Basic properties
| Modulus: | \(676\) | |
| Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | 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 676.u
\(\chi_{676}(43,\cdot)\) \(\chi_{676}(75,\cdot)\) \(\chi_{676}(95,\cdot)\) \(\chi_{676}(127,\cdot)\) \(\chi_{676}(179,\cdot)\) \(\chi_{676}(199,\cdot)\) \(\chi_{676}(231,\cdot)\) \(\chi_{676}(251,\cdot)\) \(\chi_{676}(283,\cdot)\) \(\chi_{676}(303,\cdot)\) \(\chi_{676}(335,\cdot)\) \(\chi_{676}(355,\cdot)\) \(\chi_{676}(387,\cdot)\) \(\chi_{676}(407,\cdot)\) \(\chi_{676}(439,\cdot)\) \(\chi_{676}(459,\cdot)\) \(\chi_{676}(491,\cdot)\) \(\chi_{676}(511,\cdot)\) \(\chi_{676}(543,\cdot)\) \(\chi_{676}(563,\cdot)\) \(\chi_{676}(595,\cdot)\) \(\chi_{676}(615,\cdot)\) \(\chi_{676}(647,\cdot)\) \(\chi_{676}(667,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((339,509)\) → \((-1,e\left(\frac{31}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 676 }(615, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{1}{6}\right)\) |