Basic properties
| Modulus: | \(1363\) | |
| Conductor: | \(1363\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(322\) | 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 1363.u
\(\chi_{1363}(4,\cdot)\) \(\chi_{1363}(6,\cdot)\) \(\chi_{1363}(9,\cdot)\) \(\chi_{1363}(34,\cdot)\) \(\chi_{1363}(42,\cdot)\) \(\chi_{1363}(51,\cdot)\) \(\chi_{1363}(63,\cdot)\) \(\chi_{1363}(64,\cdot)\) \(\chi_{1363}(71,\cdot)\) \(\chi_{1363}(96,\cdot)\) \(\chi_{1363}(100,\cdot)\) \(\chi_{1363}(121,\cdot)\) \(\chi_{1363}(122,\cdot)\) \(\chi_{1363}(149,\cdot)\) \(\chi_{1363}(150,\cdot)\) \(\chi_{1363}(158,\cdot)\) \(\chi_{1363}(178,\cdot)\) \(\chi_{1363}(183,\cdot)\) \(\chi_{1363}(196,\cdot)\) \(\chi_{1363}(209,\cdot)\) \(\chi_{1363}(212,\cdot)\) \(\chi_{1363}(216,\cdot)\) \(\chi_{1363}(225,\cdot)\) \(\chi_{1363}(237,\cdot)\) \(\chi_{1363}(238,\cdot)\) \(\chi_{1363}(241,\cdot)\) \(\chi_{1363}(267,\cdot)\) \(\chi_{1363}(294,\cdot)\) \(\chi_{1363}(296,\cdot)\) \(\chi_{1363}(299,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{161})$ |
| Fixed field: | Number field defined by a degree 322 polynomial (not computed) |
Values on generators
\((988,146)\) → \((e\left(\frac{11}{14}\right),e\left(\frac{7}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1363 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{322}\right)\) | \(e\left(\frac{5}{322}\right)\) | \(e\left(\frac{85}{161}\right)\) | \(e\left(\frac{95}{161}\right)\) | \(e\left(\frac{45}{161}\right)\) | \(e\left(\frac{27}{161}\right)\) | \(e\left(\frac{255}{322}\right)\) | \(e\left(\frac{5}{161}\right)\) | \(e\left(\frac{275}{322}\right)\) | \(e\left(\frac{249}{322}\right)\) |