Basic properties
| Modulus: | \(5400\) | |
| Conductor: | \(5400\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | 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 5400.ff
\(\chi_{5400}(59,\cdot)\) \(\chi_{5400}(419,\cdot)\) \(\chi_{5400}(659,\cdot)\) \(\chi_{5400}(779,\cdot)\) \(\chi_{5400}(1019,\cdot)\) \(\chi_{5400}(1139,\cdot)\) \(\chi_{5400}(1379,\cdot)\) \(\chi_{5400}(1739,\cdot)\) \(\chi_{5400}(1859,\cdot)\) \(\chi_{5400}(2219,\cdot)\) \(\chi_{5400}(2459,\cdot)\) \(\chi_{5400}(2579,\cdot)\) \(\chi_{5400}(2819,\cdot)\) \(\chi_{5400}(2939,\cdot)\) \(\chi_{5400}(3179,\cdot)\) \(\chi_{5400}(3539,\cdot)\) \(\chi_{5400}(3659,\cdot)\) \(\chi_{5400}(4019,\cdot)\) \(\chi_{5400}(4259,\cdot)\) \(\chi_{5400}(4379,\cdot)\) \(\chi_{5400}(4619,\cdot)\) \(\chi_{5400}(4739,\cdot)\) \(\chi_{5400}(4979,\cdot)\) \(\chi_{5400}(5339,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1351,2701,1001,2377)\) → \((-1,-1,e\left(\frac{5}{18}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5400 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{47}{90}\right)\) |