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.ex
\(\chi_{7581}(2,\cdot)\) \(\chi_{7581}(32,\cdot)\) \(\chi_{7581}(53,\cdot)\) \(\chi_{7581}(128,\cdot)\) \(\chi_{7581}(200,\cdot)\) \(\chi_{7581}(212,\cdot)\) \(\chi_{7581}(401,\cdot)\) \(\chi_{7581}(431,\cdot)\) \(\chi_{7581}(452,\cdot)\) \(\chi_{7581}(527,\cdot)\) \(\chi_{7581}(599,\cdot)\) \(\chi_{7581}(611,\cdot)\) \(\chi_{7581}(800,\cdot)\) \(\chi_{7581}(830,\cdot)\) \(\chi_{7581}(851,\cdot)\) \(\chi_{7581}(926,\cdot)\) \(\chi_{7581}(998,\cdot)\) \(\chi_{7581}(1010,\cdot)\) \(\chi_{7581}(1229,\cdot)\) \(\chi_{7581}(1250,\cdot)\) \(\chi_{7581}(1325,\cdot)\) \(\chi_{7581}(1397,\cdot)\) \(\chi_{7581}(1409,\cdot)\) \(\chi_{7581}(1598,\cdot)\) \(\chi_{7581}(1628,\cdot)\) \(\chi_{7581}(1649,\cdot)\) \(\chi_{7581}(1724,\cdot)\) \(\chi_{7581}(1796,\cdot)\) \(\chi_{7581}(1808,\cdot)\) \(\chi_{7581}(1997,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{83}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{171}\right)\) | \(e\left(\frac{26}{171}\right)\) | \(e\left(\frac{47}{342}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{73}{342}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{289}{342}\right)\) | \(e\left(\frac{52}{171}\right)\) | \(e\left(\frac{5}{342}\right)\) | \(e\left(\frac{11}{38}\right)\) |