Basic properties
| Modulus: | \(4205\) | |
| Conductor: | \(4205\) | 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 4205.bd
\(\chi_{4205}(12,\cdot)\) \(\chi_{4205}(133,\cdot)\) \(\chi_{4205}(157,\cdot)\) \(\chi_{4205}(278,\cdot)\) \(\chi_{4205}(302,\cdot)\) \(\chi_{4205}(423,\cdot)\) \(\chi_{4205}(447,\cdot)\) \(\chi_{4205}(568,\cdot)\) \(\chi_{4205}(592,\cdot)\) \(\chi_{4205}(713,\cdot)\) \(\chi_{4205}(737,\cdot)\) \(\chi_{4205}(858,\cdot)\) \(\chi_{4205}(1003,\cdot)\) \(\chi_{4205}(1027,\cdot)\) \(\chi_{4205}(1148,\cdot)\) \(\chi_{4205}(1172,\cdot)\) \(\chi_{4205}(1293,\cdot)\) \(\chi_{4205}(1317,\cdot)\) \(\chi_{4205}(1438,\cdot)\) \(\chi_{4205}(1462,\cdot)\) \(\chi_{4205}(1583,\cdot)\) \(\chi_{4205}(1607,\cdot)\) \(\chi_{4205}(1728,\cdot)\) \(\chi_{4205}(1752,\cdot)\) \(\chi_{4205}(1873,\cdot)\) \(\chi_{4205}(1897,\cdot)\) \(\chi_{4205}(2018,\cdot)\) \(\chi_{4205}(2042,\cdot)\) \(\chi_{4205}(2163,\cdot)\) \(\chi_{4205}(2187,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{116})$ |
| Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((842,3366)\) → \((-i,e\left(\frac{75}{116}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 4205 }(1003, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{99}{116}\right)\) | \(e\left(\frac{11}{58}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{43}{116}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{31}{116}\right)\) |