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.en
\(\chi_{3015}(83,\cdot)\) \(\chi_{3015}(122,\cdot)\) \(\chi_{3015}(167,\cdot)\) \(\chi_{3015}(173,\cdot)\) \(\chi_{3015}(218,\cdot)\) \(\chi_{3015}(248,\cdot)\) \(\chi_{3015}(257,\cdot)\) \(\chi_{3015}(317,\cdot)\) \(\chi_{3015}(428,\cdot)\) \(\chi_{3015}(437,\cdot)\) \(\chi_{3015}(473,\cdot)\) \(\chi_{3015}(488,\cdot)\) \(\chi_{3015}(542,\cdot)\) \(\chi_{3015}(572,\cdot)\) \(\chi_{3015}(668,\cdot)\) \(\chi_{3015}(797,\cdot)\) \(\chi_{3015}(992,\cdot)\) \(\chi_{3015}(1028,\cdot)\) \(\chi_{3015}(1082,\cdot)\) \(\chi_{3015}(1328,\cdot)\) \(\chi_{3015}(1373,\cdot)\) \(\chi_{3015}(1463,\cdot)\) \(\chi_{3015}(1523,\cdot)\) \(\chi_{3015}(1562,\cdot)\) \(\chi_{3015}(1643,\cdot)\) \(\chi_{3015}(1748,\cdot)\) \(\chi_{3015}(1778,\cdot)\) \(\chi_{3015}(1892,\cdot)\) \(\chi_{3015}(1982,\cdot)\) \(\chi_{3015}(2003,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((1676,1207,136)\) → \((e\left(\frac{1}{6}\right),i,e\left(\frac{8}{33}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3015 }(1082, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{65}{132}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{35}{132}\right)\) | \(e\left(\frac{61}{66}\right)\) |