Basic properties
| Modulus: | \(7524\) | |
| Conductor: | \(7524\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | 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 7524.jp
\(\chi_{7524}(119,\cdot)\) \(\chi_{7524}(587,\cdot)\) \(\chi_{7524}(707,\cdot)\) \(\chi_{7524}(1391,\cdot)\) \(\chi_{7524}(1631,\cdot)\) \(\chi_{7524}(1643,\cdot)\) \(\chi_{7524}(2039,\cdot)\) \(\chi_{7524}(2171,\cdot)\) \(\chi_{7524}(2315,\cdot)\) \(\chi_{7524}(2759,\cdot)\) \(\chi_{7524}(3683,\cdot)\) \(\chi_{7524}(4007,\cdot)\) \(\chi_{7524}(4691,\cdot)\) \(\chi_{7524}(4811,\cdot)\) \(\chi_{7524}(5063,\cdot)\) \(\chi_{7524}(5459,\cdot)\) \(\chi_{7524}(5591,\cdot)\) \(\chi_{7524}(5735,\cdot)\) \(\chi_{7524}(5747,\cdot)\) \(\chi_{7524}(6059,\cdot)\) \(\chi_{7524}(6143,\cdot)\) \(\chi_{7524}(6275,\cdot)\) \(\chi_{7524}(7115,\cdot)\) \(\chi_{7524}(7511,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{3}{5}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 7524 }(119, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{1}{5}\right)\) |