Basic properties
| Modulus: | \(676\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 676.r
\(\chi_{676}(5,\cdot)\) \(\chi_{676}(21,\cdot)\) \(\chi_{676}(57,\cdot)\) \(\chi_{676}(73,\cdot)\) \(\chi_{676}(109,\cdot)\) \(\chi_{676}(125,\cdot)\) \(\chi_{676}(161,\cdot)\) \(\chi_{676}(177,\cdot)\) \(\chi_{676}(213,\cdot)\) \(\chi_{676}(229,\cdot)\) \(\chi_{676}(265,\cdot)\) \(\chi_{676}(281,\cdot)\) \(\chi_{676}(317,\cdot)\) \(\chi_{676}(333,\cdot)\) \(\chi_{676}(369,\cdot)\) \(\chi_{676}(385,\cdot)\) \(\chi_{676}(421,\cdot)\) \(\chi_{676}(473,\cdot)\) \(\chi_{676}(489,\cdot)\) \(\chi_{676}(525,\cdot)\) \(\chi_{676}(541,\cdot)\) \(\chi_{676}(593,\cdot)\) \(\chi_{676}(629,\cdot)\) \(\chi_{676}(645,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((339,509)\) → \((1,e\left(\frac{3}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 676 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(-i\) | \(e\left(\frac{17}{52}\right)\) | \(-1\) |