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 \(\chi_{833}(57,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3332.cs
\(\chi_{3332}(29,\cdot)\) \(\chi_{3332}(57,\cdot)\) \(\chi_{3332}(113,\cdot)\) \(\chi_{3332}(141,\cdot)\) \(\chi_{3332}(309,\cdot)\) \(\chi_{3332}(337,\cdot)\) \(\chi_{3332}(449,\cdot)\) \(\chi_{3332}(505,\cdot)\) \(\chi_{3332}(533,\cdot)\) \(\chi_{3332}(617,\cdot)\) \(\chi_{3332}(673,\cdot)\) \(\chi_{3332}(813,\cdot)\) \(\chi_{3332}(925,\cdot)\) \(\chi_{3332}(1009,\cdot)\) \(\chi_{3332}(1065,\cdot)\) \(\chi_{3332}(1093,\cdot)\) \(\chi_{3332}(1149,\cdot)\) \(\chi_{3332}(1261,\cdot)\) \(\chi_{3332}(1289,\cdot)\) \(\chi_{3332}(1401,\cdot)\) \(\chi_{3332}(1457,\cdot)\) \(\chi_{3332}(1485,\cdot)\) \(\chi_{3332}(1541,\cdot)\) \(\chi_{3332}(1625,\cdot)\) \(\chi_{3332}(1737,\cdot)\) \(\chi_{3332}(1877,\cdot)\) \(\chi_{3332}(1933,\cdot)\) \(\chi_{3332}(2017,\cdot)\) \(\chi_{3332}(2045,\cdot)\) \(\chi_{3332}(2101,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{112})$ |
Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((1667,885,785)\) → \((1,e\left(\frac{6}{7}\right),e\left(\frac{15}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 3332 }(57, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{112}\right)\) | \(e\left(\frac{61}{112}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{95}{112}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{19}{56}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{71}{112}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{43}{112}\right)\) |