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 \(\chi_{2527}(163,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5054.bk
\(\chi_{5054}(163,\cdot)\) \(\chi_{5054}(235,\cdot)\) \(\chi_{5054}(501,\cdot)\) \(\chi_{5054}(695,\cdot)\) \(\chi_{5054}(767,\cdot)\) \(\chi_{5054}(961,\cdot)\) \(\chi_{5054}(1033,\cdot)\) \(\chi_{5054}(1227,\cdot)\) \(\chi_{5054}(1299,\cdot)\) \(\chi_{5054}(1493,\cdot)\) \(\chi_{5054}(1565,\cdot)\) \(\chi_{5054}(1759,\cdot)\) \(\chi_{5054}(1831,\cdot)\) \(\chi_{5054}(2025,\cdot)\) \(\chi_{5054}(2291,\cdot)\) \(\chi_{5054}(2363,\cdot)\) \(\chi_{5054}(2557,\cdot)\) \(\chi_{5054}(2629,\cdot)\) \(\chi_{5054}(2823,\cdot)\) \(\chi_{5054}(2895,\cdot)\) \(\chi_{5054}(3089,\cdot)\) \(\chi_{5054}(3161,\cdot)\) \(\chi_{5054}(3355,\cdot)\) \(\chi_{5054}(3427,\cdot)\) \(\chi_{5054}(3621,\cdot)\) \(\chi_{5054}(3693,\cdot)\) \(\chi_{5054}(3887,\cdot)\) \(\chi_{5054}(3959,\cdot)\) \(\chi_{5054}(4153,\cdot)\) \(\chi_{5054}(4225,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\((1445,1807)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{35}{57}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 5054 }(163, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{1}{19}\right)\) |