Basic properties
| Modulus: | \(2023\) | |
| Conductor: | \(2023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(408\) | 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 2023.bl
\(\chi_{2023}(2,\cdot)\) \(\chi_{2023}(9,\cdot)\) \(\chi_{2023}(25,\cdot)\) \(\chi_{2023}(32,\cdot)\) \(\chi_{2023}(53,\cdot)\) \(\chi_{2023}(60,\cdot)\) \(\chi_{2023}(93,\cdot)\) \(\chi_{2023}(100,\cdot)\) \(\chi_{2023}(121,\cdot)\) \(\chi_{2023}(128,\cdot)\) \(\chi_{2023}(144,\cdot)\) \(\chi_{2023}(151,\cdot)\) \(\chi_{2023}(172,\cdot)\) \(\chi_{2023}(212,\cdot)\) \(\chi_{2023}(219,\cdot)\) \(\chi_{2023}(240,\cdot)\) \(\chi_{2023}(247,\cdot)\) \(\chi_{2023}(263,\cdot)\) \(\chi_{2023}(270,\cdot)\) \(\chi_{2023}(291,\cdot)\) \(\chi_{2023}(298,\cdot)\) \(\chi_{2023}(331,\cdot)\) \(\chi_{2023}(338,\cdot)\) \(\chi_{2023}(359,\cdot)\) \(\chi_{2023}(366,\cdot)\) \(\chi_{2023}(382,\cdot)\) \(\chi_{2023}(389,\cdot)\) \(\chi_{2023}(410,\cdot)\) \(\chi_{2023}(417,\cdot)\) \(\chi_{2023}(450,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{408})$ |
| Fixed field: | Number field defined by a degree 408 polynomial (not computed) |
Values on generators
\((290,1737)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{95}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2023 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{204}\right)\) | \(e\left(\frac{13}{408}\right)\) | \(e\left(\frac{79}{102}\right)\) | \(e\left(\frac{257}{408}\right)\) | \(e\left(\frac{57}{136}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{13}{204}\right)\) | \(e\left(\frac{7}{408}\right)\) | \(e\left(\frac{163}{408}\right)\) | \(e\left(\frac{329}{408}\right)\) |