Basic properties
Modulus: | \(1335\) | |
Conductor: | \(1335\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1335.bw
\(\chi_{1335}(14,\cdot)\) \(\chi_{1335}(29,\cdot)\) \(\chi_{1335}(59,\cdot)\) \(\chi_{1335}(74,\cdot)\) \(\chi_{1335}(104,\cdot)\) \(\chi_{1335}(119,\cdot)\) \(\chi_{1335}(149,\cdot)\) \(\chi_{1335}(164,\cdot)\) \(\chi_{1335}(209,\cdot)\) \(\chi_{1335}(224,\cdot)\) \(\chi_{1335}(239,\cdot)\) \(\chi_{1335}(254,\cdot)\) \(\chi_{1335}(329,\cdot)\) \(\chi_{1335}(359,\cdot)\) \(\chi_{1335}(389,\cdot)\) \(\chi_{1335}(404,\cdot)\) \(\chi_{1335}(419,\cdot)\) \(\chi_{1335}(464,\cdot)\) \(\chi_{1335}(569,\cdot)\) \(\chi_{1335}(599,\cdot)\) \(\chi_{1335}(629,\cdot)\) \(\chi_{1335}(674,\cdot)\) \(\chi_{1335}(689,\cdot)\) \(\chi_{1335}(719,\cdot)\) \(\chi_{1335}(794,\cdot)\) \(\chi_{1335}(824,\cdot)\) \(\chi_{1335}(839,\cdot)\) \(\chi_{1335}(884,\cdot)\) \(\chi_{1335}(914,\cdot)\) \(\chi_{1335}(944,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((446,802,181)\) → \((-1,-1,e\left(\frac{37}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1335 }(794, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{49}{88}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{25}{88}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{63}{88}\right)\) |