Basic properties
| Modulus: | \(7581\) | |
| Conductor: | \(7581\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | 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.dm
\(\chi_{7581}(83,\cdot)\) \(\chi_{7581}(125,\cdot)\) \(\chi_{7581}(482,\cdot)\) \(\chi_{7581}(524,\cdot)\) \(\chi_{7581}(881,\cdot)\) \(\chi_{7581}(923,\cdot)\) \(\chi_{7581}(1280,\cdot)\) \(\chi_{7581}(1322,\cdot)\) \(\chi_{7581}(1679,\cdot)\) \(\chi_{7581}(1721,\cdot)\) \(\chi_{7581}(2078,\cdot)\) \(\chi_{7581}(2120,\cdot)\) \(\chi_{7581}(2477,\cdot)\) \(\chi_{7581}(2519,\cdot)\) \(\chi_{7581}(2876,\cdot)\) \(\chi_{7581}(2918,\cdot)\) \(\chi_{7581}(3275,\cdot)\) \(\chi_{7581}(3674,\cdot)\) \(\chi_{7581}(3716,\cdot)\) \(\chi_{7581}(4073,\cdot)\) \(\chi_{7581}(4115,\cdot)\) \(\chi_{7581}(4472,\cdot)\) \(\chi_{7581}(4514,\cdot)\) \(\chi_{7581}(4871,\cdot)\) \(\chi_{7581}(4913,\cdot)\) \(\chi_{7581}(5270,\cdot)\) \(\chi_{7581}(5312,\cdot)\) \(\chi_{7581}(5669,\cdot)\) \(\chi_{7581}(5711,\cdot)\) \(\chi_{7581}(6110,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((-1,-1,e\left(\frac{31}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{25}{114}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{49}{114}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{5}{19}\right)\) |