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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 987.z
\(\chi_{987}(2,\cdot)\) \(\chi_{987}(32,\cdot)\) \(\chi_{987}(53,\cdot)\) \(\chi_{987}(65,\cdot)\) \(\chi_{987}(74,\cdot)\) \(\chi_{987}(128,\cdot)\) \(\chi_{987}(149,\cdot)\) \(\chi_{987}(158,\cdot)\) \(\chi_{987}(191,\cdot)\) \(\chi_{987}(200,\cdot)\) \(\chi_{987}(212,\cdot)\) \(\chi_{987}(242,\cdot)\) \(\chi_{987}(263,\cdot)\) \(\chi_{987}(284,\cdot)\) \(\chi_{987}(296,\cdot)\) \(\chi_{987}(338,\cdot)\) \(\chi_{987}(347,\cdot)\) \(\chi_{987}(380,\cdot)\) \(\chi_{987}(401,\cdot)\) \(\chi_{987}(410,\cdot)\) \(\chi_{987}(431,\cdot)\) \(\chi_{987}(473,\cdot)\) \(\chi_{987}(494,\cdot)\) \(\chi_{987}(506,\cdot)\) \(\chi_{987}(578,\cdot)\) \(\chi_{987}(620,\cdot)\) \(\chi_{987}(632,\cdot)\) \(\chi_{987}(653,\cdot)\) \(\chi_{987}(662,\cdot)\) \(\chi_{987}(674,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{69})$ |
Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\((659,283,757)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{9}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 987 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{138}\right)\) | \(e\left(\frac{29}{69}\right)\) | \(e\left(\frac{77}{138}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{53}{69}\right)\) | \(e\left(\frac{79}{138}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{58}{69}\right)\) | \(e\left(\frac{13}{138}\right)\) | \(e\left(\frac{19}{69}\right)\) |