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 \(\chi_{931}(289,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5586.ec
\(\chi_{5586}(289,\cdot)\) \(\chi_{5586}(529,\cdot)\) \(\chi_{5586}(541,\cdot)\) \(\chi_{5586}(613,\cdot)\) \(\chi_{5586}(709,\cdot)\) \(\chi_{5586}(739,\cdot)\) \(\chi_{5586}(1087,\cdot)\) \(\chi_{5586}(1327,\cdot)\) \(\chi_{5586}(1339,\cdot)\) \(\chi_{5586}(1411,\cdot)\) \(\chi_{5586}(1507,\cdot)\) \(\chi_{5586}(1885,\cdot)\) \(\chi_{5586}(2209,\cdot)\) \(\chi_{5586}(2305,\cdot)\) \(\chi_{5586}(2335,\cdot)\) \(\chi_{5586}(2683,\cdot)\) \(\chi_{5586}(2923,\cdot)\) \(\chi_{5586}(2935,\cdot)\) \(\chi_{5586}(3103,\cdot)\) \(\chi_{5586}(3133,\cdot)\) \(\chi_{5586}(3481,\cdot)\) \(\chi_{5586}(3721,\cdot)\) \(\chi_{5586}(3733,\cdot)\) \(\chi_{5586}(3805,\cdot)\) \(\chi_{5586}(3931,\cdot)\) \(\chi_{5586}(4279,\cdot)\) \(\chi_{5586}(4519,\cdot)\) \(\chi_{5586}(4531,\cdot)\) \(\chi_{5586}(4603,\cdot)\) \(\chi_{5586}(4699,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((3725,4903,4999)\) → \((1,e\left(\frac{4}{21}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5586 }(289, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(1\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{19}{63}\right)\) |