Basic properties
Modulus: | \(987\) | |
Conductor: | \(987\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(138\) | 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 987.bc
\(\chi_{987}(11,\cdot)\) \(\chi_{987}(23,\cdot)\) \(\chi_{987}(44,\cdot)\) \(\chi_{987}(86,\cdot)\) \(\chi_{987}(107,\cdot)\) \(\chi_{987}(116,\cdot)\) \(\chi_{987}(137,\cdot)\) \(\chi_{987}(170,\cdot)\) \(\chi_{987}(179,\cdot)\) \(\chi_{987}(221,\cdot)\) \(\chi_{987}(233,\cdot)\) \(\chi_{987}(254,\cdot)\) \(\chi_{987}(275,\cdot)\) \(\chi_{987}(305,\cdot)\) \(\chi_{987}(317,\cdot)\) \(\chi_{987}(326,\cdot)\) \(\chi_{987}(359,\cdot)\) \(\chi_{987}(368,\cdot)\) \(\chi_{987}(389,\cdot)\) \(\chi_{987}(443,\cdot)\) \(\chi_{987}(452,\cdot)\) \(\chi_{987}(464,\cdot)\) \(\chi_{987}(485,\cdot)\) \(\chi_{987}(515,\cdot)\) \(\chi_{987}(527,\cdot)\) \(\chi_{987}(536,\cdot)\) \(\chi_{987}(548,\cdot)\) \(\chi_{987}(557,\cdot)\) \(\chi_{987}(569,\cdot)\) \(\chi_{987}(590,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{69})$ |
Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\((659,283,757)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{43}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 987 }(44, a) \) | \(1\) | \(1\) | \(e\left(\frac{137}{138}\right)\) | \(e\left(\frac{68}{69}\right)\) | \(e\left(\frac{7}{69}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{13}{138}\right)\) | \(e\left(\frac{26}{69}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{67}{69}\right)\) | \(e\left(\frac{109}{138}\right)\) | \(e\left(\frac{101}{138}\right)\) |