Basic properties
Modulus: | \(1363\) | |
Conductor: | \(1363\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(322\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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
\((988,146)\) → \((e\left(\frac{3}{14}\right),e\left(\frac{3}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1363 }(209, a) \) | \(1\) | \(1\) | \(e\left(\frac{181}{322}\right)\) | \(e\left(\frac{219}{322}\right)\) | \(e\left(\frac{20}{161}\right)\) | \(e\left(\frac{136}{161}\right)\) | \(e\left(\frac{39}{161}\right)\) | \(e\left(\frac{120}{161}\right)\) | \(e\left(\frac{221}{322}\right)\) | \(e\left(\frac{58}{161}\right)\) | \(e\left(\frac{131}{322}\right)\) | \(e\left(\frac{87}{322}\right)\) |