Basic properties
| Modulus: | \(1352\) | |
| 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 \(\chi_{169}(57,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1352.bh
\(\chi_{1352}(57,\cdot)\) \(\chi_{1352}(73,\cdot)\) \(\chi_{1352}(161,\cdot)\) \(\chi_{1352}(177,\cdot)\) \(\chi_{1352}(265,\cdot)\) \(\chi_{1352}(281,\cdot)\) \(\chi_{1352}(369,\cdot)\) \(\chi_{1352}(385,\cdot)\) \(\chi_{1352}(473,\cdot)\) \(\chi_{1352}(489,\cdot)\) \(\chi_{1352}(593,\cdot)\) \(\chi_{1352}(681,\cdot)\) \(\chi_{1352}(697,\cdot)\) \(\chi_{1352}(785,\cdot)\) \(\chi_{1352}(801,\cdot)\) \(\chi_{1352}(889,\cdot)\) \(\chi_{1352}(905,\cdot)\) \(\chi_{1352}(993,\cdot)\) \(\chi_{1352}(1009,\cdot)\) \(\chi_{1352}(1097,\cdot)\) \(\chi_{1352}(1201,\cdot)\) \(\chi_{1352}(1217,\cdot)\) \(\chi_{1352}(1305,\cdot)\) \(\chi_{1352}(1321,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1015,677,1185)\) → \((1,1,e\left(\frac{11}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1352 }(57, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(-i\) | \(e\left(\frac{45}{52}\right)\) | \(-1\) |