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 \(\chi_{1881}(101,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7524.il
\(\chi_{7524}(101,\cdot)\) \(\chi_{7524}(149,\cdot)\) \(\chi_{7524}(689,\cdot)\) \(\chi_{7524}(821,\cdot)\) \(\chi_{7524}(833,\cdot)\) \(\chi_{7524}(1073,\cdot)\) \(\chi_{7524}(1157,\cdot)\) \(\chi_{7524}(1469,\cdot)\) \(\chi_{7524}(1757,\cdot)\) \(\chi_{7524}(2153,\cdot)\) \(\chi_{7524}(2525,\cdot)\) \(\chi_{7524}(2741,\cdot)\) \(\chi_{7524}(2873,\cdot)\) \(\chi_{7524}(3209,\cdot)\) \(\chi_{7524}(4109,\cdot)\) \(\chi_{7524}(4241,\cdot)\) \(\chi_{7524}(4253,\cdot)\) \(\chi_{7524}(4793,\cdot)\) \(\chi_{7524}(4925,\cdot)\) \(\chi_{7524}(5177,\cdot)\) \(\chi_{7524}(5573,\cdot)\) \(\chi_{7524}(6305,\cdot)\) \(\chi_{7524}(6629,\cdot)\) \(\chi_{7524}(7229,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{1}{10}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 7524 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{1}{5}\right)\) |