Basic properties
| Modulus: | \(7581\) | |
| Conductor: | \(2527\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(57\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2527}(58,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7581.cw
\(\chi_{7581}(58,\cdot)\) \(\chi_{7581}(172,\cdot)\) \(\chi_{7581}(457,\cdot)\) \(\chi_{7581}(571,\cdot)\) \(\chi_{7581}(856,\cdot)\) \(\chi_{7581}(970,\cdot)\) \(\chi_{7581}(1255,\cdot)\) \(\chi_{7581}(1369,\cdot)\) \(\chi_{7581}(1654,\cdot)\) \(\chi_{7581}(1768,\cdot)\) \(\chi_{7581}(2053,\cdot)\) \(\chi_{7581}(2452,\cdot)\) \(\chi_{7581}(2566,\cdot)\) \(\chi_{7581}(2851,\cdot)\) \(\chi_{7581}(2965,\cdot)\) \(\chi_{7581}(3364,\cdot)\) \(\chi_{7581}(3649,\cdot)\) \(\chi_{7581}(3763,\cdot)\) \(\chi_{7581}(4048,\cdot)\) \(\chi_{7581}(4162,\cdot)\) \(\chi_{7581}(4447,\cdot)\) \(\chi_{7581}(4561,\cdot)\) \(\chi_{7581}(4846,\cdot)\) \(\chi_{7581}(4960,\cdot)\) \(\chi_{7581}(5245,\cdot)\) \(\chi_{7581}(5359,\cdot)\) \(\chi_{7581}(5644,\cdot)\) \(\chi_{7581}(5758,\cdot)\) \(\chi_{7581}(6043,\cdot)\) \(\chi_{7581}(6157,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((2528,6499,1807)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{1}{19}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(58, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{6}{19}\right)\) |