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.t
\(\chi_{676}(3,\cdot)\) \(\chi_{676}(35,\cdot)\) \(\chi_{676}(55,\cdot)\) \(\chi_{676}(87,\cdot)\) \(\chi_{676}(107,\cdot)\) \(\chi_{676}(139,\cdot)\) \(\chi_{676}(159,\cdot)\) \(\chi_{676}(211,\cdot)\) \(\chi_{676}(243,\cdot)\) \(\chi_{676}(263,\cdot)\) \(\chi_{676}(295,\cdot)\) \(\chi_{676}(347,\cdot)\) \(\chi_{676}(367,\cdot)\) \(\chi_{676}(399,\cdot)\) \(\chi_{676}(419,\cdot)\) \(\chi_{676}(451,\cdot)\) \(\chi_{676}(471,\cdot)\) \(\chi_{676}(503,\cdot)\) \(\chi_{676}(523,\cdot)\) \(\chi_{676}(555,\cdot)\) \(\chi_{676}(575,\cdot)\) \(\chi_{676}(607,\cdot)\) \(\chi_{676}(627,\cdot)\) \(\chi_{676}(659,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((339,509)\) → \((-1,e\left(\frac{31}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 676 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{5}{6}\right)\) |