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.y
\(\chi_{4205}(17,\cdot)\) \(\chi_{4205}(128,\cdot)\) \(\chi_{4205}(162,\cdot)\) \(\chi_{4205}(273,\cdot)\) \(\chi_{4205}(307,\cdot)\) \(\chi_{4205}(418,\cdot)\) \(\chi_{4205}(452,\cdot)\) \(\chi_{4205}(563,\cdot)\) \(\chi_{4205}(597,\cdot)\) \(\chi_{4205}(708,\cdot)\) \(\chi_{4205}(742,\cdot)\) \(\chi_{4205}(853,\cdot)\) \(\chi_{4205}(887,\cdot)\) \(\chi_{4205}(998,\cdot)\) \(\chi_{4205}(1032,\cdot)\) \(\chi_{4205}(1143,\cdot)\) \(\chi_{4205}(1177,\cdot)\) \(\chi_{4205}(1288,\cdot)\) \(\chi_{4205}(1322,\cdot)\) \(\chi_{4205}(1433,\cdot)\) \(\chi_{4205}(1467,\cdot)\) \(\chi_{4205}(1578,\cdot)\) \(\chi_{4205}(1612,\cdot)\) \(\chi_{4205}(1757,\cdot)\) \(\chi_{4205}(1868,\cdot)\) \(\chi_{4205}(1902,\cdot)\) \(\chi_{4205}(2013,\cdot)\) \(\chi_{4205}(2047,\cdot)\) \(\chi_{4205}(2158,\cdot)\) \(\chi_{4205}(2192,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{116})$ |
| Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((842,3366)\) → \((-i,e\left(\frac{61}{116}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 4205 }(1143, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{55}{116}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{69}{116}\right)\) | \(e\left(\frac{11}{58}\right)\) | \(e\left(\frac{43}{116}\right)\) |