Basic properties
| Modulus: | \(7581\) | |
| Conductor: | \(2527\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2527}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7581.dl
\(\chi_{7581}(37,\cdot)\) \(\chi_{7581}(151,\cdot)\) \(\chi_{7581}(436,\cdot)\) \(\chi_{7581}(550,\cdot)\) \(\chi_{7581}(835,\cdot)\) \(\chi_{7581}(949,\cdot)\) \(\chi_{7581}(1234,\cdot)\) \(\chi_{7581}(1348,\cdot)\) \(\chi_{7581}(1633,\cdot)\) \(\chi_{7581}(1747,\cdot)\) \(\chi_{7581}(2032,\cdot)\) \(\chi_{7581}(2146,\cdot)\) \(\chi_{7581}(2431,\cdot)\) \(\chi_{7581}(2545,\cdot)\) \(\chi_{7581}(2830,\cdot)\) \(\chi_{7581}(2944,\cdot)\) \(\chi_{7581}(3229,\cdot)\) \(\chi_{7581}(3343,\cdot)\) \(\chi_{7581}(3628,\cdot)\) \(\chi_{7581}(3742,\cdot)\) \(\chi_{7581}(4027,\cdot)\) \(\chi_{7581}(4141,\cdot)\) \(\chi_{7581}(4426,\cdot)\) \(\chi_{7581}(4540,\cdot)\) \(\chi_{7581}(4825,\cdot)\) \(\chi_{7581}(4939,\cdot)\) \(\chi_{7581}(5224,\cdot)\) \(\chi_{7581}(5338,\cdot)\) \(\chi_{7581}(5623,\cdot)\) \(\chi_{7581}(5737,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{5}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{91}{114}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{113}{114}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{15}{19}\right)\) |