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 \(\chi_{1881}(193,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7524.iz
\(\chi_{7524}(193,\cdot)\) \(\chi_{7524}(205,\cdot)\) \(\chi_{7524}(337,\cdot)\) \(\chi_{7524}(877,\cdot)\) \(\chi_{7524}(1921,\cdot)\) \(\chi_{7524}(2257,\cdot)\) \(\chi_{7524}(2389,\cdot)\) \(\chi_{7524}(2977,\cdot)\) \(\chi_{7524}(3373,\cdot)\) \(\chi_{7524}(3625,\cdot)\) \(\chi_{7524}(3757,\cdot)\) \(\chi_{7524}(3973,\cdot)\) \(\chi_{7524}(4297,\cdot)\) \(\chi_{7524}(4309,\cdot)\) \(\chi_{7524}(4441,\cdot)\) \(\chi_{7524}(5029,\cdot)\) \(\chi_{7524}(5341,\cdot)\) \(\chi_{7524}(5425,\cdot)\) \(\chi_{7524}(6025,\cdot)\) \(\chi_{7524}(6349,\cdot)\) \(\chi_{7524}(6397,\cdot)\) \(\chi_{7524}(6793,\cdot)\) \(\chi_{7524}(7081,\cdot)\) \(\chi_{7524}(7477,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{9}{10}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 7524 }(193, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{3}{10}\right)\) |