Basic properties
Modulus: | \(1323\) | |
Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(63\) | 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 1323.cb
\(\chi_{1323}(22,\cdot)\) \(\chi_{1323}(43,\cdot)\) \(\chi_{1323}(85,\cdot)\) \(\chi_{1323}(106,\cdot)\) \(\chi_{1323}(169,\cdot)\) \(\chi_{1323}(211,\cdot)\) \(\chi_{1323}(232,\cdot)\) \(\chi_{1323}(274,\cdot)\) \(\chi_{1323}(337,\cdot)\) \(\chi_{1323}(358,\cdot)\) \(\chi_{1323}(400,\cdot)\) \(\chi_{1323}(421,\cdot)\) \(\chi_{1323}(463,\cdot)\) \(\chi_{1323}(484,\cdot)\) \(\chi_{1323}(526,\cdot)\) \(\chi_{1323}(547,\cdot)\) \(\chi_{1323}(610,\cdot)\) \(\chi_{1323}(652,\cdot)\) \(\chi_{1323}(673,\cdot)\) \(\chi_{1323}(715,\cdot)\) \(\chi_{1323}(778,\cdot)\) \(\chi_{1323}(799,\cdot)\) \(\chi_{1323}(841,\cdot)\) \(\chi_{1323}(862,\cdot)\) \(\chi_{1323}(904,\cdot)\) \(\chi_{1323}(925,\cdot)\) \(\chi_{1323}(967,\cdot)\) \(\chi_{1323}(988,\cdot)\) \(\chi_{1323}(1051,\cdot)\) \(\chi_{1323}(1093,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((785,1081)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{1}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1323 }(337, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) |