Basic properties
| Modulus: | \(676\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 676.v
\(\chi_{676}(17,\cdot)\) \(\chi_{676}(49,\cdot)\) \(\chi_{676}(69,\cdot)\) \(\chi_{676}(101,\cdot)\) \(\chi_{676}(121,\cdot)\) \(\chi_{676}(153,\cdot)\) \(\chi_{676}(173,\cdot)\) \(\chi_{676}(205,\cdot)\) \(\chi_{676}(225,\cdot)\) \(\chi_{676}(257,\cdot)\) \(\chi_{676}(277,\cdot)\) \(\chi_{676}(309,\cdot)\) \(\chi_{676}(329,\cdot)\) \(\chi_{676}(381,\cdot)\) \(\chi_{676}(413,\cdot)\) \(\chi_{676}(433,\cdot)\) \(\chi_{676}(465,\cdot)\) \(\chi_{676}(517,\cdot)\) \(\chi_{676}(537,\cdot)\) \(\chi_{676}(569,\cdot)\) \(\chi_{676}(589,\cdot)\) \(\chi_{676}(621,\cdot)\) \(\chi_{676}(641,\cdot)\) \(\chi_{676}(673,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((339,509)\) → \((1,e\left(\frac{73}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 676 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{2}{3}\right)\) |