Basic properties
| Modulus: | \(5400\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{675}(113,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5400.fh
\(\chi_{5400}(113,\cdot)\) \(\chi_{5400}(137,\cdot)\) \(\chi_{5400}(353,\cdot)\) \(\chi_{5400}(473,\cdot)\) \(\chi_{5400}(497,\cdot)\) \(\chi_{5400}(617,\cdot)\) \(\chi_{5400}(713,\cdot)\) \(\chi_{5400}(833,\cdot)\) \(\chi_{5400}(977,\cdot)\) \(\chi_{5400}(1073,\cdot)\) \(\chi_{5400}(1217,\cdot)\) \(\chi_{5400}(1337,\cdot)\) \(\chi_{5400}(1433,\cdot)\) \(\chi_{5400}(1553,\cdot)\) \(\chi_{5400}(1577,\cdot)\) \(\chi_{5400}(1697,\cdot)\) \(\chi_{5400}(1913,\cdot)\) \(\chi_{5400}(1937,\cdot)\) \(\chi_{5400}(2153,\cdot)\) \(\chi_{5400}(2273,\cdot)\) \(\chi_{5400}(2297,\cdot)\) \(\chi_{5400}(2417,\cdot)\) \(\chi_{5400}(2513,\cdot)\) \(\chi_{5400}(2633,\cdot)\) \(\chi_{5400}(2777,\cdot)\) \(\chi_{5400}(2873,\cdot)\) \(\chi_{5400}(3017,\cdot)\) \(\chi_{5400}(3137,\cdot)\) \(\chi_{5400}(3233,\cdot)\) \(\chi_{5400}(3353,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1351,2701,1001,2377)\) → \((1,1,e\left(\frac{5}{18}\right),e\left(\frac{19}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5400 }(113, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{49}{180}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{91}{180}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{47}{90}\right)\) |