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.ca
\(\chi_{1323}(25,\cdot)\) \(\chi_{1323}(58,\cdot)\) \(\chi_{1323}(88,\cdot)\) \(\chi_{1323}(121,\cdot)\) \(\chi_{1323}(151,\cdot)\) \(\chi_{1323}(184,\cdot)\) \(\chi_{1323}(247,\cdot)\) \(\chi_{1323}(277,\cdot)\) \(\chi_{1323}(310,\cdot)\) \(\chi_{1323}(340,\cdot)\) \(\chi_{1323}(403,\cdot)\) \(\chi_{1323}(436,\cdot)\) \(\chi_{1323}(466,\cdot)\) \(\chi_{1323}(499,\cdot)\) \(\chi_{1323}(529,\cdot)\) \(\chi_{1323}(562,\cdot)\) \(\chi_{1323}(592,\cdot)\) \(\chi_{1323}(625,\cdot)\) \(\chi_{1323}(688,\cdot)\) \(\chi_{1323}(718,\cdot)\) \(\chi_{1323}(751,\cdot)\) \(\chi_{1323}(781,\cdot)\) \(\chi_{1323}(844,\cdot)\) \(\chi_{1323}(877,\cdot)\) \(\chi_{1323}(907,\cdot)\) \(\chi_{1323}(940,\cdot)\) \(\chi_{1323}(970,\cdot)\) \(\chi_{1323}(1003,\cdot)\) \(\chi_{1323}(1033,\cdot)\) \(\chi_{1323}(1066,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((785,1081)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{5}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1323 }(592, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(1\) |