Basic properties
| Modulus: | \(3344\) | |
| Conductor: | \(3344\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | 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 3344.fg
\(\chi_{3344}(35,\cdot)\) \(\chi_{3344}(123,\cdot)\) \(\chi_{3344}(139,\cdot)\) \(\chi_{3344}(195,\cdot)\) \(\chi_{3344}(283,\cdot)\) \(\chi_{3344}(347,\cdot)\) \(\chi_{3344}(403,\cdot)\) \(\chi_{3344}(435,\cdot)\) \(\chi_{3344}(491,\cdot)\) \(\chi_{3344}(579,\cdot)\) \(\chi_{3344}(651,\cdot)\) \(\chi_{3344}(739,\cdot)\) \(\chi_{3344}(899,\cdot)\) \(\chi_{3344}(1051,\cdot)\) \(\chi_{3344}(1107,\cdot)\) \(\chi_{3344}(1163,\cdot)\) \(\chi_{3344}(1195,\cdot)\) \(\chi_{3344}(1251,\cdot)\) \(\chi_{3344}(1315,\cdot)\) \(\chi_{3344}(1339,\cdot)\) \(\chi_{3344}(1355,\cdot)\) \(\chi_{3344}(1403,\cdot)\) \(\chi_{3344}(1491,\cdot)\) \(\chi_{3344}(1619,\cdot)\) \(\chi_{3344}(1707,\cdot)\) \(\chi_{3344}(1795,\cdot)\) \(\chi_{3344}(1811,\cdot)\) \(\chi_{3344}(1867,\cdot)\) \(\chi_{3344}(1955,\cdot)\) \(\chi_{3344}(2019,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((2927,837,2433,705)\) → \((-1,-i,e\left(\frac{1}{10}\right),e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 3344 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{180}\right)\) | \(e\left(\frac{127}{180}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{83}{180}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{37}{90}\right)\) |