Basic properties
| Modulus: | \(5445\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(91,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5445.cf
\(\chi_{5445}(91,\cdot)\) \(\chi_{5445}(136,\cdot)\) \(\chi_{5445}(181,\cdot)\) \(\chi_{5445}(361,\cdot)\) \(\chi_{5445}(586,\cdot)\) \(\chi_{5445}(631,\cdot)\) \(\chi_{5445}(676,\cdot)\) \(\chi_{5445}(1081,\cdot)\) \(\chi_{5445}(1126,\cdot)\) \(\chi_{5445}(1171,\cdot)\) \(\chi_{5445}(1351,\cdot)\) \(\chi_{5445}(1621,\cdot)\) \(\chi_{5445}(1666,\cdot)\) \(\chi_{5445}(1846,\cdot)\) \(\chi_{5445}(2071,\cdot)\) \(\chi_{5445}(2116,\cdot)\) \(\chi_{5445}(2161,\cdot)\) \(\chi_{5445}(2341,\cdot)\) \(\chi_{5445}(2566,\cdot)\) \(\chi_{5445}(2611,\cdot)\) \(\chi_{5445}(2656,\cdot)\) \(\chi_{5445}(2836,\cdot)\) \(\chi_{5445}(3061,\cdot)\) \(\chi_{5445}(3151,\cdot)\) \(\chi_{5445}(3331,\cdot)\) \(\chi_{5445}(3556,\cdot)\) \(\chi_{5445}(3601,\cdot)\) \(\chi_{5445}(3646,\cdot)\) \(\chi_{5445}(3826,\cdot)\) \(\chi_{5445}(4051,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((3026,4357,3511)\) → \((1,1,e\left(\frac{54}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 5445 }(91, a) \) | \(1\) | \(1\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{8}{11}\right)\) |