Basic properties
| Modulus: | \(3332\) | |
| Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{833}(405,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3332.cq
\(\chi_{3332}(41,\cdot)\) \(\chi_{3332}(125,\cdot)\) \(\chi_{3332}(181,\cdot)\) \(\chi_{3332}(209,\cdot)\) \(\chi_{3332}(265,\cdot)\) \(\chi_{3332}(377,\cdot)\) \(\chi_{3332}(405,\cdot)\) \(\chi_{3332}(517,\cdot)\) \(\chi_{3332}(573,\cdot)\) \(\chi_{3332}(601,\cdot)\) \(\chi_{3332}(657,\cdot)\) \(\chi_{3332}(741,\cdot)\) \(\chi_{3332}(853,\cdot)\) \(\chi_{3332}(993,\cdot)\) \(\chi_{3332}(1049,\cdot)\) \(\chi_{3332}(1133,\cdot)\) \(\chi_{3332}(1161,\cdot)\) \(\chi_{3332}(1217,\cdot)\) \(\chi_{3332}(1329,\cdot)\) \(\chi_{3332}(1357,\cdot)\) \(\chi_{3332}(1525,\cdot)\) \(\chi_{3332}(1553,\cdot)\) \(\chi_{3332}(1609,\cdot)\) \(\chi_{3332}(1637,\cdot)\) \(\chi_{3332}(1693,\cdot)\) \(\chi_{3332}(1805,\cdot)\) \(\chi_{3332}(1833,\cdot)\) \(\chi_{3332}(1945,\cdot)\) \(\chi_{3332}(2001,\cdot)\) \(\chi_{3332}(2029,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((1667,885,785)\) → \((1,e\left(\frac{11}{14}\right),e\left(\frac{9}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3332 }(405, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{112}\right)\) | \(e\left(\frac{67}{112}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{41}{112}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{33}{112}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{5}{112}\right)\) |