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 \(\chi_{2793}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5586.ex
\(\chi_{5586}(5,\cdot)\) \(\chi_{5586}(101,\cdot)\) \(\chi_{5586}(131,\cdot)\) \(\chi_{5586}(479,\cdot)\) \(\chi_{5586}(719,\cdot)\) \(\chi_{5586}(731,\cdot)\) \(\chi_{5586}(899,\cdot)\) \(\chi_{5586}(929,\cdot)\) \(\chi_{5586}(1277,\cdot)\) \(\chi_{5586}(1517,\cdot)\) \(\chi_{5586}(1529,\cdot)\) \(\chi_{5586}(1601,\cdot)\) \(\chi_{5586}(1727,\cdot)\) \(\chi_{5586}(2075,\cdot)\) \(\chi_{5586}(2315,\cdot)\) \(\chi_{5586}(2327,\cdot)\) \(\chi_{5586}(2399,\cdot)\) \(\chi_{5586}(2495,\cdot)\) \(\chi_{5586}(2525,\cdot)\) \(\chi_{5586}(3113,\cdot)\) \(\chi_{5586}(3125,\cdot)\) \(\chi_{5586}(3197,\cdot)\) \(\chi_{5586}(3293,\cdot)\) \(\chi_{5586}(3323,\cdot)\) \(\chi_{5586}(3671,\cdot)\) \(\chi_{5586}(3911,\cdot)\) \(\chi_{5586}(3923,\cdot)\) \(\chi_{5586}(3995,\cdot)\) \(\chi_{5586}(4091,\cdot)\) \(\chi_{5586}(4121,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3725,4903,4999)\) → \((-1,e\left(\frac{29}{42}\right),e\left(\frac{8}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 5586 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{5}{126}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{26}{63}\right)\) |