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.et
\(\chi_{7581}(86,\cdot)\) \(\chi_{7581}(242,\cdot)\) \(\chi_{7581}(317,\cdot)\) \(\chi_{7581}(326,\cdot)\) \(\chi_{7581}(338,\cdot)\) \(\chi_{7581}(485,\cdot)\) \(\chi_{7581}(515,\cdot)\) \(\chi_{7581}(641,\cdot)\) \(\chi_{7581}(716,\cdot)\) \(\chi_{7581}(725,\cdot)\) \(\chi_{7581}(737,\cdot)\) \(\chi_{7581}(884,\cdot)\) \(\chi_{7581}(914,\cdot)\) \(\chi_{7581}(1040,\cdot)\) \(\chi_{7581}(1115,\cdot)\) \(\chi_{7581}(1124,\cdot)\) \(\chi_{7581}(1136,\cdot)\) \(\chi_{7581}(1283,\cdot)\) \(\chi_{7581}(1313,\cdot)\) \(\chi_{7581}(1439,\cdot)\) \(\chi_{7581}(1514,\cdot)\) \(\chi_{7581}(1523,\cdot)\) \(\chi_{7581}(1535,\cdot)\) \(\chi_{7581}(1682,\cdot)\) \(\chi_{7581}(1712,\cdot)\) \(\chi_{7581}(1838,\cdot)\) \(\chi_{7581}(1913,\cdot)\) \(\chi_{7581}(1922,\cdot)\) \(\chi_{7581}(1934,\cdot)\) \(\chi_{7581}(2081,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{53}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(86, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{171}\right)\) | \(e\left(\frac{110}{171}\right)\) | \(e\left(\frac{41}{342}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{151}{342}\right)\) | \(e\left(\frac{73}{114}\right)\) | \(e\left(\frac{337}{342}\right)\) | \(e\left(\frac{49}{171}\right)\) | \(e\left(\frac{293}{342}\right)\) | \(e\left(\frac{29}{38}\right)\) |