Basic properties
| Modulus: | \(1003\) | |
| Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(232\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1003.q
\(\chi_{1003}(2,\cdot)\) \(\chi_{1003}(8,\cdot)\) \(\chi_{1003}(32,\cdot)\) \(\chi_{1003}(42,\cdot)\) \(\chi_{1003}(43,\cdot)\) \(\chi_{1003}(70,\cdot)\) \(\chi_{1003}(77,\cdot)\) \(\chi_{1003}(83,\cdot)\) \(\chi_{1003}(93,\cdot)\) \(\chi_{1003}(111,\cdot)\) \(\chi_{1003}(128,\cdot)\) \(\chi_{1003}(151,\cdot)\) \(\chi_{1003}(155,\cdot)\) \(\chi_{1003}(161,\cdot)\) \(\chi_{1003}(162,\cdot)\) \(\chi_{1003}(168,\cdot)\) \(\chi_{1003}(172,\cdot)\) \(\chi_{1003}(179,\cdot)\) \(\chi_{1003}(185,\cdot)\) \(\chi_{1003}(195,\cdot)\) \(\chi_{1003}(219,\cdot)\) \(\chi_{1003}(229,\cdot)\) \(\chi_{1003}(246,\cdot)\) \(\chi_{1003}(247,\cdot)\) \(\chi_{1003}(270,\cdot)\) \(\chi_{1003}(274,\cdot)\) \(\chi_{1003}(280,\cdot)\) \(\chi_{1003}(291,\cdot)\) \(\chi_{1003}(297,\cdot)\) \(\chi_{1003}(308,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{232})$ |
| Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((768,120)\) → \((e\left(\frac{3}{8}\right),e\left(\frac{5}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1003 }(32, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{116}\right)\) | \(e\left(\frac{159}{232}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{91}{232}\right)\) | \(e\left(\frac{5}{232}\right)\) | \(e\left(\frac{157}{232}\right)\) | \(e\left(\frac{1}{116}\right)\) | \(e\left(\frac{43}{116}\right)\) | \(e\left(\frac{169}{232}\right)\) | \(e\left(\frac{181}{232}\right)\) |