Basic properties
Modulus: | \(1068\) | |
Conductor: | \(1068\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1068.bf
\(\chi_{1068}(23,\cdot)\) \(\chi_{1068}(35,\cdot)\) \(\chi_{1068}(59,\cdot)\) \(\chi_{1068}(83,\cdot)\) \(\chi_{1068}(95,\cdot)\) \(\chi_{1068}(119,\cdot)\) \(\chi_{1068}(143,\cdot)\) \(\chi_{1068}(155,\cdot)\) \(\chi_{1068}(191,\cdot)\) \(\chi_{1068}(239,\cdot)\) \(\chi_{1068}(323,\cdot)\) \(\chi_{1068}(359,\cdot)\) \(\chi_{1068}(371,\cdot)\) \(\chi_{1068}(383,\cdot)\) \(\chi_{1068}(407,\cdot)\) \(\chi_{1068}(419,\cdot)\) \(\chi_{1068}(431,\cdot)\) \(\chi_{1068}(491,\cdot)\) \(\chi_{1068}(503,\cdot)\) \(\chi_{1068}(515,\cdot)\) \(\chi_{1068}(527,\cdot)\) \(\chi_{1068}(563,\cdot)\) \(\chi_{1068}(575,\cdot)\) \(\chi_{1068}(599,\cdot)\) \(\chi_{1068}(647,\cdot)\) \(\chi_{1068}(671,\cdot)\) \(\chi_{1068}(683,\cdot)\) \(\chi_{1068}(719,\cdot)\) \(\chi_{1068}(731,\cdot)\) \(\chi_{1068}(743,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((535,713,181)\) → \((-1,-1,e\left(\frac{59}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 1068 }(563, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{71}{88}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{85}{88}\right)\) | \(e\left(\frac{19}{88}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{5}{88}\right)\) | \(e\left(\frac{25}{88}\right)\) |