Basic properties
| Modulus: | \(7524\) | |
| Conductor: | \(209\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{209}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7524.it
\(\chi_{7524}(73,\cdot)\) \(\chi_{7524}(541,\cdot)\) \(\chi_{7524}(613,\cdot)\) \(\chi_{7524}(937,\cdot)\) \(\chi_{7524}(1657,\cdot)\) \(\chi_{7524}(1909,\cdot)\) \(\chi_{7524}(2125,\cdot)\) \(\chi_{7524}(2305,\cdot)\) \(\chi_{7524}(2449,\cdot)\) \(\chi_{7524}(2593,\cdot)\) \(\chi_{7524}(2989,\cdot)\) \(\chi_{7524}(3493,\cdot)\) \(\chi_{7524}(3709,\cdot)\) \(\chi_{7524}(4033,\cdot)\) \(\chi_{7524}(4177,\cdot)\) \(\chi_{7524}(4501,\cdot)\) \(\chi_{7524}(5077,\cdot)\) \(\chi_{7524}(5761,\cdot)\) \(\chi_{7524}(5869,\cdot)\) \(\chi_{7524}(6013,\cdot)\) \(\chi_{7524}(6085,\cdot)\) \(\chi_{7524}(6409,\cdot)\) \(\chi_{7524}(6553,\cdot)\) \(\chi_{7524}(7453,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((1,1,e\left(\frac{7}{10}\right),e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 7524 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{2}{5}\right)\) |