Basic properties
| Modulus: | \(7581\) | |
| Conductor: | \(7581\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | 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 7581.en
\(\chi_{7581}(5,\cdot)\) \(\chi_{7581}(80,\cdot)\) \(\chi_{7581}(101,\cdot)\) \(\chi_{7581}(131,\cdot)\) \(\chi_{7581}(320,\cdot)\) \(\chi_{7581}(332,\cdot)\) \(\chi_{7581}(404,\cdot)\) \(\chi_{7581}(479,\cdot)\) \(\chi_{7581}(500,\cdot)\) \(\chi_{7581}(530,\cdot)\) \(\chi_{7581}(719,\cdot)\) \(\chi_{7581}(731,\cdot)\) \(\chi_{7581}(803,\cdot)\) \(\chi_{7581}(878,\cdot)\) \(\chi_{7581}(899,\cdot)\) \(\chi_{7581}(929,\cdot)\) \(\chi_{7581}(1118,\cdot)\) \(\chi_{7581}(1130,\cdot)\) \(\chi_{7581}(1202,\cdot)\) \(\chi_{7581}(1277,\cdot)\) \(\chi_{7581}(1298,\cdot)\) \(\chi_{7581}(1517,\cdot)\) \(\chi_{7581}(1529,\cdot)\) \(\chi_{7581}(1601,\cdot)\) \(\chi_{7581}(1676,\cdot)\) \(\chi_{7581}(1697,\cdot)\) \(\chi_{7581}(1727,\cdot)\) \(\chi_{7581}(1916,\cdot)\) \(\chi_{7581}(1928,\cdot)\) \(\chi_{7581}(2000,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{116}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{289}{342}\right)\) | \(e\left(\frac{118}{171}\right)\) | \(e\left(\frac{8}{171}\right)\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{305}{342}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{233}{342}\right)\) | \(e\left(\frac{65}{171}\right)\) | \(e\left(\frac{110}{171}\right)\) | \(e\left(\frac{14}{19}\right)\) |