Basic properties
| Modulus: | \(5586\) | |
| Conductor: | \(2793\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2793}(251,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5586.ek
\(\chi_{5586}(251,\cdot)\) \(\chi_{5586}(377,\cdot)\) \(\chi_{5586}(461,\cdot)\) \(\chi_{5586}(503,\cdot)\) \(\chi_{5586}(671,\cdot)\) \(\chi_{5586}(1049,\cdot)\) \(\chi_{5586}(1259,\cdot)\) \(\chi_{5586}(1301,\cdot)\) \(\chi_{5586}(1385,\cdot)\) \(\chi_{5586}(1847,\cdot)\) \(\chi_{5586}(1973,\cdot)\) \(\chi_{5586}(2099,\cdot)\) \(\chi_{5586}(2183,\cdot)\) \(\chi_{5586}(2267,\cdot)\) \(\chi_{5586}(2771,\cdot)\) \(\chi_{5586}(2855,\cdot)\) \(\chi_{5586}(2897,\cdot)\) \(\chi_{5586}(2981,\cdot)\) \(\chi_{5586}(3065,\cdot)\) \(\chi_{5586}(3443,\cdot)\) \(\chi_{5586}(3569,\cdot)\) \(\chi_{5586}(3653,\cdot)\) \(\chi_{5586}(3695,\cdot)\) \(\chi_{5586}(3779,\cdot)\) \(\chi_{5586}(3863,\cdot)\) \(\chi_{5586}(4241,\cdot)\) \(\chi_{5586}(4367,\cdot)\) \(\chi_{5586}(4451,\cdot)\) \(\chi_{5586}(4493,\cdot)\) \(\chi_{5586}(4577,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3725,4903,4999)\) → \((-1,e\left(\frac{9}{14}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5586 }(251, a) \) | \(1\) | \(1\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{121}{126}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{37}{63}\right)\) |