Basic properties
| Modulus: | \(2233\) | |
| Conductor: | \(2233\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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 2233.dm
\(\chi_{2233}(4,\cdot)\) \(\chi_{2233}(9,\cdot)\) \(\chi_{2233}(93,\cdot)\) \(\chi_{2233}(158,\cdot)\) \(\chi_{2233}(179,\cdot)\) \(\chi_{2233}(207,\cdot)\) \(\chi_{2233}(212,\cdot)\) \(\chi_{2233}(312,\cdot)\) \(\chi_{2233}(324,\cdot)\) \(\chi_{2233}(361,\cdot)\) \(\chi_{2233}(410,\cdot)\) \(\chi_{2233}(499,\cdot)\) \(\chi_{2233}(515,\cdot)\) \(\chi_{2233}(555,\cdot)\) \(\chi_{2233}(564,\cdot)\) \(\chi_{2233}(676,\cdot)\) \(\chi_{2233}(702,\cdot)\) \(\chi_{2233}(709,\cdot)\) \(\chi_{2233}(718,\cdot)\) \(\chi_{2233}(730,\cdot)\) \(\chi_{2233}(863,\cdot)\) \(\chi_{2233}(905,\cdot)\) \(\chi_{2233}(933,\cdot)\) \(\chi_{2233}(961,\cdot)\) \(\chi_{2233}(1082,\cdot)\) \(\chi_{2233}(1115,\cdot)\) \(\chi_{2233}(1136,\cdot)\) \(\chi_{2233}(1164,\cdot)\) \(\chi_{2233}(1269,\cdot)\) \(\chi_{2233}(1285,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1277,1828,2003)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{5}\right),e\left(\frac{3}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 2233 }(499, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{210}\right)\) | \(e\left(\frac{1}{210}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{35}\right)\) |