Basic properties
| Modulus: | \(5586\) | |
| Conductor: | \(931\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{931}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5586.ea
\(\chi_{5586}(25,\cdot)\) \(\chi_{5586}(403,\cdot)\) \(\chi_{5586}(415,\cdot)\) \(\chi_{5586}(499,\cdot)\) \(\chi_{5586}(625,\cdot)\) \(\chi_{5586}(823,\cdot)\) \(\chi_{5586}(1201,\cdot)\) \(\chi_{5586}(1213,\cdot)\) \(\chi_{5586}(1297,\cdot)\) \(\chi_{5586}(1423,\cdot)\) \(\chi_{5586}(1453,\cdot)\) \(\chi_{5586}(1621,\cdot)\) \(\chi_{5586}(1999,\cdot)\) \(\chi_{5586}(2011,\cdot)\) \(\chi_{5586}(2095,\cdot)\) \(\chi_{5586}(2221,\cdot)\) \(\chi_{5586}(2251,\cdot)\) \(\chi_{5586}(2797,\cdot)\) \(\chi_{5586}(2809,\cdot)\) \(\chi_{5586}(2893,\cdot)\) \(\chi_{5586}(3049,\cdot)\) \(\chi_{5586}(3217,\cdot)\) \(\chi_{5586}(3691,\cdot)\) \(\chi_{5586}(3817,\cdot)\) \(\chi_{5586}(3847,\cdot)\) \(\chi_{5586}(4015,\cdot)\) \(\chi_{5586}(4393,\cdot)\) \(\chi_{5586}(4405,\cdot)\) \(\chi_{5586}(4615,\cdot)\) \(\chi_{5586}(4645,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((3725,4903,4999)\) → \((1,e\left(\frac{8}{21}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5586 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{52}{63}\right)\) |