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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7524.ii
\(\chi_{7524}(79,\cdot)\) \(\chi_{7524}(1003,\cdot)\) \(\chi_{7524}(1447,\cdot)\) \(\chi_{7524}(1591,\cdot)\) \(\chi_{7524}(1723,\cdot)\) \(\chi_{7524}(2119,\cdot)\) \(\chi_{7524}(2131,\cdot)\) \(\chi_{7524}(2371,\cdot)\) \(\chi_{7524}(3055,\cdot)\) \(\chi_{7524}(3175,\cdot)\) \(\chi_{7524}(3643,\cdot)\) \(\chi_{7524}(3775,\cdot)\) \(\chi_{7524}(4171,\cdot)\) \(\chi_{7524}(5011,\cdot)\) \(\chi_{7524}(5143,\cdot)\) \(\chi_{7524}(5227,\cdot)\) \(\chi_{7524}(5539,\cdot)\) \(\chi_{7524}(5551,\cdot)\) \(\chi_{7524}(5695,\cdot)\) \(\chi_{7524}(5827,\cdot)\) \(\chi_{7524}(6223,\cdot)\) \(\chi_{7524}(6475,\cdot)\) \(\chi_{7524}(6595,\cdot)\) \(\chi_{7524}(7279,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{1}{10}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 7524 }(79, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) |