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 \(\chi_{2527}(867,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5054.bv
\(\chi_{5054}(27,\cdot)\) \(\chi_{5054}(335,\cdot)\) \(\chi_{5054}(559,\cdot)\) \(\chi_{5054}(601,\cdot)\) \(\chi_{5054}(825,\cdot)\) \(\chi_{5054}(867,\cdot)\) \(\chi_{5054}(1091,\cdot)\) \(\chi_{5054}(1133,\cdot)\) \(\chi_{5054}(1357,\cdot)\) \(\chi_{5054}(1399,\cdot)\) \(\chi_{5054}(1623,\cdot)\) \(\chi_{5054}(1665,\cdot)\) \(\chi_{5054}(1889,\cdot)\) \(\chi_{5054}(1931,\cdot)\) \(\chi_{5054}(2155,\cdot)\) \(\chi_{5054}(2197,\cdot)\) \(\chi_{5054}(2421,\cdot)\) \(\chi_{5054}(2463,\cdot)\) \(\chi_{5054}(2687,\cdot)\) \(\chi_{5054}(2729,\cdot)\) \(\chi_{5054}(2953,\cdot)\) \(\chi_{5054}(2995,\cdot)\) \(\chi_{5054}(3219,\cdot)\) \(\chi_{5054}(3261,\cdot)\) \(\chi_{5054}(3485,\cdot)\) \(\chi_{5054}(3527,\cdot)\) \(\chi_{5054}(3751,\cdot)\) \(\chi_{5054}(3793,\cdot)\) \(\chi_{5054}(4017,\cdot)\) \(\chi_{5054}(4059,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((-1,e\left(\frac{83}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 5054 }(867, a) \) | \(1\) | \(1\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{13}{114}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{2}{19}\right)\) |