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.ce
\(\chi_{1323}(20,\cdot)\) \(\chi_{1323}(41,\cdot)\) \(\chi_{1323}(83,\cdot)\) \(\chi_{1323}(104,\cdot)\) \(\chi_{1323}(167,\cdot)\) \(\chi_{1323}(209,\cdot)\) \(\chi_{1323}(230,\cdot)\) \(\chi_{1323}(272,\cdot)\) \(\chi_{1323}(335,\cdot)\) \(\chi_{1323}(356,\cdot)\) \(\chi_{1323}(398,\cdot)\) \(\chi_{1323}(419,\cdot)\) \(\chi_{1323}(461,\cdot)\) \(\chi_{1323}(482,\cdot)\) \(\chi_{1323}(524,\cdot)\) \(\chi_{1323}(545,\cdot)\) \(\chi_{1323}(608,\cdot)\) \(\chi_{1323}(650,\cdot)\) \(\chi_{1323}(671,\cdot)\) \(\chi_{1323}(713,\cdot)\) \(\chi_{1323}(776,\cdot)\) \(\chi_{1323}(797,\cdot)\) \(\chi_{1323}(839,\cdot)\) \(\chi_{1323}(860,\cdot)\) \(\chi_{1323}(902,\cdot)\) \(\chi_{1323}(923,\cdot)\) \(\chi_{1323}(965,\cdot)\) \(\chi_{1323}(986,\cdot)\) \(\chi_{1323}(1049,\cdot)\) \(\chi_{1323}(1091,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((785,1081)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{3}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1323 }(524, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{126}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{121}{126}\right)\) | \(e\left(\frac{107}{126}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{1}{6}\right)\) |