Basic properties
| Modulus: | \(3344\) | |
| Conductor: | \(209\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{209}(129,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3344.es
\(\chi_{3344}(129,\cdot)\) \(\chi_{3344}(193,\cdot)\) \(\chi_{3344}(337,\cdot)\) \(\chi_{3344}(497,\cdot)\) \(\chi_{3344}(545,\cdot)\) \(\chi_{3344}(849,\cdot)\) \(\chi_{3344}(865,\cdot)\) \(\chi_{3344}(1009,\cdot)\) \(\chi_{3344}(1041,\cdot)\) \(\chi_{3344}(1249,\cdot)\) \(\chi_{3344}(1553,\cdot)\) \(\chi_{3344}(1713,\cdot)\) \(\chi_{3344}(1777,\cdot)\) \(\chi_{3344}(1921,\cdot)\) \(\chi_{3344}(1953,\cdot)\) \(\chi_{3344}(2065,\cdot)\) \(\chi_{3344}(2081,\cdot)\) \(\chi_{3344}(2257,\cdot)\) \(\chi_{3344}(2625,\cdot)\) \(\chi_{3344}(2769,\cdot)\) \(\chi_{3344}(2833,\cdot)\) \(\chi_{3344}(2977,\cdot)\) \(\chi_{3344}(3137,\cdot)\) \(\chi_{3344}(3297,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2927,837,2433,705)\) → \((1,1,e\left(\frac{3}{10}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 3344 }(129, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{43}{45}\right)\) |