Basic properties
| Modulus: | \(5808\) | |
| Conductor: | \(2904\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2904}(1877,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5808.dg
\(\chi_{5808}(41,\cdot)\) \(\chi_{5808}(281,\cdot)\) \(\chi_{5808}(425,\cdot)\) \(\chi_{5808}(569,\cdot)\) \(\chi_{5808}(761,\cdot)\) \(\chi_{5808}(809,\cdot)\) \(\chi_{5808}(953,\cdot)\) \(\chi_{5808}(1097,\cdot)\) \(\chi_{5808}(1289,\cdot)\) \(\chi_{5808}(1337,\cdot)\) \(\chi_{5808}(1481,\cdot)\) \(\chi_{5808}(1625,\cdot)\) \(\chi_{5808}(1817,\cdot)\) \(\chi_{5808}(1865,\cdot)\) \(\chi_{5808}(2009,\cdot)\) \(\chi_{5808}(2153,\cdot)\) \(\chi_{5808}(2345,\cdot)\) \(\chi_{5808}(2537,\cdot)\) \(\chi_{5808}(2681,\cdot)\) \(\chi_{5808}(2873,\cdot)\) \(\chi_{5808}(2921,\cdot)\) \(\chi_{5808}(3209,\cdot)\) \(\chi_{5808}(3401,\cdot)\) \(\chi_{5808}(3449,\cdot)\) \(\chi_{5808}(3593,\cdot)\) \(\chi_{5808}(3737,\cdot)\) \(\chi_{5808}(3929,\cdot)\) \(\chi_{5808}(3977,\cdot)\) \(\chi_{5808}(4121,\cdot)\) \(\chi_{5808}(4265,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3631,4357,1937,2785)\) → \((1,-1,-1,e\left(\frac{87}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 5808 }(425, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{7}{110}\right)\) |