Basic properties
| Modulus: | \(5400\) | |
| Conductor: | \(5400\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | 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.fg
\(\chi_{5400}(67,\cdot)\) \(\chi_{5400}(187,\cdot)\) \(\chi_{5400}(283,\cdot)\) \(\chi_{5400}(403,\cdot)\) \(\chi_{5400}(427,\cdot)\) \(\chi_{5400}(547,\cdot)\) \(\chi_{5400}(763,\cdot)\) \(\chi_{5400}(787,\cdot)\) \(\chi_{5400}(1003,\cdot)\) \(\chi_{5400}(1123,\cdot)\) \(\chi_{5400}(1147,\cdot)\) \(\chi_{5400}(1267,\cdot)\) \(\chi_{5400}(1363,\cdot)\) \(\chi_{5400}(1483,\cdot)\) \(\chi_{5400}(1627,\cdot)\) \(\chi_{5400}(1723,\cdot)\) \(\chi_{5400}(1867,\cdot)\) \(\chi_{5400}(1987,\cdot)\) \(\chi_{5400}(2083,\cdot)\) \(\chi_{5400}(2203,\cdot)\) \(\chi_{5400}(2227,\cdot)\) \(\chi_{5400}(2347,\cdot)\) \(\chi_{5400}(2563,\cdot)\) \(\chi_{5400}(2587,\cdot)\) \(\chi_{5400}(2803,\cdot)\) \(\chi_{5400}(2923,\cdot)\) \(\chi_{5400}(2947,\cdot)\) \(\chi_{5400}(3067,\cdot)\) \(\chi_{5400}(3163,\cdot)\) \(\chi_{5400}(3283,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1351,2701,1001,2377)\) → \((-1,-1,e\left(\frac{4}{9}\right),e\left(\frac{13}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5400 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{73}{180}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{97}{180}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{7}{45}\right)\) |