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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1323.ci
\(\chi_{1323}(5,\cdot)\) \(\chi_{1323}(38,\cdot)\) \(\chi_{1323}(101,\cdot)\) \(\chi_{1323}(131,\cdot)\) \(\chi_{1323}(164,\cdot)\) \(\chi_{1323}(194,\cdot)\) \(\chi_{1323}(257,\cdot)\) \(\chi_{1323}(290,\cdot)\) \(\chi_{1323}(320,\cdot)\) \(\chi_{1323}(353,\cdot)\) \(\chi_{1323}(383,\cdot)\) \(\chi_{1323}(416,\cdot)\) \(\chi_{1323}(446,\cdot)\) \(\chi_{1323}(479,\cdot)\) \(\chi_{1323}(542,\cdot)\) \(\chi_{1323}(572,\cdot)\) \(\chi_{1323}(605,\cdot)\) \(\chi_{1323}(635,\cdot)\) \(\chi_{1323}(698,\cdot)\) \(\chi_{1323}(731,\cdot)\) \(\chi_{1323}(761,\cdot)\) \(\chi_{1323}(794,\cdot)\) \(\chi_{1323}(824,\cdot)\) \(\chi_{1323}(857,\cdot)\) \(\chi_{1323}(887,\cdot)\) \(\chi_{1323}(920,\cdot)\) \(\chi_{1323}(983,\cdot)\) \(\chi_{1323}(1013,\cdot)\) \(\chi_{1323}(1046,\cdot)\) \(\chi_{1323}(1076,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((785,1081)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{5}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1323 }(194, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{126}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{47}{126}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(-1\) |