Basic properties
| Modulus: | \(4275\) | |
| Conductor: | \(1425\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1425}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4275.hd
\(\chi_{4275}(17,\cdot)\) \(\chi_{4275}(62,\cdot)\) \(\chi_{4275}(188,\cdot)\) \(\chi_{4275}(233,\cdot)\) \(\chi_{4275}(377,\cdot)\) \(\chi_{4275}(422,\cdot)\) \(\chi_{4275}(503,\cdot)\) \(\chi_{4275}(548,\cdot)\) \(\chi_{4275}(728,\cdot)\) \(\chi_{4275}(872,\cdot)\) \(\chi_{4275}(917,\cdot)\) \(\chi_{4275}(1088,\cdot)\) \(\chi_{4275}(1187,\cdot)\) \(\chi_{4275}(1277,\cdot)\) \(\chi_{4275}(1358,\cdot)\) \(\chi_{4275}(1403,\cdot)\) \(\chi_{4275}(1412,\cdot)\) \(\chi_{4275}(1448,\cdot)\) \(\chi_{4275}(1583,\cdot)\) \(\chi_{4275}(1727,\cdot)\) \(\chi_{4275}(1772,\cdot)\) \(\chi_{4275}(1898,\cdot)\) \(\chi_{4275}(2042,\cdot)\) \(\chi_{4275}(2087,\cdot)\) \(\chi_{4275}(2213,\cdot)\) \(\chi_{4275}(2258,\cdot)\) \(\chi_{4275}(2267,\cdot)\) \(\chi_{4275}(2303,\cdot)\) \(\chi_{4275}(2438,\cdot)\) \(\chi_{4275}(2627,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1901,1027,1351)\) → \((-1,e\left(\frac{13}{20}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 4275 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{127}{180}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{23}{180}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{91}{180}\right)\) | \(e\left(\frac{49}{180}\right)\) |