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.ba
\(\chi_{987}(5,\cdot)\) \(\chi_{987}(26,\cdot)\) \(\chi_{987}(38,\cdot)\) \(\chi_{987}(80,\cdot)\) \(\chi_{987}(152,\cdot)\) \(\chi_{987}(164,\cdot)\) \(\chi_{987}(185,\cdot)\) \(\chi_{987}(227,\cdot)\) \(\chi_{987}(248,\cdot)\) \(\chi_{987}(257,\cdot)\) \(\chi_{987}(278,\cdot)\) \(\chi_{987}(311,\cdot)\) \(\chi_{987}(320,\cdot)\) \(\chi_{987}(362,\cdot)\) \(\chi_{987}(374,\cdot)\) \(\chi_{987}(395,\cdot)\) \(\chi_{987}(416,\cdot)\) \(\chi_{987}(446,\cdot)\) \(\chi_{987}(458,\cdot)\) \(\chi_{987}(467,\cdot)\) \(\chi_{987}(500,\cdot)\) \(\chi_{987}(509,\cdot)\) \(\chi_{987}(530,\cdot)\) \(\chi_{987}(584,\cdot)\) \(\chi_{987}(593,\cdot)\) \(\chi_{987}(605,\cdot)\) \(\chi_{987}(626,\cdot)\) \(\chi_{987}(656,\cdot)\) \(\chi_{987}(668,\cdot)\) \(\chi_{987}(677,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{69})$ |
| Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\((659,283,757)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{29}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 987 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{138}\right)\) | \(e\left(\frac{2}{69}\right)\) | \(e\left(\frac{41}{138}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{56}{69}\right)\) | \(e\left(\frac{17}{69}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{4}{69}\right)\) | \(e\left(\frac{29}{69}\right)\) | \(e\left(\frac{37}{69}\right)\) |