Basic properties
| Modulus: | \(1327\) | |
| Conductor: | \(1327\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1326\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1327.p
\(\chi_{1327}(3,\cdot)\) \(\chi_{1327}(5,\cdot)\) \(\chi_{1327}(6,\cdot)\) \(\chi_{1327}(10,\cdot)\) \(\chi_{1327}(12,\cdot)\) \(\chi_{1327}(20,\cdot)\) \(\chi_{1327}(23,\cdot)\) \(\chi_{1327}(24,\cdot)\) \(\chi_{1327}(31,\cdot)\) \(\chi_{1327}(33,\cdot)\) \(\chi_{1327}(37,\cdot)\) \(\chi_{1327}(40,\cdot)\) \(\chi_{1327}(41,\cdot)\) \(\chi_{1327}(46,\cdot)\) \(\chi_{1327}(48,\cdot)\) \(\chi_{1327}(51,\cdot)\) \(\chi_{1327}(53,\cdot)\) \(\chi_{1327}(55,\cdot)\) \(\chi_{1327}(62,\cdot)\) \(\chi_{1327}(63,\cdot)\) \(\chi_{1327}(65,\cdot)\) \(\chi_{1327}(66,\cdot)\) \(\chi_{1327}(71,\cdot)\) \(\chi_{1327}(73,\cdot)\) \(\chi_{1327}(74,\cdot)\) \(\chi_{1327}(77,\cdot)\) \(\chi_{1327}(78,\cdot)\) \(\chi_{1327}(80,\cdot)\) \(\chi_{1327}(82,\cdot)\) \(\chi_{1327}(87,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{663})$ |
| Fixed field: | Number field defined by a degree 1326 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{665}{1326}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1327 }(1318, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{221}\right)\) | \(e\left(\frac{665}{1326}\right)\) | \(e\left(\frac{58}{221}\right)\) | \(e\left(\frac{857}{1326}\right)\) | \(e\left(\frac{839}{1326}\right)\) | \(e\left(\frac{57}{442}\right)\) | \(e\left(\frac{87}{221}\right)\) | \(e\left(\frac{2}{663}\right)\) | \(e\left(\frac{1031}{1326}\right)\) | \(e\left(\frac{58}{663}\right)\) |