Basic properties
| Modulus: | \(5424\) | |
| Conductor: | \(1356\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1356}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5424.fd
\(\chi_{5424}(47,\cdot)\) \(\chi_{5424}(431,\cdot)\) \(\chi_{5424}(479,\cdot)\) \(\chi_{5424}(527,\cdot)\) \(\chi_{5424}(575,\cdot)\) \(\chi_{5424}(623,\cdot)\) \(\chi_{5424}(767,\cdot)\) \(\chi_{5424}(815,\cdot)\) \(\chi_{5424}(959,\cdot)\) \(\chi_{5424}(1007,\cdot)\) \(\chi_{5424}(1055,\cdot)\) \(\chi_{5424}(1103,\cdot)\) \(\chi_{5424}(1151,\cdot)\) \(\chi_{5424}(1535,\cdot)\) \(\chi_{5424}(1775,\cdot)\) \(\chi_{5424}(1967,\cdot)\) \(\chi_{5424}(2015,\cdot)\) \(\chi_{5424}(2063,\cdot)\) \(\chi_{5424}(2159,\cdot)\) \(\chi_{5424}(2255,\cdot)\) \(\chi_{5424}(2303,\cdot)\) \(\chi_{5424}(2447,\cdot)\) \(\chi_{5424}(2735,\cdot)\) \(\chi_{5424}(2831,\cdot)\) \(\chi_{5424}(2879,\cdot)\) \(\chi_{5424}(2975,\cdot)\) \(\chi_{5424}(3071,\cdot)\) \(\chi_{5424}(3119,\cdot)\) \(\chi_{5424}(3167,\cdot)\) \(\chi_{5424}(3311,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((3391,4069,3617,1585)\) → \((-1,1,-1,e\left(\frac{31}{112}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 5424 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{112}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{27}{56}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{99}{112}\right)\) | \(e\left(\frac{101}{112}\right)\) | \(e\left(\frac{39}{112}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{15}{112}\right)\) | \(e\left(\frac{19}{56}\right)\) |