Basic properties
Modulus: | \(4023\) | |
Conductor: | \(4023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1332\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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 4023.bi
\(\chi_{4023}(2,\cdot)\) \(\chi_{4023}(11,\cdot)\) \(\chi_{4023}(14,\cdot)\) \(\chi_{4023}(23,\cdot)\) \(\chi_{4023}(32,\cdot)\) \(\chi_{4023}(38,\cdot)\) \(\chi_{4023}(41,\cdot)\) \(\chi_{4023}(50,\cdot)\) \(\chi_{4023}(56,\cdot)\) \(\chi_{4023}(59,\cdot)\) \(\chi_{4023}(65,\cdot)\) \(\chi_{4023}(74,\cdot)\) \(\chi_{4023}(77,\cdot)\) \(\chi_{4023}(83,\cdot)\) \(\chi_{4023}(92,\cdot)\) \(\chi_{4023}(101,\cdot)\) \(\chi_{4023}(122,\cdot)\) \(\chi_{4023}(128,\cdot)\) \(\chi_{4023}(131,\cdot)\) \(\chi_{4023}(137,\cdot)\) \(\chi_{4023}(146,\cdot)\) \(\chi_{4023}(164,\cdot)\) \(\chi_{4023}(167,\cdot)\) \(\chi_{4023}(176,\cdot)\) \(\chi_{4023}(200,\cdot)\) \(\chi_{4023}(209,\cdot)\) \(\chi_{4023}(221,\cdot)\) \(\chi_{4023}(227,\cdot)\) \(\chi_{4023}(236,\cdot)\) \(\chi_{4023}(239,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1332})$ |
Fixed field: | Number field defined by a degree 1332 polynomial (not computed) |
Values on generators
\((299,3727)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{95}{148}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4023 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{337}{1332}\right)\) | \(e\left(\frac{337}{666}\right)\) | \(e\left(\frac{541}{666}\right)\) | \(e\left(\frac{617}{666}\right)\) | \(e\left(\frac{337}{444}\right)\) | \(e\left(\frac{29}{444}\right)\) | \(e\left(\frac{1213}{1332}\right)\) | \(e\left(\frac{1211}{1332}\right)\) | \(e\left(\frac{239}{1332}\right)\) | \(e\left(\frac{4}{333}\right)\) |