Basic properties
| Modulus: | \(1352\) | |
| Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{676}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1352.bk
\(\chi_{1352}(31,\cdot)\) \(\chi_{1352}(47,\cdot)\) \(\chi_{1352}(135,\cdot)\) \(\chi_{1352}(151,\cdot)\) \(\chi_{1352}(255,\cdot)\) \(\chi_{1352}(343,\cdot)\) \(\chi_{1352}(359,\cdot)\) \(\chi_{1352}(447,\cdot)\) \(\chi_{1352}(463,\cdot)\) \(\chi_{1352}(551,\cdot)\) \(\chi_{1352}(567,\cdot)\) \(\chi_{1352}(655,\cdot)\) \(\chi_{1352}(671,\cdot)\) \(\chi_{1352}(759,\cdot)\) \(\chi_{1352}(863,\cdot)\) \(\chi_{1352}(879,\cdot)\) \(\chi_{1352}(967,\cdot)\) \(\chi_{1352}(983,\cdot)\) \(\chi_{1352}(1071,\cdot)\) \(\chi_{1352}(1087,\cdot)\) \(\chi_{1352}(1175,\cdot)\) \(\chi_{1352}(1191,\cdot)\) \(\chi_{1352}(1279,\cdot)\) \(\chi_{1352}(1295,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1015,677,1185)\) → \((-1,1,e\left(\frac{7}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1352 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(i\) | \(e\left(\frac{5}{52}\right)\) | \(1\) |