Basic properties
| Modulus: | \(7581\) | |
| Conductor: | \(2527\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2527}(10,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7581.ee
\(\chi_{7581}(10,\cdot)\) \(\chi_{7581}(40,\cdot)\) \(\chi_{7581}(166,\cdot)\) \(\chi_{7581}(241,\cdot)\) \(\chi_{7581}(250,\cdot)\) \(\chi_{7581}(409,\cdot)\) \(\chi_{7581}(439,\cdot)\) \(\chi_{7581}(565,\cdot)\) \(\chi_{7581}(640,\cdot)\) \(\chi_{7581}(649,\cdot)\) \(\chi_{7581}(661,\cdot)\) \(\chi_{7581}(808,\cdot)\) \(\chi_{7581}(964,\cdot)\) \(\chi_{7581}(1039,\cdot)\) \(\chi_{7581}(1048,\cdot)\) \(\chi_{7581}(1060,\cdot)\) \(\chi_{7581}(1207,\cdot)\) \(\chi_{7581}(1237,\cdot)\) \(\chi_{7581}(1363,\cdot)\) \(\chi_{7581}(1438,\cdot)\) \(\chi_{7581}(1447,\cdot)\) \(\chi_{7581}(1459,\cdot)\) \(\chi_{7581}(1606,\cdot)\) \(\chi_{7581}(1636,\cdot)\) \(\chi_{7581}(1762,\cdot)\) \(\chi_{7581}(1837,\cdot)\) \(\chi_{7581}(1846,\cdot)\) \(\chi_{7581}(1858,\cdot)\) \(\chi_{7581}(2005,\cdot)\) \(\chi_{7581}(2035,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{233}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(10, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{342}\right)\) | \(e\left(\frac{5}{171}\right)\) | \(e\left(\frac{305}{342}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{155}{171}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{110}{171}\right)\) | \(e\left(\frac{10}{171}\right)\) | \(e\left(\frac{47}{342}\right)\) | \(e\left(\frac{35}{38}\right)\) |