Basic properties
| Modulus: | \(5292\) | |
| Conductor: | \(5292\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5292.en
\(\chi_{5292}(155,\cdot)\) \(\chi_{5292}(239,\cdot)\) \(\chi_{5292}(407,\cdot)\) \(\chi_{5292}(659,\cdot)\) \(\chi_{5292}(743,\cdot)\) \(\chi_{5292}(911,\cdot)\) \(\chi_{5292}(995,\cdot)\) \(\chi_{5292}(1163,\cdot)\) \(\chi_{5292}(1247,\cdot)\) \(\chi_{5292}(1415,\cdot)\) \(\chi_{5292}(1499,\cdot)\) \(\chi_{5292}(1751,\cdot)\) \(\chi_{5292}(1919,\cdot)\) \(\chi_{5292}(2003,\cdot)\) \(\chi_{5292}(2171,\cdot)\) \(\chi_{5292}(2423,\cdot)\) \(\chi_{5292}(2507,\cdot)\) \(\chi_{5292}(2675,\cdot)\) \(\chi_{5292}(2759,\cdot)\) \(\chi_{5292}(2927,\cdot)\) \(\chi_{5292}(3011,\cdot)\) \(\chi_{5292}(3179,\cdot)\) \(\chi_{5292}(3263,\cdot)\) \(\chi_{5292}(3515,\cdot)\) \(\chi_{5292}(3683,\cdot)\) \(\chi_{5292}(3767,\cdot)\) \(\chi_{5292}(3935,\cdot)\) \(\chi_{5292}(4187,\cdot)\) \(\chi_{5292}(4271,\cdot)\) \(\chi_{5292}(4439,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((2647,785,1081)\) → \((-1,e\left(\frac{7}{18}\right),e\left(\frac{6}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5292 }(155, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{126}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{16}{21}\right)\) |