Basic properties
| Modulus: | \(1648\) | |
| Conductor: | \(1648\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(68\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1648.bh
\(\chi_{1648}(3,\cdot)\) \(\chi_{1648}(27,\cdot)\) \(\chi_{1648}(243,\cdot)\) \(\chi_{1648}(275,\cdot)\) \(\chi_{1648}(331,\cdot)\) \(\chi_{1648}(403,\cdot)\) \(\chi_{1648}(443,\cdot)\) \(\chi_{1648}(451,\cdot)\) \(\chi_{1648}(507,\cdot)\) \(\chi_{1648}(539,\cdot)\) \(\chi_{1648}(595,\cdot)\) \(\chi_{1648}(691,\cdot)\) \(\chi_{1648}(707,\cdot)\) \(\chi_{1648}(731,\cdot)\) \(\chi_{1648}(763,\cdot)\) \(\chi_{1648}(811,\cdot)\) \(\chi_{1648}(827,\cdot)\) \(\chi_{1648}(851,\cdot)\) \(\chi_{1648}(1067,\cdot)\) \(\chi_{1648}(1099,\cdot)\) \(\chi_{1648}(1155,\cdot)\) \(\chi_{1648}(1227,\cdot)\) \(\chi_{1648}(1267,\cdot)\) \(\chi_{1648}(1275,\cdot)\) \(\chi_{1648}(1331,\cdot)\) \(\chi_{1648}(1363,\cdot)\) \(\chi_{1648}(1419,\cdot)\) \(\chi_{1648}(1515,\cdot)\) \(\chi_{1648}(1531,\cdot)\) \(\chi_{1648}(1555,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{68})$ |
| Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((207,1237,417)\) → \((-1,-i,e\left(\frac{13}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1648 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{68}\right)\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{13}{68}\right)\) |