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.iw
\(\chi_{7524}(47,\cdot)\) \(\chi_{7524}(443,\cdot)\) \(\chi_{7524}(731,\cdot)\) \(\chi_{7524}(1127,\cdot)\) \(\chi_{7524}(1175,\cdot)\) \(\chi_{7524}(1499,\cdot)\) \(\chi_{7524}(2099,\cdot)\) \(\chi_{7524}(2183,\cdot)\) \(\chi_{7524}(2495,\cdot)\) \(\chi_{7524}(3083,\cdot)\) \(\chi_{7524}(3215,\cdot)\) \(\chi_{7524}(3227,\cdot)\) \(\chi_{7524}(3551,\cdot)\) \(\chi_{7524}(3767,\cdot)\) \(\chi_{7524}(3899,\cdot)\) \(\chi_{7524}(4151,\cdot)\) \(\chi_{7524}(4547,\cdot)\) \(\chi_{7524}(5135,\cdot)\) \(\chi_{7524}(5267,\cdot)\) \(\chi_{7524}(5603,\cdot)\) \(\chi_{7524}(6647,\cdot)\) \(\chi_{7524}(7187,\cdot)\) \(\chi_{7524}(7319,\cdot)\) \(\chi_{7524}(7331,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{4}{5}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 7524 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{3}{5}\right)\) |