Basic properties
Modulus: | \(4851\) | |
Conductor: | \(4851\) | 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 4851.fu
\(\chi_{4851}(20,\cdot)\) \(\chi_{4851}(104,\cdot)\) \(\chi_{4851}(335,\cdot)\) \(\chi_{4851}(356,\cdot)\) \(\chi_{4851}(482,\cdot)\) \(\chi_{4851}(608,\cdot)\) \(\chi_{4851}(713,\cdot)\) \(\chi_{4851}(797,\cdot)\) \(\chi_{4851}(839,\cdot)\) \(\chi_{4851}(1049,\cdot)\) \(\chi_{4851}(1280,\cdot)\) \(\chi_{4851}(1301,\cdot)\) \(\chi_{4851}(1406,\cdot)\) \(\chi_{4851}(1490,\cdot)\) \(\chi_{4851}(1532,\cdot)\) \(\chi_{4851}(1721,\cdot)\) \(\chi_{4851}(1742,\cdot)\) \(\chi_{4851}(1868,\cdot)\) \(\chi_{4851}(1973,\cdot)\) \(\chi_{4851}(1994,\cdot)\) \(\chi_{4851}(2099,\cdot)\) \(\chi_{4851}(2183,\cdot)\) \(\chi_{4851}(2225,\cdot)\) \(\chi_{4851}(2414,\cdot)\) \(\chi_{4851}(2435,\cdot)\) \(\chi_{4851}(2561,\cdot)\) \(\chi_{4851}(2666,\cdot)\) \(\chi_{4851}(2687,\cdot)\) \(\chi_{4851}(2876,\cdot)\) \(\chi_{4851}(2918,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4313,199,442)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{13}{14}\right),e\left(\frac{3}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 4851 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{191}{210}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{121}{210}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{103}{105}\right)\) |