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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7581.eh
\(\chi_{7581}(23,\cdot)\) \(\chi_{7581}(44,\cdot)\) \(\chi_{7581}(74,\cdot)\) \(\chi_{7581}(263,\cdot)\) \(\chi_{7581}(275,\cdot)\) \(\chi_{7581}(347,\cdot)\) \(\chi_{7581}(422,\cdot)\) \(\chi_{7581}(443,\cdot)\) \(\chi_{7581}(473,\cdot)\) \(\chi_{7581}(662,\cdot)\) \(\chi_{7581}(674,\cdot)\) \(\chi_{7581}(746,\cdot)\) \(\chi_{7581}(842,\cdot)\) \(\chi_{7581}(872,\cdot)\) \(\chi_{7581}(1061,\cdot)\) \(\chi_{7581}(1073,\cdot)\) \(\chi_{7581}(1220,\cdot)\) \(\chi_{7581}(1241,\cdot)\) \(\chi_{7581}(1271,\cdot)\) \(\chi_{7581}(1460,\cdot)\) \(\chi_{7581}(1544,\cdot)\) \(\chi_{7581}(1619,\cdot)\) \(\chi_{7581}(1640,\cdot)\) \(\chi_{7581}(1670,\cdot)\) \(\chi_{7581}(1871,\cdot)\) \(\chi_{7581}(1943,\cdot)\) \(\chi_{7581}(2018,\cdot)\) \(\chi_{7581}(2069,\cdot)\) \(\chi_{7581}(2258,\cdot)\) \(\chi_{7581}(2270,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{52}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(44, a) \) | \(-1\) | \(1\) | \(e\left(\frac{161}{342}\right)\) | \(e\left(\frac{161}{171}\right)\) | \(e\left(\frac{245}{342}\right)\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{32}{171}\right)\) | \(e\left(\frac{97}{114}\right)\) | \(e\left(\frac{8}{171}\right)\) | \(e\left(\frac{151}{171}\right)\) | \(e\left(\frac{191}{342}\right)\) | \(e\left(\frac{25}{38}\right)\) |