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.eh
\(\chi_{3015}(22,\cdot)\) \(\chi_{3015}(148,\cdot)\) \(\chi_{3015}(193,\cdot)\) \(\chi_{3015}(223,\cdot)\) \(\chi_{3015}(277,\cdot)\) \(\chi_{3015}(283,\cdot)\) \(\chi_{3015}(292,\cdot)\) \(\chi_{3015}(427,\cdot)\) \(\chi_{3015}(493,\cdot)\) \(\chi_{3015}(598,\cdot)\) \(\chi_{3015}(628,\cdot)\) \(\chi_{3015}(643,\cdot)\) \(\chi_{3015}(868,\cdot)\) \(\chi_{3015}(952,\cdot)\) \(\chi_{3015}(997,\cdot)\) \(\chi_{3015}(1087,\cdot)\) \(\chi_{3015}(1228,\cdot)\) \(\chi_{3015}(1282,\cdot)\) \(\chi_{3015}(1402,\cdot)\) \(\chi_{3015}(1447,\cdot)\) \(\chi_{3015}(1483,\cdot)\) \(\chi_{3015}(1498,\cdot)\) \(\chi_{3015}(1633,\cdot)\) \(\chi_{3015}(1672,\cdot)\) \(\chi_{3015}(1957,\cdot)\) \(\chi_{3015}(2002,\cdot)\) \(\chi_{3015}(2032,\cdot)\) \(\chi_{3015}(2092,\cdot)\) \(\chi_{3015}(2158,\cdot)\) \(\chi_{3015}(2203,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((1676,1207,136)\) → \((e\left(\frac{1}{3}\right),i,e\left(\frac{2}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3015 }(1282, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{115}{132}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) |