Basic properties
| Modulus: | \(7524\) | |
| Conductor: | \(1881\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1881}(97,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7524.ig
\(\chi_{7524}(97,\cdot)\) \(\chi_{7524}(421,\cdot)\) \(\chi_{7524}(565,\cdot)\) \(\chi_{7524}(697,\cdot)\) \(\chi_{7524}(1093,\cdot)\) \(\chi_{7524}(1105,\cdot)\) \(\chi_{7524}(1345,\cdot)\) \(\chi_{7524}(2029,\cdot)\) \(\chi_{7524}(2149,\cdot)\) \(\chi_{7524}(2473,\cdot)\) \(\chi_{7524}(3397,\cdot)\) \(\chi_{7524}(3985,\cdot)\) \(\chi_{7524}(4117,\cdot)\) \(\chi_{7524}(4513,\cdot)\) \(\chi_{7524}(4525,\cdot)\) \(\chi_{7524}(4669,\cdot)\) \(\chi_{7524}(4801,\cdot)\) \(\chi_{7524}(5197,\cdot)\) \(\chi_{7524}(5449,\cdot)\) \(\chi_{7524}(5569,\cdot)\) \(\chi_{7524}(6037,\cdot)\) \(\chi_{7524}(6169,\cdot)\) \(\chi_{7524}(6253,\cdot)\) \(\chi_{7524}(6565,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{3}{5}\right),e\left(\frac{1}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 7524 }(97, a) \) | \(-1\) | \(1\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) |