Basic properties
| Modulus: | \(10110\) | |
| Conductor: | \(5055\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{5055}(113,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 10110.ez
\(\chi_{10110}(113,\cdot)\) \(\chi_{10110}(167,\cdot)\) \(\chi_{10110}(287,\cdot)\) \(\chi_{10110}(323,\cdot)\) \(\chi_{10110}(437,\cdot)\) \(\chi_{10110}(677,\cdot)\) \(\chi_{10110}(737,\cdot)\) \(\chi_{10110}(917,\cdot)\) \(\chi_{10110}(983,\cdot)\) \(\chi_{10110}(1193,\cdot)\) \(\chi_{10110}(1253,\cdot)\) \(\chi_{10110}(1463,\cdot)\) \(\chi_{10110}(1607,\cdot)\) \(\chi_{10110}(1697,\cdot)\) \(\chi_{10110}(1793,\cdot)\) \(\chi_{10110}(1877,\cdot)\) \(\chi_{10110}(2273,\cdot)\) \(\chi_{10110}(2843,\cdot)\) \(\chi_{10110}(3263,\cdot)\) \(\chi_{10110}(3953,\cdot)\) \(\chi_{10110}(4493,\cdot)\) \(\chi_{10110}(4943,\cdot)\) \(\chi_{10110}(5483,\cdot)\) \(\chi_{10110}(5537,\cdot)\) \(\chi_{10110}(5717,\cdot)\) \(\chi_{10110}(5807,\cdot)\) \(\chi_{10110}(6173,\cdot)\) \(\chi_{10110}(6497,\cdot)\) \(\chi_{10110}(6593,\cdot)\) \(\chi_{10110}(6677,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((3371,6067,1021)\) → \((-1,-i,e\left(\frac{163}{168}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 10110 }(113, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{55}{56}\right)\) | \(e\left(\frac{43}{168}\right)\) | \(e\left(\frac{157}{168}\right)\) | \(e\left(\frac{59}{168}\right)\) | \(e\left(\frac{167}{168}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{20}{21}\right)\) |