Basic properties
| Modulus: | \(21780\) | |
| Conductor: | \(4356\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(66\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4356}(3431,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 21780.fa
\(\chi_{21780}(131,\cdot)\) \(\chi_{21780}(2111,\cdot)\) \(\chi_{21780}(3431,\cdot)\) \(\chi_{21780}(4091,\cdot)\) \(\chi_{21780}(5411,\cdot)\) \(\chi_{21780}(6071,\cdot)\) \(\chi_{21780}(7391,\cdot)\) \(\chi_{21780}(8051,\cdot)\) \(\chi_{21780}(9371,\cdot)\) \(\chi_{21780}(10031,\cdot)\) \(\chi_{21780}(11351,\cdot)\) \(\chi_{21780}(12011,\cdot)\) \(\chi_{21780}(13331,\cdot)\) \(\chi_{21780}(13991,\cdot)\) \(\chi_{21780}(15311,\cdot)\) \(\chi_{21780}(17291,\cdot)\) \(\chi_{21780}(17951,\cdot)\) \(\chi_{21780}(19271,\cdot)\) \(\chi_{21780}(19931,\cdot)\) \(\chi_{21780}(21251,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{33})\) |
| Fixed field: | Number field defined by a degree 66 polynomial |
Values on generators
\((10891,19361,4357,14401)\) → \((-1,e\left(\frac{1}{6}\right),1,e\left(\frac{5}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 21780 }(3431, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{28}{33}\right)\) |