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.fi
\(\chi_{3344}(5,\cdot)\) \(\chi_{3344}(93,\cdot)\) \(\chi_{3344}(157,\cdot)\) \(\chi_{3344}(213,\cdot)\) \(\chi_{3344}(245,\cdot)\) \(\chi_{3344}(301,\cdot)\) \(\chi_{3344}(389,\cdot)\) \(\chi_{3344}(405,\cdot)\) \(\chi_{3344}(669,\cdot)\) \(\chi_{3344}(709,\cdot)\) \(\chi_{3344}(757,\cdot)\) \(\chi_{3344}(845,\cdot)\) \(\chi_{3344}(861,\cdot)\) \(\chi_{3344}(917,\cdot)\) \(\chi_{3344}(973,\cdot)\) \(\chi_{3344}(1005,\cdot)\) \(\chi_{3344}(1061,\cdot)\) \(\chi_{3344}(1125,\cdot)\) \(\chi_{3344}(1149,\cdot)\) \(\chi_{3344}(1213,\cdot)\) \(\chi_{3344}(1301,\cdot)\) \(\chi_{3344}(1373,\cdot)\) \(\chi_{3344}(1461,\cdot)\) \(\chi_{3344}(1621,\cdot)\) \(\chi_{3344}(1677,\cdot)\) \(\chi_{3344}(1765,\cdot)\) \(\chi_{3344}(1829,\cdot)\) \(\chi_{3344}(1885,\cdot)\) \(\chi_{3344}(1917,\cdot)\) \(\chi_{3344}(1973,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((2927,837,2433,705)\) → \((1,i,e\left(\frac{2}{5}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 3344 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{180}\right)\) | \(e\left(\frac{13}{180}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{107}{180}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{13}{90}\right)\) |