Basic properties
Modulus: | \(5054\) | |
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 \(\chi_{2527}(145,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5054.bx
\(\chi_{5054}(145,\cdot)\) \(\chi_{5054}(255,\cdot)\) \(\chi_{5054}(411,\cdot)\) \(\chi_{5054}(521,\cdot)\) \(\chi_{5054}(677,\cdot)\) \(\chi_{5054}(787,\cdot)\) \(\chi_{5054}(943,\cdot)\) \(\chi_{5054}(1053,\cdot)\) \(\chi_{5054}(1209,\cdot)\) \(\chi_{5054}(1319,\cdot)\) \(\chi_{5054}(1475,\cdot)\) \(\chi_{5054}(1585,\cdot)\) \(\chi_{5054}(1741,\cdot)\) \(\chi_{5054}(1851,\cdot)\) \(\chi_{5054}(2007,\cdot)\) \(\chi_{5054}(2117,\cdot)\) \(\chi_{5054}(2273,\cdot)\) \(\chi_{5054}(2383,\cdot)\) \(\chi_{5054}(2539,\cdot)\) \(\chi_{5054}(2649,\cdot)\) \(\chi_{5054}(2805,\cdot)\) \(\chi_{5054}(2915,\cdot)\) \(\chi_{5054}(3071,\cdot)\) \(\chi_{5054}(3337,\cdot)\) \(\chi_{5054}(3447,\cdot)\) \(\chi_{5054}(3603,\cdot)\) \(\chi_{5054}(3713,\cdot)\) \(\chi_{5054}(3869,\cdot)\) \(\chi_{5054}(3979,\cdot)\) \(\chi_{5054}(4135,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{83}{114}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 5054 }(145, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{13}{114}\right)\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{2}{19}\right)\) |