) \(\chi_{3015}(1238,\cdot)\) \(\chi_{3015}(1247,\cdot)\) \(\chi_{3015}(1388,\cdot)\) \(\chi_{3015}(1397,\cdot)\) \(\chi_{3015}(1418,\cdot)\) \(\chi_{3015}(1427,\cdot)\) \(\chi_{3015}(1487,\cdot)\) \(\chi_{3015}(1508,\cdot)\) \(\chi_{3015}(1553,\cdot)\) \(\chi_{3015}(1658,\cdot)\) \(\chi_{3015}(1703,\cdot)\) \(\chi_{3015}(1793,\cdot)\) \(\chi_{3015}(1922,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((1676,1207,136)\) → \((e\left(\frac{5}{6}\right),i,e\left(\frac{5}{66}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3015 }(32, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{113}{132}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{17}{66}\right)\) |