Basic properties
| Modulus: | \(5054\) | |
| 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 \(\chi_{2527}(39,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5054.bn
\(\chi_{5054}(39,\cdot)\) \(\chi_{5054}(191,\cdot)\) \(\chi_{5054}(305,\cdot)\) \(\chi_{5054}(457,\cdot)\) \(\chi_{5054}(571,\cdot)\) \(\chi_{5054}(837,\cdot)\) \(\chi_{5054}(989,\cdot)\) \(\chi_{5054}(1103,\cdot)\) \(\chi_{5054}(1255,\cdot)\) \(\chi_{5054}(1369,\cdot)\) \(\chi_{5054}(1521,\cdot)\) \(\chi_{5054}(1635,\cdot)\) \(\chi_{5054}(1787,\cdot)\) \(\chi_{5054}(1901,\cdot)\) \(\chi_{5054}(2053,\cdot)\) \(\chi_{5054}(2319,\cdot)\) \(\chi_{5054}(2433,\cdot)\) \(\chi_{5054}(2585,\cdot)\) \(\chi_{5054}(2699,\cdot)\) \(\chi_{5054}(2851,\cdot)\) \(\chi_{5054}(2965,\cdot)\) \(\chi_{5054}(3117,\cdot)\) \(\chi_{5054}(3231,\cdot)\) \(\chi_{5054}(3383,\cdot)\) \(\chi_{5054}(3497,\cdot)\) \(\chi_{5054}(3649,\cdot)\) \(\chi_{5054}(3763,\cdot)\) \(\chi_{5054}(3915,\cdot)\) \(\chi_{5054}(4029,\cdot)\) \(\chi_{5054}(4181,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((1445,1807)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{7}{19}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 5054 }(39, a) \) | \(1\) | \(1\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{12}{19}\right)\) |