Basic properties
Modulus: | \(1323\) | |
Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1323.cj
\(\chi_{1323}(61,\cdot)\) \(\chi_{1323}(94,\cdot)\) \(\chi_{1323}(124,\cdot)\) \(\chi_{1323}(157,\cdot)\) \(\chi_{1323}(187,\cdot)\) \(\chi_{1323}(220,\cdot)\) \(\chi_{1323}(250,\cdot)\) \(\chi_{1323}(283,\cdot)\) \(\chi_{1323}(346,\cdot)\) \(\chi_{1323}(376,\cdot)\) \(\chi_{1323}(409,\cdot)\) \(\chi_{1323}(439,\cdot)\) \(\chi_{1323}(502,\cdot)\) \(\chi_{1323}(535,\cdot)\) \(\chi_{1323}(565,\cdot)\) \(\chi_{1323}(598,\cdot)\) \(\chi_{1323}(628,\cdot)\) \(\chi_{1323}(661,\cdot)\) \(\chi_{1323}(691,\cdot)\) \(\chi_{1323}(724,\cdot)\) \(\chi_{1323}(787,\cdot)\) \(\chi_{1323}(817,\cdot)\) \(\chi_{1323}(850,\cdot)\) \(\chi_{1323}(880,\cdot)\) \(\chi_{1323}(943,\cdot)\) \(\chi_{1323}(976,\cdot)\) \(\chi_{1323}(1006,\cdot)\) \(\chi_{1323}(1039,\cdot)\) \(\chi_{1323}(1069,\cdot)\) \(\chi_{1323}(1102,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((785,1081)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{11}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1323 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{5}{126}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{5}{6}\right)\) |