Basic properties
| Modulus: | \(3672\) | |
| Conductor: | \(3672\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3672.ea
\(\chi_{3672}(77,\cdot)\) \(\chi_{3672}(365,\cdot)\) \(\chi_{3672}(389,\cdot)\) \(\chi_{3672}(461,\cdot)\) \(\chi_{3672}(797,\cdot)\) \(\chi_{3672}(869,\cdot)\) \(\chi_{3672}(893,\cdot)\) \(\chi_{3672}(1181,\cdot)\) \(\chi_{3672}(1301,\cdot)\) \(\chi_{3672}(1589,\cdot)\) \(\chi_{3672}(1613,\cdot)\) \(\chi_{3672}(1685,\cdot)\) \(\chi_{3672}(2021,\cdot)\) \(\chi_{3672}(2093,\cdot)\) \(\chi_{3672}(2117,\cdot)\) \(\chi_{3672}(2405,\cdot)\) \(\chi_{3672}(2525,\cdot)\) \(\chi_{3672}(2813,\cdot)\) \(\chi_{3672}(2837,\cdot)\) \(\chi_{3672}(2909,\cdot)\) \(\chi_{3672}(3245,\cdot)\) \(\chi_{3672}(3317,\cdot)\) \(\chi_{3672}(3341,\cdot)\) \(\chi_{3672}(3629,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((919,1837,137,649)\) → \((1,-1,e\left(\frac{7}{18}\right),e\left(\frac{7}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 3672 }(2909, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{72}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{2}{3}\right)\) |