Basic properties
| Modulus: | \(5586\) | |
| Conductor: | \(931\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{931}(241,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5586.ed
\(\chi_{5586}(241,\cdot)\) \(\chi_{5586}(409,\cdot)\) \(\chi_{5586}(439,\cdot)\) \(\chi_{5586}(565,\cdot)\) \(\chi_{5586}(649,\cdot)\) \(\chi_{5586}(661,\cdot)\) \(\chi_{5586}(1039,\cdot)\) \(\chi_{5586}(1237,\cdot)\) \(\chi_{5586}(1363,\cdot)\) \(\chi_{5586}(1447,\cdot)\) \(\chi_{5586}(1459,\cdot)\) \(\chi_{5586}(1837,\cdot)\) \(\chi_{5586}(2005,\cdot)\) \(\chi_{5586}(2035,\cdot)\) \(\chi_{5586}(2161,\cdot)\) \(\chi_{5586}(2245,\cdot)\) \(\chi_{5586}(2257,\cdot)\) \(\chi_{5586}(2635,\cdot)\) \(\chi_{5586}(2803,\cdot)\) \(\chi_{5586}(2833,\cdot)\) \(\chi_{5586}(3043,\cdot)\) \(\chi_{5586}(3055,\cdot)\) \(\chi_{5586}(3433,\cdot)\) \(\chi_{5586}(3601,\cdot)\) \(\chi_{5586}(3631,\cdot)\) \(\chi_{5586}(3757,\cdot)\) \(\chi_{5586}(4231,\cdot)\) \(\chi_{5586}(4399,\cdot)\) \(\chi_{5586}(4555,\cdot)\) \(\chi_{5586}(4639,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3725,4903,4999)\) → \((1,e\left(\frac{31}{42}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 5586 }(241, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{126}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{43}{63}\right)\) |