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.ek
\(\chi_{3015}(7,\cdot)\) \(\chi_{3015}(13,\cdot)\) \(\chi_{3015}(232,\cdot)\) \(\chi_{3015}(337,\cdot)\) \(\chi_{3015}(367,\cdot)\) \(\chi_{3015}(448,\cdot)\) \(\chi_{3015}(463,\cdot)\) \(\chi_{3015}(517,\cdot)\) \(\chi_{3015}(547,\cdot)\) \(\chi_{3015}(637,\cdot)\) \(\chi_{3015}(682,\cdot)\) \(\chi_{3015}(688,\cdot)\) \(\chi_{3015}(787,\cdot)\) \(\chi_{3015}(832,\cdot)\) \(\chi_{3015}(922,\cdot)\) \(\chi_{3015}(1183,\cdot)\) \(\chi_{3015}(1213,\cdot)\) \(\chi_{3015}(1438,\cdot)\) \(\chi_{3015}(1537,\cdot)\) \(\chi_{3015}(1543,\cdot)\) \(\chi_{3015}(1573,\cdot)\) \(\chi_{3015}(1582,\cdot)\) \(\chi_{3015}(1723,\cdot)\) \(\chi_{3015}(1732,\cdot)\) \(\chi_{3015}(1753,\cdot)\) \(\chi_{3015}(1762,\cdot)\) \(\chi_{3015}(1822,\cdot)\) \(\chi_{3015}(1843,\cdot)\) \(\chi_{3015}(1888,\cdot)\) \(\chi_{3015}(1993,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((1676,1207,136)\) → \((e\left(\frac{1}{3}\right),-i,e\left(\frac{19}{66}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3015 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{132}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{25}{66}\right)\) |