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.dj
\(\chi_{7581}(248,\cdot)\) \(\chi_{7581}(647,\cdot)\) \(\chi_{7581}(761,\cdot)\) \(\chi_{7581}(1046,\cdot)\) \(\chi_{7581}(1160,\cdot)\) \(\chi_{7581}(1559,\cdot)\) \(\chi_{7581}(1844,\cdot)\) \(\chi_{7581}(1958,\cdot)\) \(\chi_{7581}(2243,\cdot)\) \(\chi_{7581}(2357,\cdot)\) \(\chi_{7581}(2642,\cdot)\) \(\chi_{7581}(2756,\cdot)\) \(\chi_{7581}(3041,\cdot)\) \(\chi_{7581}(3155,\cdot)\) \(\chi_{7581}(3440,\cdot)\) \(\chi_{7581}(3554,\cdot)\) \(\chi_{7581}(3839,\cdot)\) \(\chi_{7581}(3953,\cdot)\) \(\chi_{7581}(4238,\cdot)\) \(\chi_{7581}(4352,\cdot)\) \(\chi_{7581}(4637,\cdot)\) \(\chi_{7581}(4751,\cdot)\) \(\chi_{7581}(5036,\cdot)\) \(\chi_{7581}(5150,\cdot)\) \(\chi_{7581}(5435,\cdot)\) \(\chi_{7581}(5549,\cdot)\) \(\chi_{7581}(5834,\cdot)\) \(\chi_{7581}(5948,\cdot)\) \(\chi_{7581}(6233,\cdot)\) \(\chi_{7581}(6347,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{17}{19}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(248, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{114}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{73}{114}\right)\) | \(e\left(\frac{49}{114}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{7}{19}\right)\) |