Basic properties
| Modulus: | \(1425\) | |
| Conductor: | \(1425\) | 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 1425.cr
\(\chi_{1425}(17,\cdot)\) \(\chi_{1425}(23,\cdot)\) \(\chi_{1425}(47,\cdot)\) \(\chi_{1425}(62,\cdot)\) \(\chi_{1425}(92,\cdot)\) \(\chi_{1425}(137,\cdot)\) \(\chi_{1425}(158,\cdot)\) \(\chi_{1425}(188,\cdot)\) \(\chi_{1425}(233,\cdot)\) \(\chi_{1425}(263,\cdot)\) \(\chi_{1425}(272,\cdot)\) \(\chi_{1425}(302,\cdot)\) \(\chi_{1425}(308,\cdot)\) \(\chi_{1425}(347,\cdot)\) \(\chi_{1425}(377,\cdot)\) \(\chi_{1425}(422,\cdot)\) \(\chi_{1425}(473,\cdot)\) \(\chi_{1425}(503,\cdot)\) \(\chi_{1425}(548,\cdot)\) \(\chi_{1425}(587,\cdot)\) \(\chi_{1425}(617,\cdot)\) \(\chi_{1425}(662,\cdot)\) \(\chi_{1425}(728,\cdot)\) \(\chi_{1425}(758,\cdot)\) \(\chi_{1425}(788,\cdot)\) \(\chi_{1425}(803,\cdot)\) \(\chi_{1425}(833,\cdot)\) \(\chi_{1425}(842,\cdot)\) \(\chi_{1425}(872,\cdot)\) \(\chi_{1425}(878,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((476,1027,1351)\) → \((-1,e\left(\frac{13}{20}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 1425 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{127}{180}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{23}{180}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{91}{180}\right)\) | \(e\left(\frac{49}{180}\right)\) |