Basic properties
| Modulus: | \(7524\) | |
| Conductor: | \(2508\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2508}(251,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7524.ip
\(\chi_{7524}(251,\cdot)\) \(\chi_{7524}(575,\cdot)\) \(\chi_{7524}(719,\cdot)\) \(\chi_{7524}(1043,\cdot)\) \(\chi_{7524}(1259,\cdot)\) \(\chi_{7524}(2303,\cdot)\) \(\chi_{7524}(2555,\cdot)\) \(\chi_{7524}(2627,\cdot)\) \(\chi_{7524}(2951,\cdot)\) \(\chi_{7524}(3095,\cdot)\) \(\chi_{7524}(3239,\cdot)\) \(\chi_{7524}(3635,\cdot)\) \(\chi_{7524}(4139,\cdot)\) \(\chi_{7524}(4607,\cdot)\) \(\chi_{7524}(4679,\cdot)\) \(\chi_{7524}(4823,\cdot)\) \(\chi_{7524}(5003,\cdot)\) \(\chi_{7524}(5723,\cdot)\) \(\chi_{7524}(6191,\cdot)\) \(\chi_{7524}(6407,\cdot)\) \(\chi_{7524}(6515,\cdot)\) \(\chi_{7524}(6659,\cdot)\) \(\chi_{7524}(7055,\cdot)\) \(\chi_{7524}(7199,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((-1,-1,e\left(\frac{3}{5}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 7524 }(251, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{1}{5}\right)\) |