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.jv
\(\chi_{7524}(223,\cdot)\) \(\chi_{7524}(355,\cdot)\) \(\chi_{7524}(751,\cdot)\) \(\chi_{7524}(763,\cdot)\) \(\chi_{7524}(907,\cdot)\) \(\chi_{7524}(1039,\cdot)\) \(\chi_{7524}(1435,\cdot)\) \(\chi_{7524}(1687,\cdot)\) \(\chi_{7524}(1807,\cdot)\) \(\chi_{7524}(2275,\cdot)\) \(\chi_{7524}(2407,\cdot)\) \(\chi_{7524}(2491,\cdot)\) \(\chi_{7524}(2803,\cdot)\) \(\chi_{7524}(3859,\cdot)\) \(\chi_{7524}(4183,\cdot)\) \(\chi_{7524}(4327,\cdot)\) \(\chi_{7524}(4459,\cdot)\) \(\chi_{7524}(4855,\cdot)\) \(\chi_{7524}(4867,\cdot)\) \(\chi_{7524}(5107,\cdot)\) \(\chi_{7524}(5791,\cdot)\) \(\chi_{7524}(5911,\cdot)\) \(\chi_{7524}(6235,\cdot)\) \(\chi_{7524}(7159,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{4}{5}\right),e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 7524 }(223, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{1}{10}\right)\) |