Basic properties
| Modulus: | \(1003\) | |
| Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(116\) | 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 1003.p
\(\chi_{1003}(4,\cdot)\) \(\chi_{1003}(21,\cdot)\) \(\chi_{1003}(64,\cdot)\) \(\chi_{1003}(81,\cdot)\) \(\chi_{1003}(123,\cdot)\) \(\chi_{1003}(140,\cdot)\) \(\chi_{1003}(166,\cdot)\) \(\chi_{1003}(225,\cdot)\) \(\chi_{1003}(234,\cdot)\) \(\chi_{1003}(251,\cdot)\) \(\chi_{1003}(285,\cdot)\) \(\chi_{1003}(293,\cdot)\) \(\chi_{1003}(302,\cdot)\) \(\chi_{1003}(310,\cdot)\) \(\chi_{1003}(336,\cdot)\) \(\chi_{1003}(344,\cdot)\) \(\chi_{1003}(361,\cdot)\) \(\chi_{1003}(370,\cdot)\) \(\chi_{1003}(395,\cdot)\) \(\chi_{1003}(429,\cdot)\) \(\chi_{1003}(438,\cdot)\) \(\chi_{1003}(489,\cdot)\) \(\chi_{1003}(497,\cdot)\) \(\chi_{1003}(523,\cdot)\) \(\chi_{1003}(540,\cdot)\) \(\chi_{1003}(548,\cdot)\) \(\chi_{1003}(557,\cdot)\) \(\chi_{1003}(582,\cdot)\) \(\chi_{1003}(599,\cdot)\) \(\chi_{1003}(616,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{116})$ |
| Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((768,120)\) → \((-i,e\left(\frac{5}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1003 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{43}{116}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{91}{116}\right)\) | \(e\left(\frac{5}{116}\right)\) | \(e\left(\frac{41}{116}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{53}{116}\right)\) | \(e\left(\frac{65}{116}\right)\) |