Basic properties
Modulus: | \(8033\) | |
Conductor: | \(8033\) | 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 8033.cj
\(\chi_{8033}(236,\cdot)\) \(\chi_{8033}(296,\cdot)\) \(\chi_{8033}(361,\cdot)\) \(\chi_{8033}(441,\cdot)\) \(\chi_{8033}(573,\cdot)\) \(\chi_{8033}(584,\cdot)\) \(\chi_{8033}(709,\cdot)\) \(\chi_{8033}(718,\cdot)\) \(\chi_{8033}(729,\cdot)\) \(\chi_{8033}(767,\cdot)\) \(\chi_{8033}(818,\cdot)\) \(\chi_{8033}(847,\cdot)\) \(\chi_{8033}(850,\cdot)\) \(\chi_{8033}(883,\cdot)\) \(\chi_{8033}(962,\cdot)\) \(\chi_{8033}(995,\cdot)\) \(\chi_{8033}(1049,\cdot)\) \(\chi_{8033}(1095,\cdot)\) \(\chi_{8033}(1124,\cdot)\) \(\chi_{8033}(1135,\cdot)\) \(\chi_{8033}(1309,\cdot)\) \(\chi_{8033}(1311,\cdot)\) \(\chi_{8033}(1372,\cdot)\) \(\chi_{8033}(1401,\cdot)\) \(\chi_{8033}(1454,\cdot)\) \(\chi_{8033}(1542,\cdot)\) \(\chi_{8033}(1588,\cdot)\) \(\chi_{8033}(1658,\cdot)\) \(\chi_{8033}(1746,\cdot)\) \(\chi_{8033}(1831,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{161})$ |
Fixed field: | Number field defined by a degree 322 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((e\left(\frac{1}{14}\right),e\left(\frac{22}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(236, a) \) | \(1\) | \(1\) | \(e\left(\frac{219}{322}\right)\) | \(e\left(\frac{59}{322}\right)\) | \(e\left(\frac{58}{161}\right)\) | \(e\left(\frac{85}{161}\right)\) | \(e\left(\frac{139}{161}\right)\) | \(e\left(\frac{145}{161}\right)\) | \(e\left(\frac{13}{322}\right)\) | \(e\left(\frac{59}{161}\right)\) | \(e\left(\frac{67}{322}\right)\) | \(e\left(\frac{155}{322}\right)\) |